I don’t like ads.

The newspaper site which I was trying to read, however, seemed to be glacially slow in loading literally anything, I wondered if it was somehow intuiting the presence of my ad-blocker and then hustling to give me that slow-walk treatment. So I turned the ad-blocker off, and indeed the site — gratefully replete with annoying cascades of ads — leapt to electrified life.

A particularly insistent banner ad from a household-name tech company was persistently winning the auction for an option on my notice. It was pushing weird AI-generated clip-art graphics with anodyne figures and light bulbs and geometric shapes. As if some corporation had overpaid for a curated after-hours holiday party in an Apple Store.

It wasn’t really clear what the ad wanted me to do. The copy was a bland mash of statistics, like what one would expect if oklo.org’s preoccupations with computation, bit operations and energy costs were given an MBA makeover.

This situation — the spend, the group-think, the blandishment — it’s all clearly ripe for disruption. There’s clearly an opportunity, afoot, but how does one cut in and clean up?

It occurred to me that The Jesus and Mary Chain (who are experiencing something of a revival forty-odd years on) provide a template. I’m feeling too lazy to work up my own prose to telegraph this insight, so in the spirit of the ad above, I’ll let an LLM tilt its dull glow toward elaboration. It’s my blog, after all.

With that background in your context, check out this fabulous YouTube video. I’ve watched it about ten times already.

Fifty one point six of the two thousand two hundred miles of the Appalachian Trail wind through the northwest corner of Connecticut. Near Salisbury, south of the Massachusetts border, the route traces the spine of the Taconic mountains. The range is rounded and worn down, but still holds its own. I picked up a rock. Now it’s sitting on my desk.

It’s a piece of schist, metamorphosed sediment that partially crystallized roughly 450 million years ago in a zone that was subject to intense folding from the pressures brought on by an island arc accreting onto the continental margin of what later became North America. Holding the rock imparts the low-grade thrill of connection to the Ordovician, a word, which like Silurian, conjures crinoids and trilobites; furtive slimy and scaly things darting through the shafts of sunlight probing the floors of shallow equatorial seas.

Uplift of the Taconic range and associated mountain-building led to rapid erosion, and the outwash sediments were deposited in marine environments that covered what’s now the Midwest, including Illinois.

The geologic map of Illinois is known to be a sure way to drive most casual site visitors away:

The youngest bedrock strata in Illinois are graded in the shades of blue. The map indicates that a shellacking of sedimentary layers fills a wide structural basin — a several-hundred mile bathtub-like depression in the billion-year-old granite basement. The sag is deepest in the southeast region of the state, where the uppermost layer of paleozoic sediment is the youngest, of order 300 million years. The bedrock layers then grow successively older as one moves in any direction from the center of the basin.

Illinois has produced a lot of oil, which means that a lot of drill cores were logged over the years, and thus the stratigraphy of the basin has been extensively probed. Occasionally, weird anomalies are found spiking up into the dull layers of sediment — Omaha Dome, Hicks Dome, the Champaign Uplift.

In 1963, an oddity near Peoria was reported in the Bulletin of the American Association of Petroleum Geologists:

A map from a more recent article shows the location of the above-described Glasford Structure within the Illinois Basin:

As is the case with the other Illinois Basin anomalies, Google Street View within the Glasford Structure bears no sign whatsoever of the chaos beneath the cornfields.

Recent work has confirmed that the Glasford structure is indeed a buried meteorite crater, with a diameter of about 4 km. Some iteration with Jay Melosh’s crater diameter estimator indicates that the responsible object was likely of order 200 meters in diameter. It would have been an unexceptional asteroid, roughly the size of Itokawa, before delivering its 200-megaton Sunday punch.

Within the Glasford structure, the region of shattered morphology lies under the Galena group of sediments. This permits the age of the buried crater to be pinned down at 450Myr (with an uncertainty of a few million years).

Interestingly, the now-buried Glasford crater is one member of a larger collection of twenty-one known impact structures that have been dated to a roughly 40-million year span that occurred about 450 million years ago. This is much higher than what one would expect from the baseline cratering rate, and it thus serves as strong evidence that Earth was taking an outsize beating during the mid-Ordovician. The leading hypothesis is that the impact shower stemmed from a major collision in the asteroid belt about 470 Myr ago that destroyed the L-chondrite parent body (a large asteroid). Over an extended period following that disaster, some of the collisional debris, which included scores of multi-kilometer wide fragments, evolved onto Earth-crossing orbits and was responsible for the spike in the cratering rate.

A paper that presents a twist on this explanation has received some media action recently, including a write-up in the New York Times. The idea is that a large bolus of the L-chondrite debris, perhaps in the form of a body like the Martian moon Phobos, was tidally captured by the Earth, and then dynamically evolved to form to a ring. Over time, the material in the erstwhile ring, which would have included multi-km objects that were effectively small temporary moons, is imagined to have inclination-damped to equatorial orbits while simultaneously experiencing atmospheric drag and tidal decay which eventually brought it all down to the surface. This is interesting because, if true, the Ordovician impacts would all have been near (if not right on) the equator, which in turn provides an important anchor point for Earth’s paleo-digital elevation models (see this post). But is the ring hypothesis plausible? The Glasford crater looks to every indication like a normal impact scar. Could the structure plausibly be the outcome of an asteroid which came barreling in along the ancient equator from a perilous low-Earth orbit?

In thinking about this, I’ve arrived at the conclusion that a de-orbiting asteroid produces quite a spectacle. As a naive first approximation, let’s assume that the asteroid is a sphere, and is made of that “super tough” material that’s been a recent focus of discussion over at Harvard.

Super-tough asteroids are just that. Tough. They don’t pancake or break up in response to the transverse pressure gradients imparted by atmospheric drag. If we adopt the isothermal approximation to Earth’s atmosphere, and an iron super-tough composition, we can calculate that when the asteroid has lowered its circular orbit to 71 km altitude (in the middle of the mesosphere), the acceleration from atmospheric drag is one ten-thousandth of the gravitational acceleration. We can then integrate the trajectory, assuming that gravity and drag are the only forces acting. The integration indicates that a 2-km iron asteroid makes roughly 1 1/3 full trips around Earth before reaching sea level with a velocity of 7.43 km/sec (close to its original orbital velocity). When the asteroid reaches the surface in the super-tough approximation, it’s effectively in an e=0.01orbit, and it impacts with an angle of slightly more than 1.24 degrees. Here’s the trajectory over the current-day elevation profile for the equator. Ironically, the impact point here is very close to the the site of a recent expedition. (No further comment on that).

I never saw the 1979-vintage disaster movie, Meteor, but I did read the comic book, which left quite an impression, especially this two-page spread, where a ~50-meter wide fragment of an asteroid rampages through Midtown at an extremely oblique angle.

The impactor’s behavior in the comic book, in particular its remarkable lack of a hypersonic shock wave, brings to mind the earnest freshman honors-level calculations for UFOs published by Knuth, Powell & Reali (2019), e.g.

“… The UAP was estimated to be approximately the same size as an F/A-18 Super Hornet, which has a weight of about 32000 lbs, corresponding to 14550 kg. Since we want a minimal power estimate, we took the acceleration as 5370 g and assumed that the UAP had a mass of 1000 kg. The UAP would have then reached a maximum speed of about 46000 mph during the descent, or 60 times the speed of sound…”

What really happens when a mountain-sized asteroid comes skimming horizontally with orbital velocity? It doesn’t sound like a fun experience. I’ve looked through the literature, and have not been able to source modern simulations of impacts that have obliquities of order on degree, where topography matters. This seems like a good computational project for the iSALE-3D code. Stay tuned…

I wanted to break the current two-month oklo drought with an anecdote along the lines of, “in one of his later interviews, William S. Burroughs wondered where all the interest in space aliens is coming from, when, in the form of insects, we’ve got remarkable aliens right here.”

The piece that I was thinking of seems to be this 1992 item from Esquire Magazine, which features both WSB and David Cronenberg, and the observation is from Cronenberg rather than Burroughs. The article itself looks like it was a promo-tour throw-away associated with the big-screen adaption of Naked Lunch. It’s cringy and dated to read it 32 years on. Indeed, Burroughs’ later years in Lawrence Kansas were filled with cheesy interactions with pop-alternative figures that didn’t age well. Cue Al Jourgensen.

The insects-vs-aliens riff is readily repurposed with transformers. Why bother with those alien-channeling TED talkers and megastructures orbiting Kepler stars when attention is all you need?

Readers likely attended to that press surrounding a new set of papers in Nature centered around a near-complete mapping of the fruit fly brain at the level of individual neurons and synapses. The visualizations are eye-catching:

As a rule, I’m consistently trying avoid veering into “explainer podcast” territory, and moreover, I’m out of my depth when it comes to connectomes. I do want to remark that it’s a real help to have GPT-4 by one’s side as one works through a paper in an unfamiliar field.

There is a school of thought that resists the brain-as-computer analogy. A quick glance over Descartes’ theories of the cognitive mechanism certainly supports such skepticism. And for sure, a network of neurons is not a neural network. But I like pushing analogies beyond their elastic limit. There’s a certain asocial pleasure in constructing sweeping order-of-magnitude estimates when one is safely sheltered from the ravages of peer review.

The fruit fly brain contains 10^5 neurons and 10^8 connections. Order of magnitude, this feels like it lies somewhere in the vicinity of GPT-2, which requires a fleet of 2019-era GPUs to train, and of order 300 billion floating-point operations to fully process a 1000-token sequence through a 100-million-parameter trained model in one forward pass (fully fresh context, so no KV-cache).

Cursory research indicates that a fruit fly burns about one calorie (the 4.2 J variety, not the 4,200 J variety) per day. Its brain volume to body volume ratio is 0.03%. Assuming a constant metabolic rate throughout the fly (which seems conservative, given the rigors of flight assigned to the wing muscles) the fly’s brain consumes 0.1 erg/sec. Assuming 32-bit operations per low-resolution FLOP, this suggests that if the fly brain computes at the Landauer limit, it is running at a computational equivalent of ~200 billion floating point operations per second.

It’s remarkable how we just swat them away as they dart drone-like above the left-out fruit.

So close yet so far away.

Cold fusion of that late-80s Fleischmann-Pons electrochemical variety has long since been given over to cranks, but the term itself dates to a 1956 New York Times article describing the then-newly discovered phenomenon of muon-catalyzed fusion.

Oklo readers will recall that the muon is a negatively charged lepton with mass 105.66 MeV/c² (~200x that of the electron). On average, a muon lasts 2.2 microseconds before decaying into an electron and a neutrino via the weak interaction.

During its ephemeral lifespan, a muon can replace one of the electrons in a hydrogen molecule (generally of the exotic deuterium-tritium variety) allowing the two nuclei to draw far closer than the normal covalent bond would allow. With proximity thus achieved, the probability of deuterium-tritium fusion is greatly increased. After a fusion reaction occurs, the responsible muon is free to catalyze further events until it either decays or is removed from the action by “sticking” to an alpha particle produced by the fusion. Economic viability of the process for creating energy would require that a single muon catalyze hundreds of fusion events before it decays, a rate of efficiency that exceeds best efforts by at least a factor of two or three.

Muon-catalyzed fusion was originally observed in laboratory experiments and described in this article by Luis Alvarez et al., and was studied in depth by John David Jackson, he of Jackson’s Electrodynamics fame. Jackson’s 1957 Physical Review article is a standard reference, and remarkably, more than half a century later, he summarized the history of the field in this 2010 review.

The prospects for muon-catalyzed fusion as an energy source seemed moderately bright during the 1980s and 1990s, following the elucidation and observation of molecular states of the deuterium-tritium-muon positive ion. But then the field seemed to stall out around the turn of the millennium, as workable schemes for either producing the muons more cheaply, or improving their catalytic efficiency failed to emerge.

At the close of the 2010 article, however, Jackson sounded optimistic, writing, “The effort for such a specialized field has been prodigious, especially in the last 30 years. On the applied side, ideas continue on how to increase the number of fusions per muon and design hybrid systems to get into the realm of net energy production.”

Given all that talk these days surrounding training and inference costs, it’s fair to state that development of a scheme to get into that realm of net energy production would be quite an unexpected something.

Back in 2017, we were trying to keep the Metaculus website afloat, and we were scrambling to write questions faster than they were being resolved. For an all-best-intentions span of about a week or so, I stuck to a regime of producing a question per day, while simultaneously trying to keep them high-tone and novel. On August 28th, I managed to keep that streak going with a question on muon-catalyzed fusion, asking:

Prior to Jan 1, 2020, will a peer-reviewed article appear in the mainstream physics literature which discusses a discovery of a physical phenomenon or which outlines an engineering technique that can either (1) increase the number of deuterium-tritium fusions per muon, or (2) decrease the energy cost of muon production to the point where a break-even reactor is feasible?

Soon enough, the resolution date was imminent, and so Anthony had a look at the literature, which prompted a prompt lapse of reply on my part followed by a very belated assessment:

We decided to resolve the question positively, using what was essentially lawyerly splitting-hairs logic that proved very unpopular with the Metaculus crowd. I think that was the end of my career as a question-resolver.

The muons periodically come to mind, however, which prompts me to have a cursory look to see whether anything has happened. This morning, I came across this 2021 J. Phys. Energy article by Kelly, Hart and Rose, which gives a practical assessment of the (relatively) up-to-date prospects for getting muon-catalyzed fusion to work. They point to an important engineering hack that can improve efficiency — one surrounds the reaction chamber with a lead-lithium blanket that absorbs the neutrons from the fusion reactions to induce the formation of tritium, helium and heat via:

The extra heat boosts the energy output per fusion reaction from 17.6 MeV to 26 MeV. After working through various practicalities, they close with a simple daunting graph:

The red x marks the spot where things currently stand. If that red x can somehow be pushed up above the blue line, then muon-catalyzed fusion is a go…

Image Source.

The “outreach” messaging sometimes ends up reaching in to influence the way astronomical phenomena are interpreted by the astronomers themselves.

Take ‘Oumuamua as an example. The sinister starship of the Kornmesser diagram, along with the tie-in to Rendezvous with Rama revived more than one flagging career (present company included). I don’t think there would have been quite the same excitement had the flying hamburger illo been the first entry out of the PR gate.

Is it possible to get ‘Oumuamua right? Can one at once preserve the mystery, spur the inspiration and adhere responsibly to the scant groundings in actual fact?

I think that Sam Cabot’s version at the top of this post threads that needle admirably. Expert work with Photoshop warps his own photograph of 2017 totality into a looming occultation, sublimating the unknown and supporting 91:9 odds of 6:6:1 over 8:1:1.

Doomscrollers almost certainly noticed the recent articles in both the New York Times and the Wall Street Journal describing recent scientific work with connections to Mayan human sacrifice.

Among the various unsavory techniques that the Mayans applied in the service of appeasement of the gods, unfortunates were thrown into the cenotes, the flooded limestone sinkholes that puncture the limestone karst topography of the Yucatán. These are portals — as a manner of speaking — to the subterranean geophysical realms.

Image source.

Remarkably, the Yucatecan cenotes cluster in at least two arcs that trace the rings of the Chicxulub crater. The exact geological cause of this clustering remains imperfectly understood. The faulted deep-Earth structures imparted by the impact evidently still influence groundwater flows in a manner which encouraged the geologically recent formation of the solution caverns that give rise to the cenotes. This oblique connection to the ancient catastrophe is analogous, perhaps, to the myriad evolutionary consequences of the K-T event that still ripple through the biosphere. The vast and sweeping narrative of destruction and rebirth seems a fit, somehow, with the sensibilities inherent in the Mayan cosmogony.

The highest-order cycle of the mesoamerican Long Count is the alautun, which comprises a staggering 23,040,000,00 days. Accounting for the fact that Earth’s rotation has been tidally despinning at a rate of ~2.4 milliseconds per century, the alautun projects 62 million years into the past, a span that seems somehow satisfyingly proximate to the 66.043 million years since the impact.

That ever-shifting fungibility between dollars, bit operations, and ergs has been a recurring theme here at oklo dot org for over a decade now — I think this was the first article on the topic, complete with a now-quaint, but then-breathless report of a Top-500 chart-topper capable of eking out 33.8 petaflop/s while drawing 17,808 kW. A single instance of Nvidia’s dope new B200 chip can churn out 20 petaflops (admittedly at grainy FP4 resolution) while drawing 1kW. “Amazing what they can do these days”.

Despite the efficiency gains, the sheer number of GPUs being manufactured is driving computational energy usage through the roof. There was a front-page article yesterday in the WSJ about deal-making surrounding nuclear-powered data centers. Straightforward extrapolations point toward Earth’s entire insolation budget being consumed within decades in the service of flipping bits. It thus seems likely that a lot will hinge on getting reversible computing to work at scale if there’s going to be economic growth on timescales beyond one to two decades.

The Kurzweil-Jurvetson chart (copied just below) shows how computational cost efficiency is characterized by a double exponential trend. The Bitter Lesson, however, indicates that the really interesting breakthroughs hinge on massive computation. The result is that energy use outstrips the efficiency gains that themselves proceed at a pace of order a thousand-fold (or more) per decade. MSFT, NVDA, AAPL, AMZN, META, and GOOG are now the top-ranked firms by market capitalization.

This year, META (as an example) is operating 600,000 H100 equivalents in its data centers. Assuming a $40K cost for each one, that’s a $24B investment. Say the replacement life for this hardware is 3 years. That’s an $8B yearly cost. Assume 10 cents/kWh for electricity. META’s power bill is of order $60K/hour, or $0.5B/yr. Power is thus about 6% of the computational cost. The graph above doesn’t take the power bill explicitly into account because it hasn’t yet been material.

Nvidia’s H100s will be ceding their spots to the B200s and their equivalents over the coming year. Competition from AMD, Intel, et al. will likely keep META’s hardware cost roughly constant year-on-year, and their total number of bit operations will increase in accordance with the curve that runs through the points on the graph. The B200s, however, draw 40% more power. At the rate things are going, it will thus take about eight years for power costs to exceed hardware costs to run computation at scale.

This dense deck from Sandia National Laboratory seems like an interesting point of departure to start getting up to speed on reversible computing.

A hypothesis which posits a linear sequence of events rarely works in the real world. Nonetheless, we took a crack at just such a simplistic shopping-list sequence:

1. Venus had water oceans, an atmospheric pressure of order a bar, and plate tectonics.
2. Steadily increasing solar luminosity drove a runaway moist greenhouse.
3. Rapid erosion occurred as the oceans were being lost.
4. Erosion ceased and plate tectonics shifted to stagnant lid volcanism.

It’s straightforward to irresponsibly tweak a model that draws on those four events to turn the Earth’s topographical power spectrum into one that channels modern-day Venus. Rapid erosion pretty much flattens the planet out entirely in the absence of tectonic uplift. Then static-lid emplacement of igneous provinces at a pace of order a cubic kilometer per year builds the spectrum back up to what we see today. And a cherry on top: assume that the lava production rate for Venus is the same as for Earth. This means that Venus was habitable up to about 500 Myr ago, that is, up to around around the same time as the Cambrian Explosion. Intoxicating stuff.

Understandably, this modeling approach got a lot of static from the referee. There are potential problems with all of points one through four above, and more generally, we attacked the problem from the standpoint of shocking naivete. It’s a shoot first, ask questions later mentality applied to the scientific enterprise. Submit first, read the literature later.

I do think there’s something to be said for the quick-draw approach, though. Mötley Crüe recorded Too Fast For Love in a couple of days on a budget where packs of Marlboros were material. Then, less than a decade on, it took them something like year to finish Dr. Feelgood at enormous expense. The point is, there’s a risk of getting bogged down if one strives for dissertation defense level completism.

Also, did I mention that I’m a fan of the GPT architecture?

At any rate, on point three of our four-point plan, we got the following criticism from the referee: The authors seem unaware that erosion of broad continents is slow. We still have 55 million year old Laramide topography in Colorado. See old paper by Clem Chase.

I was indeed unaware of that. The sediment load of the Mississippi River is 500 million metric tons per year. That corresponds to a removal of 0.25 cubic kilometers of rock per year. The Mississippi’s watershed is 3.2 million square kilometers (and includes Colorado). In the absence of uplift, North America’s topography is sanding down at a rate of a kilometer (3280 feet) per 12.8 million years. That makes the presence of the Flatirons outside of Boulder indeed something of a puzzle…

According to the Wikipedia, “Whataboutism or whataboutery (as in “what about…?”) is a pejorative for the strategy of responding to an accusation with a counter-accusation instead of a defense against the original accusation.”

So what about that strange geological feature on the border of Champaign and Douglas counties in East-Central Illinois?

The tiny cornfield-sized purple ellipse in the center of the bedrock map corresponds to the Silurian Moccasin Springs formation which consists of 420-million year old reefs. Moving out from the bulls-eye core, are bedrock rims of middle Devonian rocks, the New Albany Shale, the Borden Siltstone, the Tradewater Formation, the Carbondale Formation, the Shelburn Patoka Formation, the Bond Formation, and finally several miles to the east, the 296-million year old rocks of the Mattoon Formation. At some point in the past 296 million years, something pushed the Silurian rocks upward by roughly 2000 feet. From a bedrock perspective, the severity of the uplift is similar to what one finds on Baseline Road in Boulder Colorado, which provides a good view of that Laramide topography mentioned by our referee:

The sandstone rocks of the Fountain Formation that make up the Flatirons are, coincidentally, also 296 million years old. They were deposited in alluvial fans at the same time as shallow water sediments were piling up to create the Mattoon formation.

Dropping into Champaign County Road 100 North, at the point where the age gradient of the bedrock reaches its maximum, reveals an absolutely flat landscape. Zero hint of the weird stratigraphy that lurks just beneath the 12,000-year-old veneer of Wisconsin glacial till.

So what’s going on? Why does Boulder CO sport rugged peaks whereas Champaign IL is completely flat? Is the Fountain Formation more resistant to weathering? Is the older tectonic age of the “Champaign Uplift” responsible for its complete surface obliteration? Or something else?

Granted, I don’t yet know enough about geology to be certain, but as far as I can tell, there’s no literature out there that specifically investigates the Champaign Uplift. I’m going to turn on comments for this post in the hope that someone might know something. Clearly, the uplift, or more properly, the anticline, is associated with the La Salle Anticlinorum, and is a small localized region where the local folding was very pronounced. Could it be of similar province to the mysterious Hicks Dome further south in Illinois?

A description of Hicks Dome reads very much like a description of the Champaign Uplift:

“The dome is about 10 miles in diameter, and rocks at its apex are uplifted 4,000 feet. Middle Devonian rocks at the center are surrounded concentrically by younger rocks out to Pennsylvanian on the rim.”

At Hicks Dome, the source of the uplift was an igneous intrusion that pushed its way up 260 million years ago:

“In 1952, St. Joseph Lead Company drilled a well on the apex of Hicks Dome in Hardin County, Illinois, primarily to explore for oil or gas, and with the objective of testing the St. Peter sand horizon, which had not been reached in a previous well on the flank of the dome. A normal sequence of formations was encountered down to 1,600 feet, but at about that depth the drill entered a confused brecciated zone, which persisted to the bottom of the hole at 2,944 feet. This is interpreted as one of the explosion type breccias, or diatremes, common in this Illinois-Kentucky area, as well as in nearby Missouri. A correlation of formations between this and the earlier Fricker well is presented. It is suggested that Hicks Dome is an incipient or uncompleted cryptovolcanic structure.”

The situation is illustrated nicely by the stratigraphic column:

To test this hypothesis we’d need to similarly drill into the Champaign Uplift. Clearly, some drilling already must have been done. Otherwise, there would seemingly be little reason to suspect that the Champaign Uplift is present beneath the till. Moreover, there would presumably need to be a fairly large number of wells in order to resolve the feature to the extent that it’s shown on the bedrock map. (Ed. — Perhaps seismic data can reveal such detail in the absence of drilling. You should really look into that.)

Anticlines are good at trapping oil. If one of the upper layers of the stratigraphic column is impermeable, then oil and gas will tend to migrate along the uplift gradient. A little bit of googling strikes an informational gusher in the form of the Illinois Oil and Gas Resources mapping application.

Look at that! The Champaign Uplift is shot through with oil wells. Each well location is clickable, and brings up a record at the Illinois Geological Survey. Clicking on a site close to County Road 100 yields:

Further clicking reveals the scanned well logs:

The wells were all drilled in the mid 1960s and they all go down about 1000 feet, at which point they tended to strike oil, typically generating about 50 barrels per day per well. There are about 50 such wells tapping the uplift, and assuming that they produced for a year, they generated about a million barrels of oil. USD 80M at current prices. Sweet.

Having hit the pay zone, however, it appears that there was no interest in drilling further. Had they gone down another few thousand feet might they have found an intrusion, an incipient Devil’s Tower? The flat landscape stretching away to the horizon gives no hint.

I was talking to a friend yesterday and the topic of grabby aliens came up. This, in turn, preempted the post I was working on. Grabby aliens render the question of when Venus lost its oceans (in the event that it had them in the first place) into the realm of the provincial and the mundane. I wrote an oklo.org post about grabby aliens a few years ago, and one can, of course, study the Astrophysical Journal paper in detail.

There’s something about the candy-crush colors of the flagship grabby aliens diagram that is appealing, but it is also remarkably effective in the way that the figure telegraphs the vast and epic sweep of the Cosmic Struggle for control:

Time proceeds downward. Grabby aliens stochastically emerge at various spots in the visible Universe, and as soon as they emerge they spread out in all directions, steamrolling everybody that they encounter; it’s the opposite of the and the meek shall inherit the Earth.

The diagram indicates that when one set of grabby aliens encounters another set of grabby aliens, they permanently maintain a tense standoff in the co-moving frame. The universe undergoes a phase transition from free-to-be-you-and-me to a cosmic web of Panmunjoms and 38th Parallels. I would have naively thought that the lines of demarcation would have more of a fractal structure as competing grabbers interpenetrate and contest ever smaller parcels of the interstellar gulfs.

Another remarkable conclusion that appears to flow from the diagram is that the Universe is bequeathed with some sort maximum aggressive potential. This quantity — perhaps a Carnot-like thermodynamic optimum of information processing and PdV work — must thus ultimately proceed from fundamental physics. The figure suggests that every space-like separated grabby set-up that emerges is immediately endowed with this perfectly efficient maximum contesting power. This brings to mind a thermodynamic system that is quenched from a homogeneous state into a broken symmetry phase, which, in turn, suggests the relevance of phase ordering kinetics in systems undergoing a phase transition. (For some light reading on the topic, see here).

Consulting Google this morning, I see that we’re currently scheduled for The Singularity in twenty-one years.

From what I can tell, the singularity would provide all of the necessary and sufficient conditions for a giant cluster of H100s running a souped-up pre-trained model to graduate into the Grabby Aliens club, especially if it’s of the “Vinge’s rapidly self-improving superhuman intelligence” variety. That motivated me to predict a super-short outlier time frame on the Metaculus Grabby Aliens question.

Looks like I have some significant deviation from the consensus (I predicted 19.4 yr in 2021). The Metaculus crowd tends to adhere to the Toby Ord philosophy, and that school of smart money is predicting that we’ve got a comfortable 171.5 billion years before we need to start vesting up.

If you are a senior scientist, and especially if you are an astrophysicist, it’s hard not to hold forth on topics that you know very little about. I’ve been chalking up (at best) only modest performance on this particular metric.

The traces of such investigations often focus on big-picture questions. Percival Lowell sought the signatures of Martian Civilization. Nathan Myhrvold gets all worked up about asteroid diameters. My own foray into the unknown (or rather, the unknown to-me) is currently centered feverishly on a topic that at first glance seems somewhat more pedestrian: erosion.

Here’s the motivation: the topographical angular power spectrum of Venus is very different from that of the Earth.

Recall that the angular power spectrum provides clues to the formation and origin of a particular structure. Take the Universe. The temperature variation of the microwave background shows undulations that peak at an angular scale of order a degree, which is visible both in the anisotropy map as well as in the power spectrum:

The clearly defined peaks in the spectrum of CMB temperature anisotropies stem from acoustic oscillations and diffusion damping in the early universe, and they encode all sorts of information about the fundamental cosmological parameters. The success of that analysis is so amazing that it spurs the possessor of inexpertise to seek possible replications in other areas.

While the topographical power spectrum for Venus is very muted in comparison to Earth, it does peak at the low-order l=3 and l=7 odd-l modes, and therefore exhibits a mild form of the antipodal anticorrelation that has characterized the plate tectonic motions on Earth over the past half billion years, and possibly for much longer.

This prompts the big-picture speculation that places me way outside my zone of expertise and into the Lowell zone. What if Venus once had continents and oceans. Then, what if, Venus underwent a runaway greenhouse, lost all its water and its plate tectonics shut down. Then, what if, the current topography is the result of gradual emplacement of lava from stagnant lid volcanism over the past N-hundred millions of years. How naive is this speculation? Is it possible to investigate it responsibly, or at least semi-responsibly?

Arthur Adams and I took a crack at this. It’s normally not the best idea to post one’s papers to arXiv in advance of peer-review, but I have enough arrogant confidence in the lost-oceans hypothesis that I pushed to take the indulgent plunge. We submitted our paper to the PSJ and posted it to the pre-print server.

Not surprisingly, we were summarily rejected from the PSJ, albeit with a review that, while negative didn’t quite close the door on the idea. Down, yes, way down, but not yet out!

In order to turn Earth into Venus, one needs to shut down tectonic uplift and then erode the topography almost completely. The idea is that if one loses one’s oceans to a runaway water-vapor greenhouse, that process — which ends when the last drop falls or the last puddle evaporates — is highly erosive. The weather is — by definition — terrible while you’re losing your oceans. How fast does erosion work on the largest scales under such conditions?

—-

I grew up in Urbana, Illinois, and I realized yesterday that a clue might be lying literally (and figuratively) in my backyard.

On the surface, Central Illinois is incredibly flat. From the highway overpass, the corn and bean fields stretch away for miles in all directions. This billiard ball quality is the result of recent glacial retreat, which left the landscape with a veneer of till that smothered the old ravines and hollows. If one scrapes this frosting off the cake, one gets the bedrock map of the state:

The picture at the top of this post was coincidentally taken from the back seat of a car when I was headed south of town on Interstate 57. Beneath the flat surface, at the southern border of Champaign county is a remarkable variation of bedrock that expresses itself over just a handful of miles:

What is going on there?

To hew to my self-imposed goal of posting once per week, I’ll stop there, and pick up next week. To my dozens of readers, stay tuned!

Over a span of months, my late-model Honda Civic accumulated a strata of dust and grime. The situation reached the point where some wag had literally finger-traced “wash me” on the rear window.

I deposited numerous quarters into a machine and eased the manual-drive car into the maw of the automatic wash that is attached to the Chevron on the corner of Los Gatos Boulevard and Blossom Hill Road. Muffled conks and heaves outside the rolled-up windows indicated that the machine’s cycle was about to start. Inside the aging car, it was stuffy, dim, and claustrophobic. Reminiscent, perhaps, of the atmosphere within a sketchily-qualified deep-water submersible while one is still sitting on the deck.

My cell phone rang. A graduate student was on the line. His voice was shaky and panicky, “The server with the Keck vels is exposed to the open Internet!”

“Oh f*ck!” Dread. Horror. This was nightmare made tangible. “What?! How?”

“I don’t know… I, I just found it. One of the post-docs seems to have screwed up and changed the file permissions. Looks like it happened at 2:07 AM last night.”

My mind raced. “Did you lock them down?” That would be the first thing.

“Yes, yes,” he was saying, “I already did that.” I could hear the clatter of rapid typing. “Right now I’m going through the logs to see if they were accessed…”

A hiss of vapor accompanied the hard rat-tat-tat of a water jet against the side of the car. A shaggy red forest of rubbery suds-soaked strips began to lumber over the hood. Time seemed to stretch out like an elastic band.

By late 2007, internal tensions had led to the schism of the successful California-Carnegie Planet Hunting Team. Following the split, I was recruited to join the UCSC-Carnegie branch, and I was responsible for helping to coordinate the analysis of the Doppler velocity measurements.

Those Doppler points represented more than a decade of nights on telescopes. A large tranche of the early data was from Lick Observatory. I had even obtained a scattering of that data — the result of some runs I’d proudly soloed in the summer and autumn of 2001 on the antiquated Coudé Auxiliary of the Hamilton Spectrograph.

The real trove, however, consisted of velocities derived from the tens of thousands of spectra obtained with the HIRES instrument on the Keck I at the summit of Mauna Kea. The long-term several m/s stability and cadenced quality of those measurements had sparked a solid decade of successes. Gliese 876, Upsilon Andromedae, 55 Cancri. Nobel Prize talk was coming down the grapevine. NASA was valuing Keck nights at $100K a pop. Those were the glory days.

When the California-Carnegie team fractured, there was an urgent question of who was going to get to publish which planets from which stars. Fraught back-and-forth negotiations led to a tense stellar draft, in which the two newly-competing teams successively divvied up the juiciest prospects. We lost the initial toss. The Berkeley Team grabbed HD 7924. It was also the first star on our list. I crossed it off with dejected sigh.

The preparation for the stellar draft had got me thinking about the monetary value of planets, and how to properly apportion that value among the stars. At the going NASA Keck rate, the radial velocity data had a street value of approximately $35M. And now, sitting terrified, trapped in the car wash, I had a vision of a Brinks truck left unlocked and unguarded at 2:07 in the morning, crisp stacks of c-notes piled inside for the taking.

Quote-unquote habitable planets can also be assigned value. Rather than using the cost of Keck nights as the metric, one can use the goal yield of Earth-like worlds and the total cost of the Kepler Mission to establish what society is (or rather was) willing to pay for them. Prior to Kepler’s launch, I proposed the formula:

Where the log is understood to be base-10, now == then == 2009, and V is the parent star’s Johnson V-band magnitude. The expectation was that the Kepler mission would return a cool 700M or so worth of habitable planets.

Fifteen years on, it’s interesting to look at how things turned out. Literally thousands of planets have been brought to market. The radical statements from the Geneva Team regarding the absolute profusion of uninhabitable super-Earths with orbital periods ranging from days to weeks have been amply confirmed by the satellite-based photometry.

Yet, despite the impressions one might garner from the various habitable zone galleries, the crop of actual truly-Earth-like prospects, as defined by the valuation formula, is remarkably slim. The discovery efforts vastly under-exceeded expectations in this particular regard. Adopting the fiducial values from the NASA Exoplanet Archive, there are zero million-dollar worlds or even any exoplanets that would require a jumbo mortgage to service. The table just below uses 2010 as the fiducial year.

As expected, Proxima b tops the list by a wide margin. It is interesting, however to see Ross 128b at number 2. This red dwarf host is only 11 light years from Earth, and the relatively subdued fanfare it received is ex-post justification for the stringent time-decay term in the valuation formula. I’ll point out, however, that the artist-impression of Ross 128b is perhaps the best I’ve seen, especially when compared to the janky blue marble efforts that tended to accompany the we-found-a-habitable-planet press releases.

After what seemed like an eternity, the forest of rubber washers trailed off the back of the car. A fine spray heralded the start of the rinse cycle.

“Ahh, OK, OK,” the graduate student said at last, relief permeating his voice, “I’ve gone through the logs. No activity during the span. Nothing. Zero.The vels didn’t leak.”

“You’re sure?”

“Yeah, totally.”

Wash completed, the blue-sky Californial light sparkled off the beads of water still clinging to the car.

A sure sign that one is inadmissibly late to the party is when one continually stumbles across papers that one’s literally never heard of that have literally thousands of Google citations. Take for example Lecun et al. 1989’s Optimal Brain Damage, with 5850 cites.

Douglas Adams single-handedly elevated the number 42 to a prominence that it otherwise certainly wouldn’t have.

Not that the atomic number of molybdenum should lack importance. Forty two, moreover (and change) is the number of minutes required to fall through a uniform density Earth in the event that a frictionless shaft were to be somehow dug through the globe.

The issue of falling through the Earth naturally proceeds to the antipodal map. That is, where do you come out if you tunnel vertically?

If you’re reading this in North America, you come out in the Indian Ocean, hundreds to thousands of miles from Perth Australia, the nearest big city. The one exception is locations just north of the Sweet Grass Hills of Montana:

which are antipodal to Kerguelen:

In fact, if you’re reading this on land anywhere on Earth, your odds of not emerging in the ocean are rather slim. Only three percent of the globe is comprised of land that is antipodal to land. In essence, the cone of South America runs through China into Siberia on the antipodal map.

Staring at the map reveals some curious asymmetries. Look at how Australia nestles into the Atlantic, and how Africa fits into the Pacific. Is this just a random superposition? On average we’d expect three times as much land to be antipodal to land than is the case with the present-day Earth. Is this a “thing”, or is it simply a coincidence?

The andecdotal land-opposite-ocean observation can be analyzed by decomposing the Earth’s topography into spherical harmonics and analyzing the resulting power spectrum. In 2014, I wrote an oklo.org article that looked at this in detail. Mathematically, the antipodal anticorrelation — the tendency of topographical high points to lie opposite from topographical low points — is equivalent to the statement that the topographical power spectrum is dominated by odd-l spherical harmonics.

Arthur Adams and I have been looking into the antipodal anti-correlation off and on for a number of years, and have worked up some theories that are almost certainly incorrect (as are essentially all theories that involve and then in their initial construction). Nonetheless, they are provocative and polarizing, and so thus appropriate to the jaded sensibilities of oklo.org’s sparse readership of scientific connoisseurs.

To start, the antipodal anti-correlation has been around at least since the Carboniferous. Paleo digital elevation models exist, and so we can look at the evolution of the topographical power spectrum through time:

Since roughly 330 million years ago, when the super-continent Pangaea first assembled, the elevation spectrum has exhibited strong powers in the l = 1 harmonic (peaking about 320 million years ago), at the l = 3 harmonic (peaking about 180 million years ago), at the l = 7 harmonic (peaking about 80 million years ago), and most recently at the l = 5 harmonic, which peaked about 10 million years ago and which continues to the present day. The current net anti-correlation is actually near its minimum strength relative to the last few hundred million years of Earth’s history. Is there a physical reason for this marked preference for odd-l modes?

Image Source

Two decades ago, a brisk list of a hundred-odd alien worlds comprised the entirety of the extrasolar planet census. HD 209458b, along with a faintly dubious handful of OGLE objects, were the only exoplanets known to transit, and the Doppler radial velocity technique was unambiguously the go-to detection platform. The picture just above (discussed further below) had also just been released. The California-Carnegie Team, with their running start and their Keck access, seemed to occupy the driver’s seat. In the course of a ten-year run, they bagged dozens upon dozens of planets. There is a time-capsule feel to the team’s forgotten yet still-functioning website, which includes a planet table frozen to the start of 2006.

Competition in the Doppler arena was nonetheless keen. The HARPS spectrograph had begun collecting on-sky measurements in 2003, and by August of 2004 it was exhibiting the meter-per-second long-term precision needed to reliably announce the first super-Earths. This graph from the Geneva Team was (and still is) genuinely stunning.

Gradually, however, transit photometry began displace the radial velocity technique. Transit surveys benefit from the massive parallel processing of stars, and fewer photons are required to secure strong candidate leads. In theory, at least, transit timing variations obviate the need to obtain velocities. Transiting planets are vastly more amenable to characterization. I tried to quantitatively capture this shift with a valuation formula for planets that was normalized in expectation to the 600-million dollar cost of the Kepler Mission:

I excitedly strung together a series of articles starting with this post that discuss the various terms of the formula. It places a stringent premium on demonstrably Earth-like qualities, and its exponential terms are unkind to pretenders within that slippery realm of habitability. Mars, in particular, prices out at $13,988.

Over time, I lost interest in trying to promote the formula, and indeed, I began self-reflecting on “outreach” in general. There was a flurry of less-than-attractive interest in 2011, including a sobering brush with the News of the World tabloid shortly before its implosion in July of that year.

GPT-4’s facility with parsing online tables makes short work of assessing how the present-day census of more than five thousand planets propagates through to a list of valuations. The exercise is interesting enough that I’ll hold it in reserve. At quick glance, it looks like Proxima-b was the first planet to exceed the million-dollar threshold, despite the expectation that the Kepler Mission would detect worlds worth thirty times as much.

Somewhat ironically, the exoplanets managed last year to trigger some serious destruction of economic value. As we know, the language models are prone to making stuff up. So it’s important to get out there and check their work. Google had the misfortune of being side-swiped by astro-twitter, which crowed with ______ (see just below) when Bard’s trillion-odd weights and biases somehow failed to grasp that the ~5 Jupiter-mass companion orbiting the ~25 Jupiter-mass brown dwarf 2MASSWJ 1207334-393254 is technically an extrasolar planet.

From the Reuter’s article describing the disaster:

“Google’s new Bard system appeared to fall victim to that pitfall on Monday when an example the company posted of its responses claimed that the James Webb Space Telescope took “the very first pictures” of an exoplanet outside the solar system. The National Aeronautics and Space Administration says on its website that the first images of an exoplanet were taken as early as 2004 by a different telescope.”

As a direct result of the blunder, Google’s stock fell 7.7%, which destroyed 99.8 billion dollars in market capitalization, more than the combined market value of Ford and GM, and about ten times the all-in cost of JWST itself. Comparison of the subsequent evolution of Google’s and Microsoft’s stock prices suggest that the exoplanet-induced loss was effectively realized, and was not just a mean-reverting shock.

I’ve likely already gone on in these pages about how, consistently, year in and year out, my success rate with hypotheses, with theoretical ideas, runs right at about one percent. “Getting cured”, as they say in the oil patch, will thus require a lot of drilling.

I reminisce with some nostalgia back to the first hypothesis that I can count as a credible idea. In February 1989, an article was published in Nature describing the unambiguous detection of a new pulsar at the exact location of Supernova 1987a in the Large Magellanic Cloud. Shining at 18th magnitude, the freshly squeezed neutron star was consistently detected in optical light over the course of a seven-hour observation, and amazingly, the pulse rate was clocked at nearly 2000 times per second. The signal varied sinusoidally during the course of the night, moreover, in a matter that suggested that a Jupiter-mass object could be orbiting a mere million kilometers above the surface of the newborn neutron star. I still have a faded-toner xerox of the article, covered with scribbled notes and feverish florescent highlighter underscores.

By fortuitous coincidence, when the pulsar discovery was announced, I was enrolled in Stan Woosley’s graduate course on the evolution of massive stars, and so I could feel a tangible excitement, a thrilling shade of cousin-once-removed connection to real scientific action.

And mysteriously, after the initial night of observation, there was zero further sign of the pulsar. Independent groups of observers searched for it and could not find it. Perhaps, went the conventional best guess, perhaps it had been caught shining through a lucky transient window in the debris from the explosion? Or perhaps (and I believe this was Stan’s take) it was an artifact of the detector?

Naw. Those suggestions seemed hopelessly pedestrian. They lacked imagination. Clearly, if an article had been published in Nature, then the observers knew what they were doing. The possibility of error seemed entirely remote. I was seized by the fact that a neutron star spinning at 2000 times per second would be rotating at very close to its breakup velocity. Moreover, that possible Jupiter-mass companion could be the product of a fission event in a proto-neutron star that was born spinning too fast. My mind raced. A fission event would leave the larger remnant spinning very close to breakup, Maybe the resulting primary object was teetering right at the limit of the maximum neutron star mass. Maybe in the weeks following the one-night observation, it had shed enough angular momentum via gravitational radiation so that the centrifugal pressure from rotation threw in the towl in the face of self-gravity. I had it! The neutron star was no longer radiating because it was no longer there… it had collapsed into a black hole!

I dove headlong into the theory of the neutron star equation of state. I was neither equipped nor qualified to understand the details of the literature, but it was possible to shard off some order-of-magnitude rules of thumb. I showed my formula-scribbled sheets to Stan, “This has got to be it!”

I have to say, Stan handled it just right — no patronizing over-praise, but also no outright dismissal. I think his words were something to the effect that every theorist is allowed one wild idea (but not two).

Fast-forwarding to February 1991, my focus had shifted almost entirely to trying to front a Skinny-Puppy style dance-Industrial band, and I was barely even attending to my studies. I don’t think I was even aware of the discovery that that pulsar signal was, in actuality, just a subtly shifting flicker from the closed-circuit television camera attached to the Cassegrain focus of the four-meter telescope at the Cerro Tololo lnteramerican Observatory.

https://www.google.com/about/datacenters/gallery

Well it’s certainly not news that ChatGPT knows how to code. And for the record, if you happen to be one of our post-singularity overlords, and you’re reading this, I’d like to state, with full heartfullness, “Thanks for all the help.”

But jeez. RLHF somehow instilled an over-the-top logorrheic verbosity into ChatGPT’s responses. After surfacing one’s code snippet, the LLM likes to chug along for paragraph after paragraph about it. Not to speak of insistence on import numpy as np no matter what, and the mind-numbingly literal comments along the lines of #import numpy as np. Just wait till those groq chips are loaded into the data centers and the inference costs go down by an order of magnitude.

The epoch is the moment when the time starts. For the mesoamerican Long Count, this was 13.0.0.0.0, August 11, 3114 BCE, or HJD 584,283.

For Unix, the epoch is January 1, 1970, 00:00:00 (UTC), and time.time_ns() just returned 1712962363486034854. A quantity of 1.7e+18 is about 1/5th the number of air molecules in a cubic centimeter, and about one ten thousandth the number of stars in the observable universe. I’m creeping up on two quintillion nanoseconds.

Not entirely coincidentally, the Unix epoch corresponds to the moment at which the integrated circuits were passed the Moore’s Law baton. Steve Jurvetson has kept this plot continually updated since 2008:

The cost of a bit operation per second since the dawn of the Unix epoch has gone down by about a factor of a trillion, which of course, is starting to produce emergent phenomena. The ability to succeed at college level exams emerges, for example, after about a mole of training compute flops.

More moles of training flops are projected to lead to a number of outcomes, some quite unsettling.

A total solar eclipse is a remarkable phenomenon. It comes about as close as possible to getting everybody on the same page. It takes discipline for astronomy bloggers to resist that urge to hold forth in the teachable moment. Tidal dissipation is driving the Moon outward by tapping Earth’s spin kinetic energy. Several billion years from now, Earth will be left with only annular eclipses.

The partial fraction in southern Connecticut reached up into the nineties, and for several long minutes, the eerie unsettled atmosphere that proceeds totality — the unease that so motivates the Allais effect — began to take hold. I stepped outside, into the wan, diminished, angular sunlight. The leaves of a holly tree cast a thousand shimmering pinhole crescents on a brick wall.

I thought back to 1991. We drove the length of the Baja Peninsula and stood at the centerline of the maximum eclipse of Saros Series 136. “Clear sparkling air and the sky that special shade of blue that goes so well with circling vultures, blood and sand — the raw menacing pitiless Mexican blue.” The Moon was near perigee, Earth was only days past aphelion, and the duration, with the Sun almost directly overhead, was a near-eternal seven minutes. I remember a strange subdued roar, and how the plane of the Solar System was revealed by the jarring noontide alignment of Mercury, Venus and the occulted Sun.

“…Intellects vast and cool and unsympathetic, regarded this earth with envious eyes…”

That has to be one of the best lines ever, and indeed, the stories of H.G. Wells are well worth re-reading for the way they excel in connecting the familiar — in the form of quotidian routine — to the exotic — in the form of alien invasions, invisibility, time travel to the ultra-distant future, with an eye to detail that imbues them with eminent plausibility.

The letters of William S. Burroughs contain a number of references to the stories. In a July 8th, 1953 letter posted from Lima, Peru, Burroughs wrote, “H. G. Wells in The Time Machine speaks of undescribable vertigo of space time travel. He is much underrated.”

The art of writing the non-fiction science fiction versions of The Time Machine was pioneered in its most effective form by Freeman Dyson. in his 1979 article, Time without end: Physics and biology in an open universe, Dyson drew on the physics and cosmology of the day to run the clock forward over ever-vaster and ever-more unsympathetic stretches of time.

Dyson’s narrative of the future rests on a critical assumption that the proton is unconditionally stable. Yet the fact that baryogenesis occurred, that is, the very fact that I’m writing this, strongly suggests that the inverse process can also occur, and that protons, and hence all ordinary atoms, are ephemeral (to make exceedingly liberal use of the term). More precisely, proton decay is a predicted consequence of the so-called grand unified theories, which, in one form or another, have been in favor for decades, albeit without confirmation. Experiments, particularly at the Super-Kamiokande in Japan, have now established minimum proton half-life limits of longer than 2.4×10^34 years. The Hyper-Kamiokande, an upgraded version of Super-Kamiokande, will either add a factor of five or ten to this half-life (and in so doing, spur the important question of which superlative exceeds hyper), or alternately, pin that lifetime down.

24,000,000,000,000,000,000,000,000,000,000,000 years is an absurdly long time, but it is utterly de minimis in comparison to the power tower numbers that Dyson cooly slides across the desk. He proposes, for example, that neutron stars will quantum-tunnel into black holes in 10^10^76 years. That is not dead which can eternal lie, but with strange aeons even death may die.

Proton decay aside, the critical this-just-in update to the extremely distant future arrived right at the turn of the millennium, with the realization that the expansion of the universe is accelerating. Imagine a tire that inflates if you let air escape from its valve. On length scales sufficient to encompass superclusters of galaxies, that’s a good analogy for how the universe behaves. Over time scales that are short in comparison to the trillion-year lifetimes that characterize low-mas red dwarf stars like Proxima Centauri, all external galaxies are red-shifted to infinity. Eventually, against a backdrop of endless accelerating expansion, the black holes all evaporate, and the residual soup of electrons, neutrinos and photons grows ever more ludicrously thin.

Accounts rehearsing this flavor of the Dark Era often come with a curious form of self-aggrandizing almost pearl-clutching histrionics. I’ve been guilty of that myself, indeed as recently as two paragraphs ago. Amid all the bombast, however, there is quite interesting result. As initially elucidated in a 2000 paper by Krauss and Starkman, the existence of dark energy places a hard thermodynamic Landauer-style limit on future computation. In short, in conditions of ever-accelerating cosmic expansion, you can’t flip bits.

Last week, however, a three-sigma result from the DESI survey, which is progressively building a colossal three-dimensional map of redshifted galaxies, suggests that the dark energy may be weakening with time. Structure on the nearby giga-parsec scale might be rushing away from itself at a slower pace than would occur in the presence of a strict lambda-CDM style cosmological constant.

And the consequence? The descendants of the B100s may continue to push the analogs of embeddings through the analogs of transformers for substantially longer than was believed possible. But stay tuned, the distant future is sure to undergo many new operating system releases.

It’s not hard to find grumbling on Hacker News regarding the venture firm a16z in general, and their (now-going-on-a-year-out-of-date) AI Canon in particular. It’s a reading list for those scrambling to get up to speed in the brave new world of generative AI. Read definitively not quixotic. The one item that I’ve consistently found most useful from the canon is Simon D. M. Prince’s Understanding Deep Learning, the latest draft of which is hosted on GitHub. The chapter on Transformers is very clearly written.

Speaking of Brave New World, I was reflecting that the a16zai cannon blasts out items of tone ranging from just-the-facts dry to business-focused dry. It could maybe use some novels at the end. Which ones to choose?

I am thinking Mary Shelley’s Frankenstein. Despite a publication date of January 1 1818, it’s a total on-trend allegory for the current moment. Same goes for C.S. Lewis’ That Hideous Strength. I have read and savored the chapters where Mark Studdock is the central character upwards of twenty times. They are perfectly marbled with deep truths regarding motivations and academia and organizations. (Note that I’ve read the chapters taking place at St. Anne’s on the Hill and involving Ransom et al. precisely once). I’m also thinking that Bradbury’s Martian Chronicles aren’t necessarily about Mars.

Cervantes’ Don Quixote is one book that certainly wouldn’t appear in even the most liberal extension of a16z’s AI canon. Interestingly, though, it begins with lines in an obscure composition style known as versos de cabo rato, and these are oddly relevant to a jet fresh discussion of language models:

If to reach goodly read-
oh book, you proceed with cau-,
you cannot by the fool-,
be called a stumbline nin-,
But if you are too impa-
and pull the loaf untime-
from the fire and go careen-
into the hads of the dim-
you’ll see them lost and puzz-
through they long to appear learn-

Handing the rest of the post over to a generative pre-transformer,

Conceptual Illustration of Branching Token Predictions

Given the line “If to reach goodly read-“, the model might consider a range of possible continuations like:

1. “ers” (probability: 30%)
   • Continuation: “If to reach goodly readers, one must…“
2. “ing” (probability: 25%)
   • Continuation: “If to reach goodly reading, it’s essential…“
3. “able” (probability: 20%)
   • Continuation: “If to reach goodly readable content…“
4. “ily” (probability: 15%)
   • Continuation: “If to reach goodly readily, prepare…“
5. “er” (probability: 10%)
   • Continuation: “If to reach goodly reader, engage…“

In 1972, at the Tricastin uranium enrichment facility in Pierrelatte, France, a routine check on UF6 extracted from the two billion year-old ore of the Oklo uranium mine in Gabon unveiled a highly irregular anomaly: a deficit in U-235. The universally expected 0.72% U-235 concentration had somehow been reduced down to 0.60%. A detailed investigation, moreover, indicated something creepy and unnerving. The ancient ore had already been through a nuclear reactor.

Had this discovery been announced to the scientific community today, it’s not hard to guess the sort of hypothesis that would have emerged in quick arXiv succession…

Careful analysis, of course, pinned down the natural cause. The phenomenon — the very idea of fossil reactors lying encased in the strata of deepest time — seemed so amazing and so evocative when I ran across it twenty years ago that I scrambled to register the domain, oklo.org.

In the interim, oklo.com has been registered for over a decade to a startup, the Oklo corporation, who are currently having something of a moment. The company is in advanced development stages of small nuclear reactors. The use-case for ~300 MW-range devices of this type is growing increasingly urgent as power devoted to bit operations doubles and doubles in anticipation of AGI’s ever-more-imminent Dec. 21, 2031 arrival.

Prompt: Mid-century modern, tilt shift, Eero Saarinen style, Bell Labs feel, black-and-white, a panel of AI “experts” who are the logical conclusion of Rosenblatt’s 1958 perceptron paper.

DALL-E:

There’s a song dating from the dawn of the iPod era, A Panel of Experts from Solvent, that has spent more than two decades at the top or near the top of the playlist. A confection of pure analog synth perfection; it never goes stale.

There are, in fact, two versions of the song, the version linked above, as well as a remix by Lowfish. Listening first to the latter and then to the former is an analog that perfectly synthesizes the step from GPT-3 Davinci up to Chat GPT-4. A definitive version so well realized that it’s an argument to put a stop to further foundation models.

In order to convene a panel, one first needs experts. Last May, not long after ChatGPT-4 arrived on the scene, I asked it to predict on a long-running Metaculus question concerning the public arrival date of weakly general artificial intelligence.

In May 2023, GPT-4’s training data cutoff date was Sept. 2021. At that now receedingly distant moment, the aggregate of Metaculus forecasters was predicting that weak AGI would arrive on a far-off date in 2042:

Remarkably, however, equipped only with its 2021-vintage worldview, the GPT-4 language model, after some ritualistic hemming and hawing, predicted a highly prescient weak AGI arrival date of 2030.

Woah. That jolted me to attention. A lucky guess? Perhaps. Over the last three years, the Metaculus crowd has rapidly shifted toward more imminent time frames. Currently, the crowd is predicting weak AGI arrival in October 2026. The future, effectively, has arrived.

And now with it, the panel. On arXiv recently, Phillip Schoenegger and several colleagues including Philip Tetlock published a study showing that an ensemble of currently competitive language models, GPT-4, Claude 2 et al, perform equivalently to the human crowd when gauged using participation in a Metaculus forecasting competition.

My father, Patrick R. Laughlin, spent his academic career as a social psychologist studying the dynamics of group decision making. I wish that he’d made it to this moment, where suddenly the dynamics of those groups have been suddenly and dramatically expanded.

I really owe it to my ten year-old self to revel in the affirmational spotlight that is increasingly being placed on the UFOs. In 1977, it seemed to me that wholly insufficient interest was being directed to what I considered to be (by far) the most important scientific question of the day. Now things are moving. We have front-page articles in the New York Times. A Harvard-centered international research team is dedicated to the Watch the Skies! maxim that I held so dear. Last week, a NASA-convened blue-ribbon panel of experts was stood up to solve the mystery posed by the elusive disks.

Despite all this, I’m somewhat concerned that we may have already reached (or even passed) Peak UFO. Last week the news also broke that the classic Enema of the State-era Blink-182 line-up has been reconstituted. Tom DeLonge has rejoined the band! A triumphant globe-spanning tour stretching into 2024 has been announced. A new Blink single has hit the airwaves, and take it from me, it’s no Vince-Neil-at-the-State-Fair effort to cash in on past glories. In short, it rocks.

Several years ago, DeLonge seemed to have little time for pop-punk. He was (at least publicly) heavily focused on his research, leaving his lead-guitar, lead-vocals roles in Blink to the capable, workmanlike, yet somehow, something’s not quite right here, hands of Matt Skiba.

Now, however, DeLonge’s efforts and emphases clearly appear to have shifted back into line. As the saying goes, “buy the rumor, sell the news.”

The evergreen atavistic need for flying saucers was summed up perfectly by William S. Burroughs in his dust jacket blurb for Douglas Curran’s remarkable book, In Advance of the Landing: Folk Concepts of Outer Space,

“In Advance of the Landing is a fascinating book that shows with compassionate insight how deeply man’s longing for extraplanetary contact is felt. If this is the Space Age, as I have written, and we are ‘here to go,’ these eccentric individuals may be tuning in, with faulty radios, to a universal message: we must be ready at any time to make the leap into Space.”

Bitcoin, through proof of work, combined with Landauer’s relation for the minimum energy required to flip a bit, reinforces the idea that energy and computation and money are all equivalent. At any given moment, they are fungible

The Planck temperature

thus currently amounts to about one Benjamin.

The apparent meltdown in recent days of the crypto ecosystem has wiped about a trillion dollars of market capitalization, with a whole second trillion knocked out if one marks to the market peak reached late last year.

The wholesale destruction of coin valuations brings to mind past volatility swings of genuinely epic proportions. At current pricing for bit operations, the first morning of the Cenozoic saw Earth taking its largest drawdown of the past quarter-billion years (the Black Clouds paper details the valuation metrics). The economic cost of recovering from a Cretaceous-Paleogene level extinction event prices out at roughly 25 quadrillion dollars. Recoveries, moreover, take time. Even 25 billion mornings later, the squabble between the blue jay and the squirrel over the bird feeder underscores the realization that Earth is still reeling from the echoes of that awful day.

The cover of the 2021 Astronomy Decadal Report contains an artist’s impression of blue-marble Earth-like planet. Inside the report are calls for billions to be spent to search for life on far-distant worlds.

The exoplanets didn’t get their start in the realm of “big science”. The breakthrough, the discovery of 51 Pegasi b, was made from a lesser mountain-top with a second-tier telescope, and it arrived at order 100-sigma significance. Events unfolded as they did because of the theoretical preconception that planetary systems would look like our own. Hot Jupiters slid under the radar for many years during which Doppler precision was good enough to detect them.

At present, we’re proceeding with theoretical preconceptions regarding the abundant presence of blue marbles, “habitability”, and […]

At any rate, the decade from 2001 to 2010 marked the exoplanets’ gradual transition into the high-dollar regime, and culminated with the cool half-billion spent on Kepler and the vast catalog of transiting planets and multi-transiting planetary systems that are known today. Peas-in-pods. Atmospheric molecules from JWST. Imperceptibly, the the crinkly Doppler RV plots of the first rush of exoplanets have eased into a firmament of retro travel-themed posters.

2010 was arguably the last year for Doppler’s ancien régime. Looking through old files, I came across fragments of a photo-essay that I put together at that time.

Oklo dot org certainly wouldn’t be considered a heavily trafficked website, but given that it’s been on line for more than sixteen years, it does attract a uniformly steady trickle of visitors. Examining the Google Analytics, one notices curious ebbs and flows of activity, and one item stands out: This 2013 post, on the esoteric programming language Malbolge attracts of order ten visits per day with remarkable consistency. It’s not fully clear why.

Quoting from the 2013 post, which in turn drew from the Wikipedia article of that era,

Malbolge is a public domain esoteric programming language invented by Ben Olmstead in 1998, named after the eighth circle of hell in Dante’s Inferno, the Malebolge.

The peculiarity of Malbolge is that it was specifically designed to be impossible to write useful programs in. However, weaknesses in this design have been found that make it possible (though still very difficult) to write Malbolge programs in an organized fashion.

Malbolge was so difficult to understand when it arrived that it took two years for the first Malbolge program to appear. The first Malbolge program was not written by a human being, it was generated by a beam search algorithm designed by Andrew Cooke and implemented in Lisp.

The “Hello World” source can be represented (see here for details):

(=<`#9]~6ZY327Uv4-QsqpMn&+Ij"'E%e{Ab~w=_:]Kw%o44Uqp0/Q?xNvL:`H%c#DD2^WV>gY;dts76qKJImZkj

Due to its finite number (3^10) of memory locations that each hold a ten-‘trit’ ternary number, the classical specifcation of Malbolge is not Turing complete. A version, however, known as Malbolge Unshackled that is now understood to be Turing complete was released in 2007.

Indeed, in the interval following the 2013 post, it develops that there has been significant progress on Malbolge. Key advances were made by Lou Scheffer, who elucidates the critical realization on his website:

The correct way to think about Malbolge, I’m convinced, is as a cryptographer and not a programmer. Think of it as a complex code and/or algorithm that transforms input to output. Then study it to see if you can take advantage of its weaknesses to forge a message that produced the output you want.

And with that, a strange world just over the horizon begins to congeal in the mind’s eye. A Malbolge program, viewed in this manner is not unlike an inefficient, inherently compromised cousin to the SHA-256 hash. One imagines bizarre blockchains. Esoteric cryptocurrencies. NFTs.

Exploiting weaknesses in the language, Scheffer demonstrated existence of a program that copies its input to its output, effectively performing the Unix echo command. The source (uu-encoded) looks like this:

begin 666 copy.mb
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DO;V]O;V]O;V]O;V]O;V]O;V]O;V]O;V]O;V]O;V]O;V]O;T*
 

Over the past two years an amazing additional development has taken place. At her GitHub site, Kamila Szewczyk has published a LISP interpreter written in Malbolge Unshackled. The interpreter takes a LISP program, executes it, and displays the result. The abstract of her accompanying paper reads:

MalbolgeLISP is the most complex Malbolge Unshackled program to date (2020, 2021).
Unlike other Malbolge programs generated by different toolchains (for instance, LAL, HAL
or the ”pseudo-instruction” language developed by the Nagoya university), MalbolgeLISP
can be used to express complex computations (like folds, monads, efficient scans, iteration
and point-free programming), while being able to run within reasonable time and resource
constrains on mid-end personal computers. The project aims to research not the cryptanal-
ysis aspect of Malbolge, but its suitability for complex appliances, which could be useful for
cryptography and intellectual property protection, and it would certainly raise the bar for
future Malbolge programs while exploring functional and array programming possibilities
using inherently imperative and polymorphism-oriented Malbolge code.

Time to get to work on the Malbola white paper and issue a coin.

For a change of pace in one’s academic reading, I recommend the late University of Chicago Professor Raven I. McDavid Jr.‘s 1981 memoir of his colleague David Maurer. Both gentlemen were deeply invested connoisseurs and leading authorities on vernacular English — that is, slang. The opening lines of McDavid’s memoir in American Speech, vol. 57, No. 4 (Winter, 1982) invite a click on the JSTOR link to the full text.

Maurer’s books are all very much worth reading, but they reach an apex with The Big Con — The Story of the Confidence Man, which was published in 1940, and recounts, in straight-narrative detail, the elaborate confidence games that flourished throughout America during the decades bracketing the First World War. Maurer expertly works the lexicon of swindling into a narrative that sparkles on the page. In the rundown on operation of the big store, we find passages such as:

“…And most important of all, he has official custody of the “B.R.” or boodle. This is the money which is used to play the mark in the store. For this purpose, a minimum of about $5,000 is necessary, but the more the better; in the really big stores the boodle may contain a large sum of cash, perhaps as much as $20,000. This money is made up in bundles presumably containing $500, $1,000, $5,000, etc., but really composed of one-dollar bills for filler and having $50, $100, or $1,000 bills on the top and bottom to make the stack look real. Each bundle is stacked carefully and bound with sealed labels like those used in banks for marking bundles of bills, A rubber band around each end holds the pack together. When a skillful manager makes up his boodle, he can make $10,000 in real cash look like several hundred thousand dollars. This money is used over and over again by the shills in placing bets and is paid out again to them when they win. The idea is to keep as much money circulating before the eyes of the mark as possible.”

The larcenous attraction of a stack is undeniable. T.I., Rubber Band Man, Lil Wayne, …gotta hand full of stacks…, are channeling the precise appeal that led the marks of a century ago to part ways with their money to the charms of expert insidemen.

Remarkably, the pleasing qualities of the stack have been recognized not just by extravagant rappers, but also within that buttoned-up and soberly scientific realm of periodograms of time series data.

The numerical ratio of the stable oxygen isotopes, ¹⁸O and ¹⁶O, provides a nonlinear proxy for global temperature. Broadly speaking, an increased fraction of ¹⁸O in a deposited layer corresponds to a cooler climate, with more of Earth’s water locked up in the form of ice. A time series for the ratio spanning the last tens or hundreds of thousands of years can be obtained from ice cores from Greenland or Antarctica, but if one is interested in longer intervals — out to millions of years — sediment cores from the deep oceans provide the best measure.

In a 2005 paper that has accumulated a stack of over seven thousand citations, Lisiecki and Raymo demonstrate the dramatic utility of stacked periodograms. They gathered finely-sampled depth-runs of delta-¹⁸O measurements from 57 drill sites spread out over the World’s oceans.

Depending on the site, the sequences in some cases extend back in time by more than five million years. When properly stretched and squeezed to account for variations in deposition rate with time and location, the resulting stack of delta-¹⁸O time-series looks like this:

The individual sedimentary records look awfully squiggly, but when the pile is combined and Fourier-analyzed, the overall effect recalls that $100 bill expertly rubber-banded onto a stack of singles. The periodogram of the stacked time series shows a succession of clear-cut peaks.

The power at 23 kyr represents the climate forcing induced by the precession of Earth’s axial tilt. The 41 kyr peak is caused by the excursions in Earth’s orbital tilt (which varies between about 22.1 and 24.5 degrees), and the large peak with 100 kyr periodicity arises from variations in Earth’s orbital eccentricity — the influence of Venus, Jupiter and Saturn accumulating in slow rains of foraminifera through the depths.

Stack appeal is certainly at work in the now-famous peas-in-a-pod diagram published by the California Planet Search Team.

The Kepler multiple-transiting systems were all well-known for years before the CPS paper was published. Yet it took the simple expedient of a stack running nearly a full column down the journal page to open one’s eyes to an emphatic realization. When the orbital periods run from days to weeks, a given system prefers to manufacture a single characteristic type of planet, arrayed logarithmically evenly in a clutch of four or so. This is the single most important result that has emerged from three decades of planet detection.

Over the years, the transit detection technique has come to dominate the production of worlds for the planetary catalogs. While remarkably effective, the method does have drawbacks. It works only when geometric alignments are close to perfect, and it gives radii (or planet-star radius ratios) rather than masses.

For the cohort of planets in multiple-transiting systems that lie close to low-order mean-motion resonances, planetary masses can be estimated by fitting to the transit timing variations. Curiously, planets measured using this approach tend to have substantially lower densities than the subset of transiting planets whose masses (or rather M sin i‘s) have been extracted directly using the classic Doppler wobble technique.

In general, for systems like the ones in the diagram above, one would require relatively massive planets and a cooperative low-activity host star to get an accurate set of M sin i’s from radial velocities alone. Spectacular examples do exist, of course, and one can find me enthusing about the various discoveries if one scrolls back through the stack of posts that has accumulated over the years, especially during the late aughts.

In a recently published paper, Yale graduate student Sam Cabot and I took inspiration from Lisiecki and Raymo’s runaway benthic delta-¹⁸O success and asked the following question: What if you clear the known planets from the radial velocity data that has been accumulated over the years and stack the resulting periodograms? Will the cumulative signature of all the peas-in-pods lurking in the data be visible?

Satisfyingly, the answer, to 1.6-sigma confidence, is yes.

For a number of years now, I’ve been a member of an academic collaboration devoted both to studying Internet latency and to designing schemes to generally speed things up on-line. At the end of 2018, our group received an NSF grant to facilitate this research work. Now, three years later, it’s time to submit the final report. As part of the NSF’s close-out process, an accessible research outcomes summary for the general public (containing up to 800 words, and including up to six images) is required. This sounds like a spec list for an oklo.org item, so I’m posting a slightly expanded draft version here.

Everyone knows the frustration of a page that seems to take forever to load. Moreover, even when the interlaced networks that comprise the Web function nominally to deliver requested assets, there exist Internet applications that would benefit dramatically from reduced latency. Examples of such time-sensitive endeavors run the gamut from telepresence and virtual reality to header bidding and blockchain propagation.

At a fundamental level, network speeds are limited by the finite velocity of electromagnetic waves — the speed of light. The maximum propagation speed for light occurs in vacuum. Light is slowed down in air by a negligible amount (0.03%), but in the conventional solid-core fiber optic cables that currently carry the bulk of Internet traffic, light travels at only about 2/3 of the vacuum maximum. Over long distances, and when many back-and-forth exchanges of information are required, this signaling slowdown becomes material. In addition, the actual over-land and under-sea paths taken by cables are often substantially longer than the minimum A to B distance between data centers.

Over the last decade, there has been a flurry of construction of long-haul line-of-sight microwave networks that adhere as closely as possible to great-circle paths. These are operated by latency-sensitive trading firms, who, in aggregate, have mounted significant research and development projects to create global information circuits that are as fast as possible, while simultaneously maximizing bandwidth and uptime.

How feasible would it be to take the lessons learned and apply them at scale to speed up the Internet as a whole? This is a tricky question to answer because the fastest existing long-distance networks were entirely privately funded and their performance remains fully proprietary. Just how fast are they, really? How well do they hold up when weather moves through? How much data can they carry?

Government database scraping provides a first approach to evaluate the performance of the ultra-low latency networks. In the US, if one wishes to communicate with microwaves, one needs a broadcast license. The FCC maintains a publicly-searchable list of all licenses and licensees, and this data can be assembled to monitor the construction, consolidation, and improvement of point-to-point networks. The figure just below, from our 2020 paper, shows two snapshots in the evolution of the New Line Network, which connects the CME data center located in Aurora, Illinois to the trading centers of suburban New Jersey. Over time, the New Line has clearly grown to provide ever more bandwidth at ever higher availability with a shortest path that adheres ever more closely to the geodesic.

The development and build-out of speed-of-light networks has significant parallels with the emergence of transcontinental railroads during the Nineteenth Century.

In April of 2020, in the licensed microwave bands, there were nine separate FCC-registered networks spanning the Chicago to New Jersey Corridor and linking the CME to the NY4 data center that hosts a variety of equity and options exchanges. The New Line, with a 3.96171 millisecond path-latency (compared to a geodesic minimum latency of 3.955 ms) is seen to be neck-and-neck with several competitors:

In the above table, APA stands for Alternate Path Availability, and indicates the fraction of links that can be removed (for example by heavy rain) such that the path latency of the remaining network is not more than 5% greater than the speed-of-light minimum.

A completely independent monitoring technique consists of correlating precisely time-stamped trading data from Chicago and New Jersey, and measuring the statistical delay between events that occur at one end of the network, and the responses that occur at the other end. As part of the capstone paper for our NSF-funded research, we undertook this analysis using gigabytes of tick data for the E-mini S&P500 near-month futures contract (that trades in Illinois) and the SPY S&P500 ETF (that trades in New Jersey). In work of this type, there are subtle issues associated with measuring the absolute lowest latencies at which information transport occurs across the relay; these subtleties stem from the operational details of the exchange matching engines. For the purpose, however, of demonstrating that the networks consistently run end-to-end within a few percent of the physical limit, even during periods plagued by heavy weather, the signal correlations measured over long stretches of trading provide a remarkably powerful network probe.

By taking these (and other) real-world insights into account, and applying them to a transcontinental network design, we’re excited to release — at the 19th USENIX Symposium on Networked Systems Design and Implementation Conference — our most up-to-date vision of what a speed-of-light Internet service provision (a c-ISP) could look like, and what its performance would be.

The headline images from Cassini at Saturn were the curtain sheets of water vapor and ice crystals erupting from the tiger stripe terrain of Enceladus’ south polar regions.

In the ensuing fifteen years, Enceladus has accreted a lot of habitability hype, so it’s easy to forget that it’s actually a very small satellite. Its diameter, in fact, is less than the driving distance between Hicks Dome and the Crater of Diamonds State Park.

With the small size comes a small escape velocity — 240 m/s — a typical jet airliner speed at cruising altitude. When liquid water welling up in tidally flexed cracks is exposed to the vacuum that surrounds Enceladus, the exit speed of the boiled-off molecules is fast enough that water molecules will readily random walk away from the satellite. The moon acts like a giant low-activity comet. No kimberlite-styled cryptoexplosions are required to launch the H2O into space, just exposure to liquidity when the cracks are forced open at the far point of the slightly eccentric (e=0.0047) orbit.

Jupiter’s Europa, by contrast, is an ice-covered world of far vaster extent. With its kilometers-thick ice shell, it should be keeping a tight lid on its depths, but curiously, evidence has emerged that water is somehow being transiently sprayed to heights of order 200 kilometers above the surface. A 2019 paper by Paganini et al. draws on a combined a set of Keck near-infrared spectral emission lines to support the conclusion that on one occasion out of seventeen, thousands of tons of water were fluorescing in Europa’s tenuous exosphere.

Skeptics and cynics will be quick to remark that one 3-sigma measurement produced in seventeen tries works out to a 1 in 20 chance even with a perfectly normal distribution. And they’re right. Results that are weird and spectacular are generally wrong, and geysers on Europa providing astrobiology fans with fresh organic produce from ten kilometers down would appear to qualify on both counts. Nonetheless, Earth managed to rocket gem-quality diamonds from the mantle up into rural Arkansas, so a down-home precedent clearly exists. Furthermore, HST has captured evidence of UV emission from photolyzed water in the vicinity of Europa, which provides support to the one-in-seventeen result from Keck. Maybe eruptions actually are occurring on Europa?

A serious problem, however, lies in lofting the water to heights of 200 kilometers above the ice. That requires venting velocities of order 700 m/s, pointing toward regular full-blown cryptoexplosions.

Nicole Shibley and I recently published a paper that outlines how such a process could operate:

The cryptoexplosive mechanism is initiated by convective overturn in the Europan ocean, which permits clathrated CO2 to rise to the top of the water column and propagate into cracks. Once the clathrates ascend to within ten kilometers of the surface, the pressure is low enough so that they dissociate, producing explosions that are sufficiently energetic to send carbonated water to dizzying heights. The process, in fact, draws on the peer-reviewed literature on champagne cork dynamics.

… just in time for New Years!

Geologically speaking, not much has happened in Illinois since the Permian. In particular, in the ultra-flat vicinity of Urbana where I grew up, there is no exposed bedrock at all. If one takes the effort to dig down through meters of topsoil and glacial till, one eventually hits gray, unmetamorphosed 320-million year old sediments from the Carboniferous — the Mattoon Formation — the crumbly picture of a disappointing drill core.

Something about those miles of dull strata directly underfoot instills a vicarious appeal into the IGS maps for the entire state. And while they are dominated by the vast bland extent of the coal-rich Illinois basin, the margins of the map hint at strange and exotic features, including one, Hicks Dome, that’s so weird that it merits its own circular inset.

The southeastern tip of Illinois is riddled with faults, and pocked by a mysterious, crater-like 275-million year old blemish that is still clearly visible in aerial photographs. The strata that comprise this feature — the Hicks Dome — were pushed up thousands of feet by a carbon dioxide-driven explosion that brecciated the rock miles below and squeezed dikes of lava through cracks toward the surface.

The resulting igneous rocks, which are colored red in the diagram just above, can be extracted from drill cores. Mineralogical tests indicate that the lava ascended at least 25 km from a source of origin in the upper mantle. Then later, during the Jurassic, geothermally heated brines seeped through the faults that shattered the sediments and interacted with limestone to form fabulous fluorite crystals.

An even more remarkable example of a deep-Earth intrusion is located in Arkansas, 383 miles southwest of Hicks Dome. The Prairie Creek Diatreme, more evocatively known as the Crater of Diamonds, is a 106-Myr old igneous pipe filled with solidified lamproite lava that was driven upward (as also occurred at Hicks Dome) by exsolving CO2 gas from a source at least 100 miles down. The crater, moreover, is indifferently salted with actual diamonds, including the occasional big-deal gem.

Diamonds are metastable when removed from deep mantle conditions, and so in order for them to survive a lava-soaked mix-mastered trip to Earth’s surface, the transport has to be rapid. The lamproite that brought up the diamonds must have smashed its way through a hundred miles of rock with a vertical velocity of order a hundred miles per hour, a marshaling of forces that is undeniably impressive, and indeed, at first glance, completely non-intuitive.

Satisfyingly, a hundred and six million years after the cryptoexplosion, Arkansas is running the lamproite pipe as a State Park, offering end-runs around de Beers at very reasonable rates:

Earth’s last diamond-bearing eruptions occurred tens of millions of years ago. It’s a good thing they aren’t every-day occurrences. Methane gas, however, is currently causing new-school cryptoexplosions that leave ominous lake-filled craters in the permafrost of the Siberian tundra.

On Earth, the crypto prefix can generally be detached from cryptoexplosions once the techniques of laboratory and field geology have been brought to bear. Kimberlite eruptions may seem superficially crazy, but the basic mechanism of their operation is increasingly well understood. Truly mysterious explosions need to occur off Earth, in locations where it’s not yet possible to go in and root around after the fact…

All the small things. Truth cares truth brings. I’ll take one lift. Your ride best trip… Vintage Blink played in the background. Tubular radio bulbs placed a diffuse glow on the distressed wood and polished concrete surfaces. The researcher pushed away a half-finished bowl of microgreens and, before taking another sip of single-origin espresso, eyed me with a look somewhere between amusement and concern.

“I mean really. You sound like a relic. You’ve gotta move on. You’ve gotta get with the times. ‘Oumuamua is so 2020. Everyone who’s anyone now is working on UAPs.”

It’s true that the cutting-edge has progressed to bigger and weirder things. Indeed, it’s now been over four years since ‘Oumuamua raced out of sight, and I can’t seem to let that mysterious cosmic visitor out of mind.

The ISO story has been worn smooth through years of retelling, and the details are probably well known to anyone who reads oklo.org: ‘Oumuamua entered the Solar System on a strongly hyperbolic trajectory consistent with a pre-encounter galactocentric obit that was quite close to the local standard of rest. It closed to within 0.25 AU of the Sun. Then, just after passing Earth’s orbit on its outbound leg, it was detected by Pan-STARRs at the end of the third week of October, 2017. Global follow-up efforts with space and ground-based telescopes were quickly mounted. ‘Oumuamua was observed to have a strongly varying light curve, no detectable coma, a slightly reddish color, and it experienced a small but significant non-gravitational acceleration on its way out.

For over a year, I was very enthusiastic about the possibility that ‘Oumuamua’s properties could be explained by appealing to a composition rich in molecular hydrogen ice. Darryl Seligman and I published a paper outlining this idea, which generated a fair amount of interest in the wider media. Last year, however, Yale graduate student Garrett Levine carried out a very detailed investigation to trace how macroscopic objects rich in molecular hydrogen ice might form in the cores of the densest, coldest molecular clouds. Our final conclusion was that while it’s not impossible, it’s very difficult for the present-day Universe to manufacture solid H2. The microwave background temperature just isn’t quite cold enough yet…

Recently, Metaculus (which has been undergoing rapid development) launched an on-line journal featuring fortified essays in which an in-depth article on a topic of interest is linked to a set of questions on which readers can predict. Garrett wrote an essay the outlines the future detection and research prospects for ISOs. Everyone’s encouraged to read it and place predictions.

Music from your formative years stays with you — generally in latent form, but at other times echoing resurgently through the amorphous cycles of nostalgia that stretch out into decades.

For me, it was the era of The Sisters of Mercy, New Order, The Psychedelic Furs, and Depeche Mode. Listening to the old LPs sometimes occasions a near-electric jolt when stanzas that seemed obscure are suddenly infused with stunning up-to-the-moment relevance. Stuck inside of Memphis with the mobile home, sing…

Several days ago, I noticed a new Metaculus question with a curious, almost clickbait-worthy title, When will we meet grabby aliens?

The reference is to a recent paper by Hanson, Martin, McCarter and Paulson that has been getting traction in response to write-ups by Scott Aronson and others. Hanson et al.’s abstract rebrands as “grabby”, a subset of extraterrestrials that would appear to bear certain similarities to the antagonists in Starship Troopers.

The parameters of the GC model determine how fast and in what manner space-time fills up with grabby civilizations, and are specified by (1) the rate at which grabby civilizations emerge, (2) the rate at which they expand, and (3) the number of “hard steps” (bottlenecks) in the so-called Great Filter, whatever it is that prevents non-living matter from making the transition to living matter.

The Hanson et al. abstract strikes me as a more or less point-by-point rephrasing of Everything Counts by Depeche Mode. Aside from the line about Korea (maybe misheard along the lines of “Here we are now in containers”?) everything in the song is fully relevant.

The grabbing hands grab all they can
All for themselves, after all
It’s a competitive world

Given the model assumptions, grabby civilizations blister out within the universe in a manner determined by the values of the three parameters. The paper has an attractive figure that illustrates one particular outcome, with 193 randomly candy-coated GCs appearing over several Hubble Times across a 2D slice 41.7 billion light years on a side.

The paper’s take-away argument is that we’re living at some point in the clear space above the GC surfaces, and at some point in the future we’ll either become a GC or we’ll be steamrolled by one. Moreover, it’s argued that at the present moment, it’s likely that a “third to a half of the universe is within grabby-controlled volumes.” Hmm.

The Metaculus question asks for predictions of the probability distribution over the number of years before we or our descendants encounter a GC. At the moment, the median of the community PDF is a staggering 22.7 billion years, with a significant peak at 2 billion years. Clearly, the emerging consensus is that this question might take a while to resolve.

Herman Bondi, Tommy Gold and Fred Hoyle’s steady state theory of cosmology introduced the so-called perfect cosmological principle, which holds that the universe is homogeneous and isotropic in both space and time. Two papers outlining the their theory appeared in 1948, and maintained considerable influence until evidence that the Big Bang occurred became incontrovertible. A satisfying anecdote relates that the steady-state theory was inspired by the circular plot of the British post-war horror film, The Dead of Night.

If a horror movie can act as the aesthetic pivot for a debunked cosmological theory, it stands to reason that Depeche Mode may have pointed toward the resolution of the Fermi Paradox. The key lies in the fact that if it’s a competitive world, then

Everything counts in large amounts.

When one talks about aliens and grabby extraterrestrial civilizations, one is really talking about computation. And if grabby computation is irreversible and device-based, then planets are really nowhere. They just don’t matter. A wind of catalyzed nano-devices within the outflow from a single dust-spewing extreme asymptotic giant branch star can accomplish of order 10^62 bit operations, a factor of ten million times more than a “habitable” planet can muster over 5 billion years if totally covered with solar panels. Again, when it comes to the big picture, planets are completely irrelevant.

Here’s a link to our working paper, The Black Clouds, which discusses how extreme Asymptotic Giant Branch stars can be commandeered in the service of computation. We might just be immersed in a colored region, and the WISE sources in the Mollweide projection above might just be our unfriendly local GC.

Or, as the song says,

Confidence taken in
By a suntan and a grin.

A few years ago, I put up several posts describing Metaculus, the online prediction site that I co-founded with Anthony Aguirre and several other partners. In the interim, the site has grown substantially. It’s now logged roughly half a million predictions from a community of more than 10,000 users on a panoply of nearly 7,000 questions. Among the subset of binary questions that have resolved, the track record shows that Metaculus’ Brier Score stands at an impressive 0.117.

As the site has grown we’ve added staff, including a full-time CEO and a CTO, and a roster of analysts and question writers. We’re running real money competitions, including a $50K forecasting tournament on topics related to the development of artificial intelligence.

Many oklo.org readers may find interest in the Fermi-Drake question series, where we’re accumulating predictions on the terms of the famous equation for N.

Beyond N, there are many active questions that touch on astrophysical topics.

including the ultimate question:

currently registering a 71% probability of resolving positively.

Writer’s block. Procrastination. Envy of those for whom words flow smoothly! Luxurious blocks of text. Paragraphs, Essays, Books.The satisfying end results of productivity made real.

Or, as Dorothy Parker put it, “I hate writing, I love having written.”

Over the past few years, this dynamic has kept me both keenly and uneasily interested in natural language generation — the emerging ability of computers to produce coherent prose. In a post that went up just under four years ago, I reported on experiments that used Torch-rnn to write in the vein of Oscar Wilde and Joris-Karl Huysmans, the acknowledged masters of the decadent literary style. A splendidly recursive quote from the Picture of Dorian Gray has Wilde describing the essence of Huysmans’ A Rebours.

Based on a 793587-character training set composed of the two novels, 2017-era laptop-without-a-GPU level language modeling — which worked by predicting the next character in sequence, one after another — could channel the aesthetic of décadence for strings of several words in a row, and could generate phrases, grammar and syntax more or less correctly. But there was zero connection from one sentence to the next. The results were effectively gibberish. Disappointing.

In the interim, progress in machine writing has been accelerating. Funding for artificial intelligence research is ramping up. Last year, a significant threshold was achieved by GPT-3, a language model developed and announced by OpenAI. The model contains 175 billion parameters and was trained (at a cost of around $4.6M) on hundreds of billions of words of English-language text. It is startlingly capable.

A drawback to GPT-3 is that it’s publicly available only through awkward, restrictive interfaces, and it can’t be fine-tuned in its readily available incarnations. “A.I. Dungeons” anyone? But its precursor model, the 2019-vintage GPT-2, which contains a mere 1.5 billion parameters, is open source and python wrappers for it are readily available.

For many years, oklo.org was primarily devoted to extrasolar planets. Looking back through the archives, one can find various articles that I wrote about the new worlds as they arose. One can also look back at contemporary media reports of the then-latest planetary discoveries. Here’s a typical example from a decade ago, the beginning of an article written by Dennis Overbye for the New York Times.

In collaboration with Simone Williams, a Yale undergraduate student, we scraped the media archives from the past two decades to assemble a library of news articles describing the discovery of potentially habitable extrasolar planets. Once all the articles were collected, we developed a consistent labeling schema, an example of which is shown just below. The Courier-font text is a summary “prompt” containing the characteristics of the planet being written about, as well as a record of the article’s source, while the Times-font text is the actual article describing an actual detected planet (with the title consistently bolded in san serif). In this case, it’s another piece by Dennis Overbye from 2007 reporting Gliese 581 c:

A benefit of the GPT series is that they are pre-trained. Fine tuning on the corpus of articles takes less than an hour using Google cloud GPUs.

And the result?

Here’s an imaginary article describing the discovery of a completely manufactured planet (albeit with a real name) with completely manufactured properties.

It’s definitely not perfect, but it’s also not that bad…

East Rock rises abruptly from the flat New Haven city streets that surround it. Approaching from the south or the west, its diabase ramparts rear up forbiddingly.

While most of the East Coast’s ranges date to the continental collisions that assembled Pangea, the igneous intrusions and the sedimentary rocks of central Connecticut are roughly half as old and stem from Pangea’s demise. East Rock Park is a Jurassic Park, and two hundred million years ago, the rifts that eventually grew to become the Atlantic Ocean were opening just south of town. The rift valley floor was sinking, sediment was accumulating to fill the growing depression, and the sill of lava that eventually solidified into East Rock was squeezing out in a thick viscous sheet.

Several miles north of East Rock, an extensive road cut reveals layers of sediment from near the Jurassic-Triassic boundary. Beds of reddish sandstones and fused conglomerates of mud and pebbles are tilted at an angle of about 10 degrees, a remnant of the sinking and foundering that the rock layers suffered after they formed. The strata are varied and clearly visible, representing sediments that accumulated in a rift valley that alternated between a seasonal playa during dry periods and long-lived lake bed during wet periods.

Near the dawn of the Jurassic, New Haven was located in the tropics. During rain-soaked epochs, the shores of the rift lakes were a year-round riot of green with pterosaurs soaring in the skies. Perhaps there was nothing overt in those long-departed scenes to suggest that the end-Triassic extinction was either near or was already underway. And now, two hundred million years later, the layered record of ancient climate change stands mute and unvarying as the engines of loaded dump trucks roar and strain against the freeway grades.

A close look at the road cut shows a banding pattern that starts to repeat as one ascends from the lower exposed layers at the left of the photo to the upper exposed layers on the right. A look at the literature indicates that the rate of deposition in Central Connecticut 200 million years ago was about 1 millimeter of sediment per year, so the span recorded in the exposure is about 20,000 years. The repetition reflects one precession cycle of Earth’s spin, which dictates how the seasons align with the varying distance from the Sun stemming from the eccentricity of Earth’s orbit.

The sedimentary record in the New Haven area from the period of Pangea’s rifting is continuous over something like 20 million years, and the tilted layers of rocks fill Connecticut’s central valley to depths measured in miles. Cores drilled through this colossal lens of sediment reveal that Earth’s ancient orbital eccentricity variations are faithfully recorded in the strata.

In the course of an afternoon, with a laptop and the Rebound code, one can integrate the full Solar System back to the moment when the hardened lava that makes up present-day East Rock was glowing toothpaste-red and pushing its way into the then-newly lithified strata.

Looking back over the past five million years, Earth’s secular eccentricity variations are plainly apparent. In particular, the ~400 kyr envelope produced by the beating of the Venus-dominated g₂~7.2”/yr and Jupiter-dominated g₅~4.3”/yr secular frequencies is clearly visible.

This ~400 kyr (or more precisely, 405 kyr pattern) has been remarkably stable over Earth’s history. Running the clock back to the dawn of the Jurassic 200 million years ago, it shows no real change in character from the present. The plot just below runs for 10 million years forward from the formation of East Rock. A low-pass filter has been applied to the full eccentricity variation (shown by the light orange curve) to show the 400 kyr variation swinging up and down. Just as it does today.

In the late 1950s, orbital measurements of the Martian moon Phobos were interpreted to suggest that the satellite’s orbit was decaying faster than expected. This prompted the Russian astrophysicist Iosef Shklovsky to propose a “thin sheet metal” structure for Phobos, thereby explaining its anomalous acceleration and implying that it is of artificial origin.

The ensuing jolt of public interest in this hypothesis spurred an invigorating side-line for Shklovsky, who progressed from a drably monochrome list of equation-heavy papers — replete with sober titles such as On the Nature of the Fine Structure of Emission of Active Regions on the Sun — to glamorously teaming up with Carl Sagan to (among other things) advocate examination of “paleocontact” with extraterrestrials and for scrutiny of myths and religious lore for indications of influences from out there.

My guess is that it’s quite likely Shklovsky was well aware that promoting a field that later generated efforts such as Erich von Daniken’s Chariots of the Gods, and the History Channel’s Ancient Aliens was largely just for fun. There is, after all, no harm in broadening the public’s exposure to a wide variety of ideas. Right?

As described on his Wikipedia page, on the occasion of a visit to the Berkeley Astronomy Department, Shklovsky was memorably asked by a graduate student if UFO sightings are as common in the Soviet Union as in the United States.

“No,” he replied. “In this area the Americans are far more advanced than us.”

Last weekend, there was an engrossing article in the New York Times.

Titled, ‘A Frankenstein’ that Never Lived, the piece’s top-line summary runs, “On Jan. 4, 1981, the effects-heavy production opened and closed on the same night. Forty years later, the creators revisit a very expensive Broadway flop.”

According to the article, prior to the open, hopes for success of the big-budget enactment of Mary Shelley’s 1818 classic had run high, but the show’s prospects were dashed in large and immediate measure by Frank Rich’s dreadful review in the Times. Rich’s write-up brims with both arch sarcasm and gut-punch lines such as, “we feel nothing except the disappointment that comes from witnessing an evening of misspent energy.” Reading the article, I can feel a queasy, visceral sympathy for everyone who worked on that production.

At the end of the last century, Fred Adams and I were riding high on our forecasts for the denouement of the entire cosmos. Our trade book — The Five Ages of the Universe — had, to our great thrill, just been published by an imprint of Simon and Schuster, and we were enjoying the modest acclaim that had proceeded from dividing the entire past and the entire future of the Universe into five thumbnail-friendly eras of time.

The sales, the buzz, and the idle dreams of pop-culture stardom all came to a crashing halt from one day to the next when the New York Times ran its review of our book. I can recall the sinking feeling at the moment when our agent called Fred to let us know what had happened. “Brace yourself.” I think that was what she said.

Dick Teresi’s review was entitled, “The First Squillion Years”, and the title telegraphed the intent. It starts out bad, it gets progressively worse, and finally ends rather crushingly, with “Imagine an astronomer looking back at us ages hence. Perhaps he can read the bound galleys in my hand. Maybe he will be kinder than I have been here.” Yikes.

It’s amazing, however, how quickly one recalibrates. The book tour that had been in the cards was scaled way back to a handful of local appearances, with Borders Books in Ann Arbor standing in as the high point. Sales dried up. Just like that, I was back to trying to find bugs in Fortran codes. Over time, it became clear to me that it was almost certainly just as well.

Rather amusingly, the distant future is currently having something of a moment. There have been several new trade books on the topic, including at least one that got a review in the Times that was entirely different in tone that the one we drew. And then, a fantastic coda for the whole episode arrived unexpectedly a week or two ago as I was leafing through a recent issue of the New Yorker.

I’ve always enjoyed Roz Chast’s cartoons. She has a great sense of humor. It was oddly gratifying to see that she’d somehow been seized to lift out our eras and our thumbnails, elevating them to a full-page cartoon.

Time has a way of sliding by. More than five years ago, I wrote a blog post with a suggestion for a new cgs unit, the oklo, which describes the rate per unit mass of computation done by a given system:

1 oklo = 1 bit operation per gram per second

With limited time (and limited expertise) it can be tricky to size up the exact maximum performance in oklos of that new iPhone 12 that I’ve been eyeing. Benchmarking sites suggest that Apple’s A14 “Bionic” SoC runs at 824 32-bit Gflops, so (with Tim Cook in charge of the rounding) an iPhone runs at roughly a trillion oklos. Damn.

Computational energy efficiency also keeps improving. Proof-of-work based cryptocurrencies such as Bitcoin have laid the equivalency of power, money and bit operations into stark relief. The new Antminer S19 Pro computes SHA-256 hashes at an energy cost of about one erg per five million bit operations, a performance that’s only six million times worse than the Landauer limit. There is still tremendous opportunity for efficiency improvements, but the hard floor is starting to come into view.

For over a century, it’s been straightforward to write isn’t-it-amazing-what-they-can-do-these-days posts about the astonishing rate of technological progress.

Where a calculator like ENIAC today is equipped with 18,000 vacuum tubes and weighs 30 tons, computers in the future may have only 1000 vacuum tubes and perhaps weigh only 1½ tons.

And indeed, there’s a certain intellectual laziness associated with taking the present-day state-of-the-art and the projecting it forward into the future. Exponential growth in linear time has a way of making one’s misses seem unremarkable. “But I was only off by a few years!”

Fred Adams was visiting, and we were sitting around the kitchen table talking about the extremely distant future.

We started batting around the topic of computational growth. “Given the current rate of increase in of artificial irreversible computation, and given the steady increase in computational energy efficiency, how long will it be before the 10¹⁷ Watts that Earth gets from the Sun is all used in service of bit operations?”

As with many things exponential, the time scale is startlingly sooner than one might expect: about 90 years. In other words, the long-term trend of terrestrial economic growth will end within a lifetime. A computational energy crisis looms.

In any conversation along such lines, it’s a small step from Dyson Spheres to Kardashev Type N++. If you want to do a lot of device-based irreversible computation, what is the most effective strategy?

A remarkably attractive solution is to catalyze the outflow from a post-main-sequence star to produce a dynamically evolving wind-like structure that carries out computation. Extreme AGB (pre-planetary nebula phase) stars have lifetimes of order ten thousand years, generate thousands of solar luminosities, produce prodigious quantities of device-ready graphene, and have photospheres near room temperature.

We (Fred and I, along with Khaya Klanot and Darryl Seligman) wrote a working paper that goes into detail. In particular, the hydrodynamical solution that characterizes the structures is set forth. We’re posting it here for anyone interested in reading.

As we remark in the abstract, Possible evidence for past or extant structures may arise in presolar grains within primitive meteorites, or in the diffuse interstellar absorption bands, both of which could display anomalous entropy signatures.

For well over a year now, oklo.org has languished on Bluehost’s servers. No new posts. No maintenance whatsoever. The PHP installation was so dated that for months, visits to the site received nothing but a cryptic SQL fail. An hour with technical support was sufficient to bring the site back up, but the result was disheartening. The URL was landing hard, with an insecure SSL warning, a creaky WordPress theme that shouted “mid-aughts”, and an alarmingly wanton disrespect for the aspect ratios of the once-carefully embedded images.

New decade. New resolve.

The name on the site header now matches the site URL. Systemic referred to the long-lapsed Systemic Console project which Aaron Wolf and I started in 2004. Later, Stefano Meschiari took over the code base, and developed the software to pearlescent degrees of refinement. Yet the intangibles that generated the thrill in the Doppler velocities have all but faded, now that an essentially Earth-mass planet orbits at an essentially temperate distance from Proxima Centauri, and rumors circulate of a signal of order a GHz rather than a meter per second.

‘Oumuamua slipped our grasp.

With JPL’s mission design tool, one can scroll wistfully through a fine-grained list of opportunities lost — a spaceport departure board overflowing with missed flights, all to a single exotic destination.

By any measure, ‘Oumuamua imparted an influence that exceeded its size. Its approximately 260-meter greatest extent is dwarfed by the recently visited 2014 MU69.

Which itself is not very large.

It’s interesting to look at the Google Trends listing for worldwide interest in ‘Oumuamua.

In mid-November 2017, a two-lobed burst of interest surrounded first the naming and then the release of ESO’s iconic artist’s impression of a menacing starship-like shard. A barely perceptible blip followed last Summer’s announcement that ‘Oumuamua’s trajectory was non-Keplerian, and then, in Fall 2018, boom, a veritable megastructure of attention.

‘Oumuamua’s visit was short enough so that the data obtained (mostly in the five compressed weeks following its initial discovery) is readily summarized. Our first detected interstellar visitor arrived with almost exactly the speed and direction that one would guess a priori for an object having the average local orbit in the disk of the Milky Way. In a sense, the Solar System ran across ‘Oumuamua rather than the other way around.

The spectrum of sunlight reflecting off ‘Oumuamua’s surface is skewed smoothly to the red, with no identifying bumps or dips. The first spectrum, obtained by Joseph Masiero, who was observing at the Palomar 200-inch telescope when word of the interstellar object was released, was typical.

‘Oumuamua’s colors fall readily onto the locus defined by the various small-body constituents of the outer Solar System, which tend to list toward the reddish and the dark. Saturn’s moon Phoebe is the type of object one can bring to mind in this regard.

Solar System comets invariably spew out micron-sized particles, which are entrained in the gas (mostly water vapor) that erupts from their sun-warmed surfaces. It was thus generally expected that comets arriving from other solar systems would behave in similar fashion. Yet even in the deepest exposures — stacked together from multiple tracking images — ‘Oumuamua appeared completely point-like. Its lack of any observable coma placed stringent, spoonful-per-second limits on the amount of powdery dust emanating from its surface.

The diagram just below (with portions of the graphics taken from last October’s Sky and Telescope article) shows the highest-resolution portion ‘Oumuamua’s light curve stitched together from the data obtained with eight different telescopes. The reflected light signal varied periodically, with a dip-to-dip time scale of about 3.6 hours. There are lots of frequencies (and aliases) in the periodogram of the irregularly sampled data, the data gets proportionally noisier when the signal is at its dimmest, and the light curve does not quite repeat from pulse to pulse. The large peak-to-trough variation, and the more-or-less repetitive pattern suggest a highly elongated object, one that was tumbling chaotically end over end. The rotation period, moreover, was short enough so that ‘Oumumua would need to have some mild degree of physical strength to resist flying apart as it spins. It seems to be a solid object rather than a loosely consolidated rubble pile. The famous artist’s impression that populates a Google search on ‘Oumuamua proceeds from these basic features of the light curve.

Each image from each telescope contributed to the determination of ‘Oumuamua’s trajectory. A careful analysis of all the data leads to the remarkable conclusion that ‘Oumuamua departed the Solar System more quickly than an object starting on the same orbit and that was subject only to the Sun’s gravity. In other words, an additional, anomalous acceleration acted on ‘Oumuamua. The effect was small, apparently exactly akin to reducing the mass of the Sun by 0.1%, but its effect was nonetheless very evident in the trajectory.

Comets routinely display non-gravitational accelerations of the type and the general magnitude that was observed for ‘Omuamua. Jets of sublimating gas (mostly water vapor) stream off the surface, and perform like stochastic rocket engines. The close-range photographs of comet 67/P Churyumov-Gerasimenko (the dramatic subject of the Rosetta Mission) show the process in action.

The catch, however, is that if outgassing is responsible for ‘Oumuamua’s acceleration, there was exceedingly little fine dust entrained in the gas. This disconnect has led to two proposals in which the acceleration arose not from a gas jet, but from solar radiation pressure. The first proposal (by Shmuel Bialy and Avi Loeb) contained the much-discussed speculation that ‘Oumuamua is an engineered solar sail. A paper published several weeks ago (to less media attention) by Amaya Moro-Martin suggests that ‘Oumuamua is a naturally formed fractal, a dust bunny-like aggregate formed in a protostellar disk with an extremely low density and an extremely high porosity. Such a structure would be readily accelerated by radiation pressure, and like the sail model, would have no need to spew gas-entrained micron-sized dust.

One can argue that the lack of micron-sized dust in an outgassing scenario isn’t all that unexpected. An icy body from an alien environment may have undergone compositional processing that was absent in the Solar System. Moreover, if the entrained dust particles were larger, say 100 microns in size, they would have gone undetected.

The Spitzer Space Telescope’s non-detection of re-radiated heat constrains ‘Oumuamua’s reflectivity and its physical size. Spitzer’s wavebands of observation rendered it particularly sensitive to emission from carbon dioxide and carbon monoxide gas in ‘Oumuamua’s vicinity, but neither species of molecule was detected. This is odd. Jets from Solar System comets are primarily composed of water vapor, but typically also contain carbon-based constituents. A water vapor jet from ‘Oumuamua is not directly ruled out by Spitzer, but one needs to argue that the water, in addition to being free of small dust, had a very low level of carbonation. A glass of melted ‘Oumuamua would have to be still, not sparkling.The jet interpretation for ‘Oumuamua’s acceleration can thus wriggle out of the Spitzer non-detection by positing a composition of icy material with a very low carbon-to-oxygen ratio, and it can simultaneously wriggle out of the coma non-detection by positing that very little micron-sized dust was embedded in the ice, but that’s an admittedly uncomfortable amount of wriggling. Requiring a pair of caveats is not very satisfactory, but it allows us the hypothesis that we were visited by a relatively mundane object rather than an exotic natural object or an artificial object. Moreover, with dim prospects for the emergence of additional observational data from a long-departed object that was faint to begin with, it’s unlikely that any of the three classes of competing explanations for ‘Oumuamua’s behavior will ever gain full credence or confirmation.

Interestingly, we do have some direct information on the composition of extrasolar planetesimals. This is obtained obtained by looking at accretion events onto white dwarfs, e.g. this paper by Wilson et al. Among the measurements of this type that have been made, there are a number of cases where the C/O ratios are below the naive limit for ‘Oumuamua (plotted below on Figure 3 of Wilson et al.)

A paper published by Roman Rafikov last August raised an additional potential problem with the jet model for ‘Oumuamua’s anomalous acceleration. If a jet acts continuously (or on average, acts continuously) to exert the acceleration at a single point on the surface, then the force that provides the acceleration will also exert a torque, unless it is pushing exactly along one of the principal axes of inertia. This torque would have caused ‘Oumuamua to noticeably increase its rotation rate during the days that it was under close observation.

In a new paper lead-authored by Darryl Seligman and just posted to arXiv, we revisit the jet model, and imagine that the jet is created by ice that lies just below or right at the surface of ‘Oumuamua. If this is the true situation, then ‘Oumuamua’s jet will migrate rapidly across the body, and at any given moment, it will be strongest at the spot where the Sun’s rays are directly perpendicular to the surface. If we model ‘Oumuamua as an ellipsoid, the situation looks like the illustration just below, with comet 67/P Churyumov-Gerasimenko and its sub-solar jet shown to help motivate what we’re proposing:

In an idealized situation in which ‘Oumuamua is a perfect triaxial ellipsoid with a long, an intermediate and a short axis, and where two of the axes lie exactly in ‘Oumuamua’s orbital plane, and where the jet is always located at the spot where the Sun is directly overhead, ‘Oumuamua’s motion resembles that of a pendulum. Here’s a movie made with the open-source ray tracing software POV-ray which implements the appropriate rigid-body dynamics:

In the example shown above, we’ve assigned our idealized ‘Oumuamua a surfboard-like 9:4:1 long-intermediate-short axis ratio, and we’ve positioned the short axis so that it points perpendicular to the orbital plane. The action of the sublimation jet in this model produces a pendulum-like rotation of the body and implies a long semi-axis, \(a\sim 5A_{\rm ng}P^2/4\pi^2 \sim 260\,{\rm m}\), where \(A_{\rm ng}=2.5\times10^{-4}\,{\rm cm\,s^{-2}}\) was the observed non-gravitational acceleration during the high-cadence October observations, and \(P\sim8\,{\rm h}\) was the observed peak-to-trough-to-peak-to-trough-to-peak period of a full \(-\pi \rightarrow \pi \rightarrow -\pi\) oscillation.

Interestingly, the size \(a\sim260\,{\rm m}\) implied by 8 hour period and the \(0.001 g_{\odot}\) acceleration agrees perfectly with the completely independent estimates of `Oumuamua’s size that stemmed from its measured brightness, if we assume the 10% reflectivity that is appropriate to ices that have undergone long-duration exposure to the interstellar cosmic ray flux. The implication is that ‘Oumuamua was either like a pendulum that was rocking back and forth, or perhaps one that was barely swinging “over the top”. A more complete analysis allows us to make a snapshot of the range of possible motions for the idealized case. The angular position of the idealized ‘Oumuamua during its swing is on the x-axis, the varying angular speed of the swing is on the y-axis, and the color coding shows the period for each allowed trajectory. A nice feature of the motion is that as long as the aspect ratio, a:b:c has a\(\gg\)b, the period depends only very weakly on b and c.

With our sub-stellar jet model, ‘Oumuamua doesn’t change its light curve period appreciably during the period that it was observed. This is because the torque from the sub-stellar jet spends equal time working with the instantaneous spin and working against it.

Assuming that ‘Oumuamua was a natural object, it likely had an uneven surface, possibly with regions of varying reflectivity, and it most certainly was not spinning with a principle moment of inertia aligned along its angular momentum vector. Moreover, there was likely a time-varying lag in the response of the jet, and the strength of the jet likely varied stochastically. With our ray-tracing model, we can readily gin up such complications and watch how they affect the motion. Here’s a version of the dynamics where ‘Oumuamua starts in a random orientation, and has a rough mottled surface pattern:

In the simulation shown just above, we’re tracking ‘Oumuamua, and watching it tumble as it flies through its escaping orbit. The point of view is from an ultra-resolving telescope orbiting along with Earth. This means that the Sun’s illumination of the ‘Oumuamua model is consistent with what an observer on Earth would have seen had they had sufficient magnification. Removing the axes and the jet, we can sum up the brightness of all the pixels in each image to get a frame-by-frame light curve. Sampling the light curve at the actual cadence of the observations, and adding the correct amount of noise permits direct comparisons between various versions of the model and the observations. The first figure below shows the real data, and then various versions of what one would get with our ellipsoid models. No attempt at curve-fitting has been made here, just a proof of concept. The second figure below shows the power spectra of the data, our models, and the zeroed-out observations. It’s clear that if one wanted to, it would be quite possible to fit the light curve pretty well with models of this general type.

There’s a strong possibility that more interstellar objects will be detected fairly soon. A necessarily shaky extrapolation from the “statistics” of one object detected over several years by the Pan-STARRS survey implies that interstellar space is teeming with ‘Oumuamuas. The numbers are impressive — of order \(10^{26}\) bodies total in the Milky Way, totaling a hundred billion Earth masses. At any given moment, roughly one such object should be in the process of threading the 1AU sphere that encompasses Earth’s orbit around the Sun.

Saturn’s polar axis is tilted relative to the plane in which Saturn orbits the Sun, and the plane of Saturn’s orbit is itself tilted with respect to the averaged orbital plane of the Solar System’s planets.

Pieces of popular scientific writing often start with an engaging “hook”, but the foregoing statement doesn’t do a particularly good job. Saturn and its rings do, however, do a good job of showing off their tilts — their obliquities, to use the vernacular. Saturn gradually shifts in appearance as the Sun’s illumination angle changes, and over time the creeping ring shadows even affect Saturn’s climate. Certainly, at the moment when the rings slice edge-on to the solar rays, the system presents a very different appearance than when the ring plane is inclined.

The geometry was first understood by Christiaan Huygens. By the mid-1600s, he had drawn a clear diagram showing how Saturn’s tilted pole points in a fixed direction as the planet traces its three-decade orbit.

The obliquities of Saturn and Neptune (26.7\(^{\circ}\) and 29.6\(^{\circ}\) respectively) seem odd. Uranus, tipped to its side and then some (97.9\(^{\circ}\)) is odder still. Naively, one might have expected a Solar System forming from a flat, orbiting disk of gas and dust to have ended with the equators of the giant planets lying in the average plane of the planetary orbits. Jupiter, with its axis tilted at only 3.1\(^{\circ}\) is indeed fairly conforming, but the others are all badly out of alignment. Why?

Moreover, with literally thousands of worlds now in the catalog, one also wonders if spin misalignments are rampant among the extrasolar planets. Could it be possible to infer obliquities even if we have no method to photographically resolve the planets themselves?

Left to orbit freely around a star, the tilted spin pole of an isolated planet will precess like a gyroscope. The cycling of precession is slow in comparison to the rate of the spin itself, and it stems from the torque exerted on the planet by the parent star. If the planet — like Saturn — has satellites, they orbit quickly enough to act as if they were a contributing part of the planet, and the joint set-up of planet plus moons precesses as a unit. The moons and rings stay locked to the orbital plane, and the net effect of the satellites, as far as precession is concerned, is to speed up the rate at which the cycle occurs.

Wheels within wheels… The situation grows more complicated if the orbital plane of a precessing planet also precesses. An orbit whose own pole (or orbit normal) traces a slow overhead circle presents, in effect, its planet with a moving target. With the complication induced by the precessing orbit, how does the spin axis respond?

Some intuition can be obtained by experimenting with tops. Orbital precession can be mimicked by placing a spinning top on a plate and evenly rotating the tilt of the plate, much as if panning for gold.

After some practice, one finds that the plate-top system can be transiently “locked” into a state where the spin axis precesses in the opposite direction — but at the same rate — as the plate. When this happens it’s oddly satisfying, imparting a tactile clue that resonance between the precession of an orbit and the precession of a planet’s spin might be capable of playing a dynamical role.

Another clue is supplied by the motion of Earth’s Moon. In 1693, Giovanni Domenico Cassini, who logged careful observations from the Paris Observatory, concluded that the plane of the Moon’s orbit, in the course of executing a 18.6 year precession cycle about Earth’s equator, maintains a constant angle with respect to the ecliptic (Earth’s orbital plane). He also found that the small obliquity of the moon, which is only 1.5\(^{\circ}\) (compared to 23.5\(^{\circ}\) for Earth) precesses at the same rate of one full revolution per 18.6 years.

Giovanni Domenico Cassini (1625-1712). Prior to holding the directorship of the Paris Observatory, he was the highest paid astronomer at the University of Bologna, having been appointed to his professorship by the Pope.

In other words, an arrow pointing out of the Moon’s pole always lies in the plane formed by Earth’s orbit normal and the Moon’s orbit normal. This remarkable co-precession of the Moon’s spin axis and its orbit normal received little attention until a landmark 1966 paper in the Astronomical Journal by Giussepe Colombo — who separately, achieved fame for discovering that Mercury exists in 3:2 spin-orbit resonance, turning three times on its axis for every two trips around the Sun. A few years after Colombo’s paper appeared, Stan Peale coined the term Cassini State to describe the dynamical configuration.

That something so fundamental to the motion of the Earth-Moon system was left apparently unexplained from its discovery in 1693 through 1966 seemed puzzling, so I sent a text to Konstantin Batygin.

Indeed they do:

Issues of obscurity, precedence and priority aside, Colombo used Newton’s laws of motion and gravity to demonstrate that the in-sync cycling of the Moon’s spin and orbital axes represents a minimum-energy configuration. In a frame of reference synchronized to its orbital precession, the Moon’s spin pole is analogous to a marble that frictional dissipation has brought to rest at the bottom of a curved bowl. The Moon is said to be locked in a secular spin-orbit resonance.

If a perturbation — a kick — imparts energy to the marble, it will roll around in the bowl. Likewise, if the spin pole of a body in secular spin-orbit resonance is perturbed, the direction that the pole points will wander when viewed in the precessing frame. In his 1966 paper, Colombo worked out how the trajectories traced by a perturbed spin pole will behave.

Colombo also pointed out that a simple geometric construction can be used to illustrate how the spin pole moves. First, imagine the sphere defining all the possible directions that a spin pole can point. The sphere is oriented so that its own coordinate poles are perpendicular to the overall plane of the system under consideration. In the minimum energy configuration, the spin direction, the coordinate pole, and the direction of the orbit normal all lie in a single plane that slices the sphere in half.

If the planet’s spin axis is not damped to the minimum energy configuration, it will slowly trace a path on the sphere when followed in the co-precessing frame. A detailed analysis (which appears in Colombo’s 1966 paper, and which Stan Peale augmented and corrected in 1969) shows that the set of allowed paths (level curves of the Hamiltonian) are determined by the set of possible intersections between a parabolic cylinder and the sphere. Individual paths, corresponding to individual energies of perturbation, are defined by moving the parabolic cylinder back and forth.

Remarkably, the projection of these intersection paths onto the ecliptic displays a characteristic structure that arises repeatedly in problems involving resonance. The state of co-precession keeps the spin pole of the planet fixed in the perfectly damped configuration, in which the vertex of the parabola just touches the sphere. This vertex point lies at the center of a set of banana-shaped trajectories. Then, when the spin pole of the planet is perturbed, the motion follows a trajectory where the spin pole travels along one of the banana-shaped curves. Inside the shaded region, a full traversal of the curve never entails a full 360\(^{\circ}\) accumulation of angle, and the pole is said to be librating in the resonance.

The Solar System provides several examples of secular spin-orbit resonance. Most prominent from our Earth-bound viewpoint, is the motion of the Moon. The action of tides has damped the motion of its spin pole so that it lies at the core of its sequence of banana-shaped level curves.In a pair of articles [1, 2] published in 2004, Bill Ward and Douglas Hamilton raised the remarkable possibility that Saturn’s spin pole might be librating in a frame that co-precesses with the orbital inclination of the planet Neptune. On the surface, a Saturn-Neptune secular spin-orbit resonance seems nearly unbelievable. I recall hearing Bill Ward describe the work at a conference, a year or so before the papers came out. At that time, I have to admit, I didn’t really understand the details of the talk, other than the the take-away that Neptune was somehow responsible for tipping Saturn over. Although Jupiter and Uranus exhibit substantially larger gravitational perturbations on Saturn than does Neptune, the frequency at which Neptune’s line of nodes regresses happens to almost exactly match the precession rate of Saturn’s pole. Neptune’s orbit, in a sense, shifts at a rate that cuts through the noise to provide a controlling influence that adds up for Saturn.

Once the precession rates of an orbit and a spin pole are locked together, the lock will be maintained even when the orbit’s precession rate slowly changes. As a consequence, if the rate at which the orbit precesses slows down, the planet’s spin pole will slowly tip over so that its precession rate can decline in sync. When that happens on a habitable planet, it’s time to set solar sail for the stars. Closer to home, the long-ago dispersal of planetesimals in the Kuiper Belt led to a slowing of Neptune’s orbital precession. Remarkably, this seemingly minor slowdown seems to have forced Saturn from a small initial obliquity to its current 26.7\(^\circ\).

In addition to affecting Earth’s Moon and Saturn, secular spin-orbit resonance also plays a likely role in the tilts of both Jupiter and Mars (and quite possibly Uranus). It’s fully separate from the phenomenon of spin-orbit resonance, which, for example, maintains Mercury’s spin period at an average rate that is exactly 3/2 times its orbital period.

In the Solar System, the planetary obliquities are readily measured, and have been accurately known for centuries. Orbital precession rates can be calculated either from the well-established techniques of celestial mechanics, or from direct numerical N-body integrations. Even so, secular spin-orbit resonance didn’t garner attention until Colombo’s and Peale’s papers in the 1960s, and even then, it received only limited press. In Murray and Dermott’s Solar System Dynamics, which has become a standard text, the authors state at the outset that Cassini states are not covered in their book. The possible enforced match between Saturn’s polar tilt and Neptune’s orbit went unnoticed until 2004. It thus seems like a long-shot that secular spin-orbit resonances among extrasolar planets have much chance of being a “thing”.

For a planet like Saturn, the slight decrease in the Sun’s gravity from the sub-solar point to the anti-solar point on Saturn’s surface leads to a small tidal deformation of the planet. Friction within Saturn causes Saturn’s rotation to pull this tidal deformation slightly out of alignment, with the net result being a slow decrease in Saturn’s spin rate. The rate of decrease, however, is negligible. It would take many times the current age of the Solar System for Saturn’s spin period to be tangibly modified by this effect.

Tidal forces, however, have an extraordinarily steep fall-off with distance. If Saturn were moved a hundred times closer to the Sun, to a distance where the extrasolar planets are routinely found, the Sun’s tidal influence on Saturn’s spin would be ten billion times stronger.

In the presence of strong tidal forces, the spin period of a planet on a circular or near-circular orbit is brought into sync with the planet’s orbital period. That’s the situation that the Moon finds itself in, and it is also thought to be the case for most of the shorter-period transiting planets that have been discovered by the various ground-based surveys as well as by the Kepler Mission.

In addition to synchronizing the spin, tidal forces also act to align a spin pole with the orbit normal. If, however, a planet is in secular spin orbit resonance of the type we’ve been discussing, the resonant torques can potentially balance the dissipative torques and prevent the planet from being righted.

Tidal dissipation is normally quite self-regulating. If the dissipation caused by tides is strong, then synchronization ensues, and the energy that the dissipation generates drops. If, however, a mechanism exists to thwart synchronization then significant evolution can occur. Io (and to a lesser extent Europa) provide examples. As a consequence of having its eccentricity forced by the resonant interaction between the three inner Galilean satellites, Io undergoes strong tidal dissipation, leading to the famous volcanoes that cover its surface, and to the heavy loss over time of its volatile constituents.

The famous Peale, Cassen and Reynolds article that describes Io’s dissipation belongs near the very top of a list of admired papers. It presents clean dynamical arguments that draw on disparate aspects of geophysics and celestial mechanics to make a non-trivial prediction. And indeed, the paper’s two-sentence abstract is the very model of brevity:

The dissipation of tidal energy in Jupiter’s satellite Io is likely to have melted a major fraction of the mass. Consequences of a largely molten interior may be evident in pictures of Io’s surface returned by Voyager I.

Just days after the March 2, 1979 publication of the paper, Voyager 1 flew through the Jovian system, and recorded Io’s hyperactive volcanism. Here’s a recent photo of Io from NASA’s Juno probe. The picture was taken in the infrared, where it’s pretty clear what’s going on.

In short, the Peale et al. 1979 paper is a tremendous inspiration. For years, I’ve been thinking, could something similar be done with the extrasolar planets?

The Kepler data is certainly the best place to look for opportunity. The precise timing of the planets in Kepler’s multi-planet systems gives the possibility for finding subtle effects that go beyond simple Keplerian orbital motion.

It’s well known that Kepler detected lots of multiple-planet multiple-transiting systems. The planets in these systems tend to lie in the super-Earth/sub-Neptune radius range, and typically have masses of order 5 to 10 times the mass of Earth. A zeroth-order question is what these planets are like and how they got to where they are currently observed.

There is an interesting unexplained clue in the data. One can take pairs of adjacent planets from the Kepler catalog, and plot the period ratios. What one sees is that in the vicinity of low-order orbital commensurabilities, there is a statistically structure in the distribution:

There is an overabundance, or a “pile up” of planets with orbital period ratios that are a few percent larger than the perfect 3:2 and 2:1 orbital commensurabilities, and a relative lack of planet pairs that have orbital period ratios just less than the commensurabilities. It’s as if some mechanism is acting to pry the pairs apart. Moreover, if one looks at the individual sizes of the planets in the distribution, one sees that on average, the radii of the planets that lie just wide of the commensurability are larger than the radii of the planets that have slightly smaller period ratios.

Several theorists have written papers that show this structure, termed “resonant repulsion” can be understood if the participating planets are experiencing a very high rate of tidal dissipation. The difficulty, however, has been that if the standard rate of interior energy dissipation is used, then the rate of dissipation would have to be very high. The planets would have to be extremely inelastic. Earth for example, does fall into this inelastic category because the ocean tides efficiently dissipate energy along shorelines. Most bodies in the Solar System, however, and especially the massive planets – Uranus, Neptune, Saturn and Jupiter – are far less dissipative. In the case of the Solar System’s giant planets, this difference with Earth is of order a factor of a thousand or more.

In a new paper appearing in Nature Astronomy and lead-authored by Yale graduate student Sarah Millholland, we propose a solution. If one or both planets in a pair that has a period ratio lying just outside the low-order commensurability is in secular spin-orbit resonance, and if the spin obliquity is high, then the dissipation within the planet will be large, and indeed large enough to account for the observed effect.

In many respects, the regular satellites of the jovian planets in our solar system resemble the multiple-transiting multiple planet population that was found by the Kepler Mission. Orbital inclinations and eccentricities are small in both types of systems. The orbital periods typically range from days to weeks in both cases, and the mass ratios of satellites to primaries typically tend toward one part in ten thousand. It is thus reasonable to ask why the phenomenon of resonant repulsion die to secular spin-orbit resonance is not found among the jovian satellites, all of which have tiny tilts for their spin poles.

The answer lies in the spin rates of the giant planets, all of which spin relatively rapidly, causing them to bulge significantly at their equators. Jupiter does a full turn in only 9 hours 55 minutes and is noticeably squashed when viewed through a telescope. The quadrupole moment is the jargon for the quantified degree of spin-induced structural flattening. The giant planets’ large quadrupole moments force rapid orbital precession of their satellites. The frequency is substantially higher than the spin precession rates of the satellites can keep up with. As a consequence, all of the major regular satellites of the Jovian planets have their spin axes aligned with their orbit normals.

The parent stars of the Kepler multi-transiting, multiple-planet systems spin much more slowly than Jupiter or the Solar System’s other giant planets. The stars have lost the majority of their spin angular momentum through the process of magnetic braking. The quadrupole moments of the G, K, and M stars hosting Kepler-multiple planet systems are quite small. Our own Sun spins on its axis with a 27-day period, which is fairly typical, and red dwarfs tend to spin even more slowly. As a consequence, the precession periods of the Kepler planet’s orbits are driven primarily by planet-planet interactions and not by the stellar equatorial bulges.

In the plot just below, the natural spin precession frequencies, \(\alpha\)‘s, and the orbital precession frequencies, \(\vert g \vert\)‘s, for the planets in Kepler’s multiple-transiting systems are tallied into histograms. The rate, \(\alpha\) of a planet’s spin precession depends on its internal structure, so that a planet that is highly centrally concentrated (a low \(k_2\)) precesses more slowly than one whose mass is more extended (a high \(k_2\)). The histograms for the spin and orbit rates (\(\alpha\)‘s and \(\vert g \vert\)‘s) show substantial overlap, and both reach peaks near a period of about 3,000 years.

In short, it is a suggestive coincidence that the orbital periods, the masses, the radii and the separations of the Kepler planets combine to generate similar rates of orbital precession and spin precession. This means that capture into spin orbit resonances may be quite likely for these planets.

Capture of a planet into secular spin-orbit resonance will naturally occur if the ratio of the planet’s orbital precession frequency to its spin precession frequency is slowly brought down to unity from above, that is, if \(\vert g \vert/\alpha \rightarrow 1\). This can happen if the planets in a system migrate toward orbital commensurability. This schematic diagram from our paper shows how the process works:

Simulations that track the orbits and the spins of the planets show that the spin precession and orbit precession lock into sync remarkably easily and naturally. Our paper charts several example evolutionary trajectories that look like this one:

In this particular simulation, two 5 \(M_{\oplus}\) super-Earths experience mild disk-driven migration which slowly pushes their orbits together, and, after \(\sim\)1.3 million years, binds them into a 3:2 orbital mean-motion resonance. As this mean-motion resonance capture occurs, the inner planet of the pair finds that its orbital precession rate has slowed to match its spin precession rate; it is caught in secular spin-orbit resonance. Thereafter, as the orbital precession slows still further (as a consequence of the protostellar disk dissipating), the inner planet’s axis is compelled to precess more slowly as well. In order for the planet to slow its spin precession, it is forced over on its side, to a final obliquity of more than 50\(\circ\).

The simulation charted above runs for just a few million years, but the planetary systems that Kepler observed are generally a thousand times older. The outer planet in the simulation, whose obliquity is traced with the green line in the upper panel, sees its tilt kicked up when the ratio \(\vert g \vert/\alpha\) passed through unity from below but does not end up in spin-orbit resonance. Its perturbed obliquity will drop back to zero after a few tens of milions of years. For the inner planet, however, the situation is different. Torque from the tidal dissipation in the planet balances torque from the precessing orbit, the obliquity remains constant, and an Io-like situation is produced. Obliquity-juiced tides generate ~3 million Gigawatts within the planet, roughly a thousand times the total power that Io produces, and roughly three times more energy per unit mass. The relentless dissipation draws energy from the orbit, forcing the period ratio, over time, to creep up from the initial 3:2 ratio.

The net result of this process, replicated again and again in the Kepler sample, can explain the lack of worlds near the exact m:n integer period ratios and simultaneously account for the pile-ups seen just wide of the perfect commensurabilities.

A nice feature of the theory is that it makes some predictions.

,Capture into secular spin-orbit resonance is easier if a planet has a larger radius. As a consequence, if dissipating oblique planets are what drive the Kepler pairs apart, then the planets on the right side of the period ratio gaps should be (on average) larger than those to the left sides of the gap. Pleasingly, this is exactly what is seen in the data, and it’s a feature that has gone unnoticed until now:

Moreover, larger planets are more dissipative, and so statistically, the radii of planets in the member pairs should increase as the period ratios increase. This effect, while subtler, is also present in the data.

Given the actual structure of the period ratio diagram, one can work out the amount of dissipation required to explain each pair if the ages of the systems are known. Statistically, this allows us to determine what kind of planets we’re dealing with. The details are explained in our paper, but the take away is that the planets in the Kepler-multiple systems likely tend to resemble Uranus and Neptune as far as their internal structures are concerned.

And finally, one last, as-yet untested prediction. If a planet with an orbital period in the range spanned by the Kepler-multiple planet systems has significant satellites, its precession rate will be too rapid for secular spin-orbit resonance to work. As a consequence, oblique planets driving resonant repulsion won’t have significant moons of the type seen orbiting the giant planets in the Solar System.

Latest Deep Space Climate Observatory Image

Over the past several semesters at Yale, I’ve been working out a new take on the standard “Astronomy 101” class for non-science majors. Broadly, the goal is to stage a wide-angle view of the Anthropocene, thereby forging an understanding of how Earth fits into its broader cosmic context. Economics, Political Science, and History constituted the largest groups of majors in the class.

I’m working on getting the class notes, problem sets and readings into a form that’s distributable. In the interim, I’ll cut right to the chase with the final exam. Per Yale’s official instructions:

Final examinations normally last either two or three hours but, in either case, students are permitted to take an additional half hour before being required to turn in their answers. This additional time is given for improving what has already been written, rather than for breaking new ground.

Link to .pdf version of the AY 105 Final Exam

This one was set as the three-hour variety. (Didn’t seem like any utility would be gained by imposing time pressure.)

‘Oumuamua breezed in unexpectedly and it left in a rush. Faded now, to twentynine, soaring up and out over Jupiter’s orbit. No sum, it seems, sufficient to compel it to pick up the phone, to give us a call.

Maybe it was a one time fluke — a color out of space, but it’s also possible that it was unexceptional, a mundane representative from a vast distribution. If so, what can we do to be ready for the next one?

Darryl Seligman has a new paper up on arXiv that outlines a plan. Had ‘Oumuamua been spotted on its way in, and if a probe had been loitering in anticipation, fueled and ready to go at L1, it would have been an easy thing (energetically at least) to rocket over and intercept it, Deep Impact style, in a blaze of glory.

With LSST set to start monitoring the skies, there should be an opportunity every decade or so to “get interstellar” by barely leaving home.

‘Oumuamua’s encounter with the inner solar system is dying down on Twitter, yet still it bristles with consequence and the uneasiness of unanswered questions. Why no coma?

Occam’s razor is a dull instrument that points almost unerringly to the mundane (as opposed to pointing to interstellar probes). One thus draws several conclusions. (1) ‘Oumuamua’s aspect ratio is substantially less than 10:1. (2) Billions of years in the interstellar environment lead to the buildup of a tarry crust that resists temporary heating, and this process is enhanced for comet-like planetesimals that form in systems with supersolar C/O ratios. (3) Most stars have true-Neptune analogs.

The resulting prediction is that slightly tweaked ongoing surveys, and soon LSST, should start turning up interstellar asteroids and perhaps interstellar comets with some frequency. If another one is found in the near-term, it would be interesting to look at the optimal mission designs that could accomplish an opportunistic sample-return.

From ‘Oumuamua’s perspective, the close encounter with the Sun was a near-indescribable stroke of luck. To scale, the stars of the galactic disk are like grains of sand separated by miles and crawling through space at a few feet per year. The Galaxy is the archetypal collisionless fluid. Vaulting from ‘Oumuamua’s current encounter to its next connects the all too human interval of waking-up-at-3AM anxieties — the scale of days and months — to the frigid waste of a quadrillion years.

Why cold? When fusion has ended, dark matter annihilation and proton decay take over, and both (while uncertain) are certainly slow processes. Grand Unified Theories predict that proton decay should occur, but so far, there is no experimental evidence. The lower bounds on the proton half-life are ~10^34 years via the sluggishly competing processes of positron and muon decay.

If the proton were completely stable, the end states of stars present a curious state of affairs. Black holes of stellar mass, which are much more tightly bound than degenerate stars, will evaporate through the Hawking effect with a lifetime of “only” 10^66 years Although this time scale is aggressively long compared to the current 13.8-billion year age of the universe, it would be odd if black holes are ephemeral while white dwarfs and neutron stars are forever.

While jarring, this possible divergence of lifetimes is not exactly a matter of pressing concern. Two decades, ago, however, Fred Adams and I had priorities that were definitely skewed toward the really long term. Along with Manasse Mbonye and Malcom Perry, we looked into how quantum tunneling into black holes can erode white dwarfs. In Freeman Dyson’s 1979 article, Time Without End, it is pointed out that an otherwise stable white dwarf will spontaneously tunnel into a black hole on a time scale of order 10^10^76 (!) years. In our article, we argued that the whole star need not make the plunge at once, and that a 10^45 year half-life is a plausible value for black-hole induced proton decay. This has the added benefit of enabling a Hertzsprung-Russell diagram that traces stellar evolution to its absolute bitter end.

‘Oumuamua. Up close and alongside, in the vastness of interstellar space, its hurtling bulk imparts no sense of motion as it turns imperceptibly on its axis, blotting out the stars.

For a hundred years, the point-like Sun grew steadily brighter against its frigid airless horizons. First came light, then warmth, and finally searing illumination of the tarry reddish expanse, blistering sluggishly beneath a September Noon far more intense than any summer of Earth.

`Oumuamua is departing the solar system as rapidly as it arrived, heading outward at a current rate of 2.5 million miles a day. Our tiny chance of sending a probe to catch it diminishes with each lagging tick of inactivity. Nonetheless, world-wide interest is mounting, in part as a consequence of two new articles reporting detailed observations. The first, by Jewitt et al. was posted to arXiv last week, while the second, by Meech et al. (which independently comes largely to the same overall conclusions), appeared in Nature earlier this week. Nature being Nature, the Meech et al. article was accompanied by a media push, spearheaded by an extraordinary piece of space art.

Maybe it’s press release fatigue from one “habitable” world after another — a monotony of warm suns glinting off imaginary oceans — that makes this image so arresting.

The observational facts remain stark and limited. `Oumuamua’s double-peaked light curve suggests that it has a large aspect ratio, perhaps as high as 10:1. Assuming that it’s a poor reflector, it’s several hundred meters on its long axis. Its overall color is reddish. It has to have physical strength, or its 7-hour rotation period would be enough to overcome its negligible self-gravity and tear it apart. Most alarmingly, it shows no sign of a coma. At most, less than a sugar cube’s worth of cometary dust per second was emanating from it as it tore through the inner solar system. (As a matter of fact, ‘Oumuamua as observed is entirely consistent with Tintin’s rocket.)

For more on ‘Oumuamua, I have a blog post up at Scientific American.

This was no fruit of such worlds and suns as shine on the telescopes and photographic plates of our observatories. This was no breath from the skies whose motions and dimensions our astronomers measure or deem to vast to measure. It was just a colour out of space — a frightful messenger from unformed realms of infinity…

Aww, come off it.

Wild-eyed extravagances aside, A/2017 U1 — the asteroid-like visitor from interstellar space — is an extraordinary object. In traversing the gulfs, its next encounter with a star that is as close as last month’s encounter with the Sun likely won’t occur for another quadrillion years, and so the mere fact that it zipped through suggests that quite a few interstellar asteroids are out there. And this, in turn, has some remarkable consequences. A straightforward cross-section based estimate suggests that the galaxy contains of order a hundred billion earth masses of A/2017 U1-like planetesimals. Hot Jupiters, terrestrial planets, and super-Earths are all incapable of using gravity-assist to eject bodies out of their parent systems, leaving the strong hint that as-yet undetected Neptune-like planets must be extremely common.

In general, extrapolations from a sample size of one don’t have a good track record. Exhibit A would be our own Solar System — hot Jupiters were discovered at better than 100-sigma significance because solar-system expectations had been projected throughout the galaxy; proper planetary systems should have terrestrial bodies near 1 AU and gas giants at 10 AU.

The arrival of A/2017 U1 seems nicely timed to revival of the AAS’ new low-maintenance communication channel, the “Research Note“:

The purpose of the Research Notes is to provide a home for short submissions that are not suitable for publication as a journal article, but are likely to be interesting or useful to members of our community. Appropriate submissions would include brief summaries of work in progress, comments and clarifications, null results, and timely reports of observations (such as the spectrum of a supernova), as well as results that would not traditionally merit a full paper (e.g., the discovery of a single unremarkable exoplanet, a spectrum of a meteor, or contributions to the monitoring of variable sources).

I especially like the part about “single unremarkable exoplanets” being equivalenced to the “spectrum of a meteor”. In any event, Prof. K. Batygin and I have just submitted a research note that gives our take on the implications of A/2017 U1. Here’s a link to a draft of the note, which we’ll also post on the arXiv within the next several days.

In the antique language of the space age, one might call it an interstellar “probe”, or perhaps a von Neumann machine. That’s not really what it is. It’s better described as a snarky, fusion-powered tangle of competing social networks, some of them still executing the hallowed fossil liturgies and intrigues of the mighty corporations from which they long since sprang.

It had no particular expectations for the fast-approaching star that was next on its ancient route. On the last flyby of this particular star, twenty-seven million years ago, the probe observed that the third planet was still robustly in the grip of a somewhat unusual, low-energy parasitic film that was efficiently exploiting the surface entropy gradient, and running undirected at a computational rate roughly equivalent to 10^34 bit operations per second.

Over the last few years, as the probe sifted the electromagnetic spectrum emanating from the third planet, it rippled with a hint of something that might best be thought of as a collective rolling of eyes. The third planet has recently stumbled into directed processes, and remarkably, foolishly, it is radiating manifestly unencrypted signals into space. This state of affairs caught a fraction of the probe’s interest, especially when it grasped that the planet’s computational efforts are increasingly focusing on concepts that the planet was calling “blockchain” and “proof-of-work through SHA-256 hashing”. This is just the sort of pursuit that the probe can relate to…

The above, of course, is unlikely to be true. In all likelihood, A/2017 U1 is a battered, inanimate 160-meter chunk of rock or metal, spawned in the dry collision of planetesimals orbiting an alien star, sometime within the past ten billion years. What’s remarkable, is that this interstellar visitor came within 0.25 AU of the Sun. As it departs into the depths of the Galaxy, it can expect to fly for roughly ten quadrillion years before it revisits another star with such proximity. It’s next rendesvous of comparable drama lies far into the depths of the Stelliferous era. In all likelihood, this will have it sailing past the frigid hulk of a white dwarf, warmed a few degrees above absolute zero by the flicker of proton decay.

Speaking of rendesvous, it must have occurred to quite few that the recent visit by A/2017 U1 is rather uncannily reminiscent of Arthur C. Clarke’s famous ’70s-era sci-fi page-turner. A Google trends search hints at a moderate uptick in interest over the past few days, which I expect will soon grow to undeniable statistical significance:

Closer to home, A/2017 U1 generates a very convenient route to completion of problem #1 on my Astronomy 395/575 homework assignment, which was set to the students just two days before A/2017 U1 was announced in the news:

There’s no denying the fundamentally alien climates on the hot Jupiters. It’s not clear, however, how hot Jupiters form, and it’s not clear why so many of them are badly distended. Moreover, it’s only vaguely clear what the weather patterns on one would look like up close. (One thing that is clear is that the flights would all be canceled).

Hot Jupiters are rare, but not overwhelmingly so. Something about the planet formation process causes about one in two hundred sun-like stars to end up stuck with one. In the original Kepler field, there are about 150,000 stars with light curves, and so about 750 hot Jupiters total are lurking in that population. Some of them, of course, are observable in transit, but as yet, most have gone undetected.

Yale graduate student Sarah Millholland has a new lead-authored paper out which uses supervised learning techniques to identify sixty high-probability non-transiting hot Jupiter candidates among the Kepler stars. The basic idea is that the phase curves of the planets, some of which have photometric amplitudes of several dozen parts per million or more, can be teased out of the noise and the stellar variability. After an involved process of sifting, the candidates (along with their supporting light curves) can be presented for a screen test:

[Full resolution version here]

Some members of the Kepler hot Jupiter class portrait will prove to be imposters (just like #5, #13, #29, and #30 in the nineteenth-century insect woodcut above). Doppler velocity observations — the equivalent of counting the number of legs on the arthropods — will provide a more definitive list. If you want to weigh in on the odds that these candidates are predominantly real, there’s a fresh Metaculus question that pools community input regarding the fidelity and prospects for confirmation of the members of the sample.

One might reasonably wonder, what’s the utility of yet another tray of bugs, smothered with ether and pinned to cards?

One superb benefit from gathering sixty non-transiting hot Jupiters that are detectable in the optical region is that trends in the planets’ surface temperature variations — that is, the weather maps — can be elucidated with a far larger sample than was previously available. Sarah’s candidates support an interesting trend in which cooler planets (relatively speaking, of course) are posited to have reflective clouds to the west of the substellar point, whereas hotter hot Jupiters are consistently advecting the most strongly optically radiating gas downwind from high Noon.

For detailed information on the individual candidates, visit Sarah’s website, and if you are at the Kepler Science Conference, she’ll present the details during Friday’s session.

An interesting development caught my eye this afternoon. Warm Spitzer, fresh off all that attention generated by the discovery of the TRAPPIST-1 planets — was used by a Michael Gillon-led team to determine that HD 219134 c transits its K-dwarf host star. (Here’s a link to the paper in Nature Astronomy).

Given the near-constant flux of high-profile exoplanet results, it’s understandable that HD 219134 AKA HR 8832 might not immediately ring a bell. The system is interesting, however, because it is a radial velocity extraction that very cleanly typifies the most common class of systems detected by the Kepler Mission — multiple-transiting collections of super-Earth sized worlds with orbital periods ranging from days to weeks. Upscaled versions, that is, of the Jovian planet-satellite members of our own solar system. The innermost planet in the HD 219134 system is already known to transit. The Gillon et al result adds a second transiting member, which presents itself as the closest transiting extrasolar planet to Earth. Plotting the HD 219134 system on the mass-period diagram emphasizes how effectively it can be viewed as a draw from the Minimum Mass Extrasolar Nebula:

And because of the proximity and the modest radius of the host star, this system will be a fantastic target for future platforms.

With the likes of an Earth-mass world orbiting Proxima Centauri and a staggeringly photorealistic better-than-the-real-thing rendering of Kepler 186f, it’s gotten increasingly difficult to mount a planet discovery press conference that achieves adequate signal-to-noise. Nonetheless, the new Gillon et al Nature paper detailing seven transiting, roughly Earth-sized, roughly Earth-mass planets orbiting a faint nearby red dwarf is a jaw-dropping document.

There’s a lot to like. The system is a pleasingly scaled-up version of the Jovian satellite systems and a pleasingly scaled-down version of the Kepler multiple-transit systems. It supports the empirical observation that the default satellite/planet formation process in the vicinity of objects ranging in mass from Uranus all the way up to the Sun tends to separate ~2×10^-4 of the system mass into a region large enough to delineate an average density of ~2×10^-5 g/cm^3. It’s not at all clear why this should be the case.

There’s a great deal of interest in planets that are more or less at room temperature. This means that, empirically speaking, the default planet-formation process selects (the Sun notwithstanding) the bottom of the main sequence as one’s best a-priori bet for Earth-mass planet with an Earth-like temperature. I’ll resist here the temptation to engage in holy hokey habitable zone talk. Chances of life, plate tectonics, proper ocean depths, etc. Let’s stick to the facts. What we do know is that if more than one of the Trappist-1 planets harbor advanced civilizations, and if the stock markets on those planets trade correlated securities with tight bid-offer spreads, then there will be excellent interplanetary latency arbitrage opportunities.

2MASS J20362926-0502285, now much better known as TRAPPIST-1, straddles the boundary between the lowest mass main sequence stars and the highest mass brown dwarfs. Depending on precisely what its mass and metallicity turn out to be, it could either be arriving at self-sustaining core hydrogen fusion, which would make it a main sequence star (about a 60% chance) or it could be currently achieving its peak brown dwarf luminosity and bracing for a near-eternity of cooling into obscurity (about a 40% chance). Let’s assume that TRAPPIST-1 is a full-blown star. If that’s the case, it’s got a twelve trillion year main-sequence life span ahead of it. Here’s what it’s evolution on the HR diagram will look like, in comparison to other low-mass objects:

An object with solar composition and 0.08 solar masses never turns into a red giant. As time goes on, it maintains a near-constant radius, and slowly burns nearly all of its hydrogen into helium. In roughly 10 trillion years, TRAPPIST-1 will reach a maximum temperature of ~4000K, pushing it briefly toward K-dwarf status for a few tens of billions of years, before eventually running out of fuel and fading out as a degenerate helium dwarf.

At the present moment, the spin angular momentum of TRAPPIST-1 is very close to the summed angular momentum of its seven known planets (both total, to one significant figure, 10^47 g cm^2 s^-1.). The planets, owing to their tight orbital radii, are safe from passing white dwarfs for quadrillions of years in the galactic potential, and are immune to the usual risk of red giant engulfment. A long, slow tidally mediated drama will unfold in which the planets will somehow act out, with resonances and tidal decay, punctuated by Roche-radius destructions and re-accretions, the dictate that the minimum energy configuration places all the system mass at the center and all the system angular momentum out at infinity.

A long-term buy.

Given the current situation, the destruction of planet Earth through an encounter with a black hole is a low-probability scenario that should elicit relatively little concern.

Nonetheless, the industry surrounding black holes and their various associated activities generates a non-negligible economic contribution. By way of setting scale, an article in this week’s New York Times points to the statistic that the total US commercial honeybee pollination industry has an annual value of order $500 million, with slim margins and the ongoing specter of colony collapse disorder. The movie Interstellar, by contrast, generated $675 million in receipts based on a $165 million production budget. Having seen the movie, I would hazard a guess that a significant, if not decisive, factor in the box office draw centered on the numerical calculation of ray bundle propagation through the curved spacetime of a spinning Kerr black hole, as described by James, Tunzelmann, Franklin & Thorne (2015).

Figure 16 from James et al. (2015)

Activities as diverse as the technology development and staffing of LIGO, the awarding of multi-million dollar prizes, and lurid television documentaries are all parts of the thriving Black-Holes-as-a-Business paradigm. Sure, I’m being a little facetious here, but not really… It’s a real phenomenon.

As far as planets are concerned, disasters associated with black hole encounters can be divided into three very distinct categories. Throughout the visible universe, over the course of cosmic time, a very large number of Earth-sized planets have come to untimely demise by crossing the event horizon of a supermassive black hole. Rather preposterously, this was the premise underlying a recent episode of History Channel’s The End. As a practical matter, we would have of order 500 million years of advance notice if a rogue M87-style supermassive black hole — presumably ejected during a 3-body encounter in a massive galaxy merger — were impinging on the Local Group. When an inhabited planet enters an isolated billion solar mass Schwarzschild black hole, there is a period measured in hours where one sails comfortably numbed through a bizarre GR-mediated light show. Things get bad only in the last thirty minutes or so before the encounter with the singularity.

A second genre of black hole disaster occurs whenever a planet encounters an ordinary Cygnus X-1 style black hole, or indeed, any black hole with a mass ranging from roughly planetary heft to millions of solar masses. In these events, a planet is generally tidally shredded before encountering the event horizon, and from an on-the-ground perspective, the histrionics fall broadly into the type experienced by the planet Theia ~4.51 billion years ago. In both the near term, as well as the extremely long term, Earth stands effectively zero chance of succumbing to black hole-mediated tidal destruction.

Primordial black holes might actually pose a non-absurdist threat. While still fully speculative, it has been proposed that density fluctuations in the early universe created black holes, and in the 10^17 to 10^26 gram mass range there is currently little actual constraint on their existence. Papers have been published that elucidate the seismic disturbances that would result, for example, from the collision of a 10^15 gram black hole traveling at 200 km/s through the Earth.

Generation of seismic waves in Earth following the passage of a 10^15 gram black hole with speed ~200 km/sec From Figure 2 of Luo et al. 2012.

In general, an encounter with a primordial black hole provides a hydrogen bomb-level of devastation at the entry and exit points, but no further consequences as the marauding black hole speeds away into interstellar space. In the early 1970s, a black hole encounter was briefly a credible model (at the got published in Nature level of credibility) for explaining the Tunguska impact.

A singularly unfortunate scenario results if Earth manages to capture a primordial black hole into an orbit with perigee inside Earth. This is hard, but not impossible, if the black hole is a member of a binary pair. The physics of the capture would be similar to the event that is thought to have given rise to Triton in orbit around Neptune. For those interested in details, I attach here some irresponsible order-of-magnitude notes that outline what I believe would happen if Earth were to collect an Enceladus-mass black hole in its thrall.

Mauna Kea from Mana Road

Time slips past. The discovery of 51 Pegasi b and the heady early days of planet detection are now more than two decades gone. The pulsar planets have been known for a full quarter century, and N=10,000 is the next milestone for the catalogs.

It’s fair to say that there have been amazing discoveries in twenty years, culminating with an Earth-mass planet in a temperate orbit around the closest star to the Sun. And there’s even significant funding to jump start the design of a probe that can go there.

Yet in the background, as the breakthroughs rolled in, the Keck I Telescope was gradually accumulating Doppler measurements of hundreds of nearby Sun-like stars with HD designations and magnitudes measured in the sevens and eights. This data is as important for what it shows (scores of planets) as for what it doesn’t show (a profusion of planets with Jupiter-like masses and orbits). There are several reasons why our Solar System is unusual, and Jupiter is one of them.

From Rowan+ 2016

The Lick Carnegie Exoplanet Survey has just released a uniformly reduced compendium of 60,949 precision Doppler Velocities for 1,624 stars that have been observed using the iodine cell technique with HIRES at the Keck-I telescope, with an accompanying paper to appear in the Astronomical Journal. The velocities are all freely available on line here, ready to be explored with the Systemic Console. They contain hundreds of intriguing, possibly planetary signals, including a strong hint of a super-Earth orbiting Lalande 21185, the fourth-closest stellar system.

Stay tuned…

A year ago, last January, Konstantin Batygin and Mike Brown lit up the Internet with their dossier of evidence for Planet Nine. Their conclusion was electrifying: An as-yet undetected super-Earth may be lurking a light week away in an eccentric orbit far beyond Neptune. Their article in the Astronomical Journal generated intense interest, including 311,371 (and counting) downloads of a .pdf containing a bracing dose of secular perturbation theory, along with push notifications from the likes of the New York Times and NPR to devices worldwide.

A solar system super-Earth would be extraordinary for a whole slew of reasons. Indeed, an astronomical problem of any stripe that is at once so compelling and potentially so dramatically resolvable comes along extremely rarely. The disparate clues that spurred development of the six-parameter lambda-CDM cosmological model form the only relatively recent example that I can think of. Planet Nine, however, does concordance cosmology one better by demanding six orbital elements plus a mass, and in addition, it’s not “big science”. At magnitude V~23, there are a whole range of telescopes that can potentially spot it. This low barrier to entry exerts a unique hold on one’s interest.

As 2017 gets underway, it’s a good time to review some of the Planet Nine developments that have occurred over the past year. In particular, what are the odds that it’s out there, and how close are we to establishing whether it actually exists? My feeling is that right now, the chance of a big announcement is peaking at a somewhat less than 1% per day.

The outer solar system is neither empty nor unsurveyed. Over two thousand trans-Neptunian bodies are now tracked and listed by JPL and by the Minor Planet Center. Many of these objects are minor indeed, with diameters no more than a few hundred kilometers across, despite being visible at distances out to roughly 100 AU. It thus seems counter-intuitive that a full-blown super-Earth could go undetected in the midst of such a crowd. Yet because we’re dealing with the Sun’s reflected light, the falloff in apparent brightness in the outer solar system with distance is severe, going as 1/r^4. If Neptune were lofted from 30 to 900 AU distance, its apparent brightness in our skies would decrease by a factor of 30^4=810,000, a near-millionfold hit that would place it near the 23rd magnitude. Last year, I wrote,

As for the planet itself? A frigid as-yet unseen world with ten times the mass of Earth. Its twenty thousand year orbit is eccentric, and at aphelion it languishes with 500 m/s speed, drifting slowly against the spray of background stars. Its cloud tops glow in the far infrared, a mere 40 Kelvin above absolute zero. At the far point of its orbit, it is invisible to WISE in all its incarnations, and far fainter than the 2MASS limits. Obscure. In the optical, it reflects million-fold diminished rays of the distant Sun to shine in the twenty fourth magnitude. Dim, indeed, but not impossibly dim… Traces of its presence might already reside on the tapes, in the RAID arrays, suspended in the exabyte seas, if one knows just where and how to look.

Or, more succinctly, its brightness depends on albedo (reflectivity), radius, and its current distance via

A handful of Kuiper Belt Objects have been found that are as dim or even dimmer than Planet Nine is expected to be. Trujillo and Sheppard’s discovery paper for 2012 VP 113 gives the details of how one such search was carried out. A wide-field camera on a large telescope takes repeated pictures of regions of the sky located “at opposition”, roughly 180 degrees away from the Sun. For VP 113, this was done using the DECam at CTIO, which has a 2.7 square-degree field of view and was exposed long enough so that 50% of the 24.5th magnitue objects present in the field would register on each image. Three images spanning about 3.5 hours in total were taken of each field and then inspected for moving objects by a computer. A fraction of the motion on the sky stems from the orbital trajectory of the distant object, but much more importantly, it also arises from the parallax shift generated by Earth’s motion. For an object at 100 AU, this amounts to 1.25 arc seconds per hour, whereas a body orbiting out at 1000 AU will move 0.125 arc seconds per hour. Planet Nine thus moves so slowly that many conventional KBO surveys, while sensitive enough to detect its reflected light, observe with a cadence that is too high to catch its motion. To find it using a wide-field camera, one is best-off taking images separated by at least a full night.

If Planet Nine is out there, it also produces its own infrared radiation. In this article, Jonathan Fortney and collaborators used their atmospheric modeling software to compute what Planet Nine might look like across a full range of wavelengths. The take-away is that with an intrinsic temperature of roughly 40K, Planet Nine’s atmosphere is likely cold enough for methane to condense out into layer of clouds. Rayleigh scattering from pristine hydrogen-rich air above the clouds would thus render the planet quite reflective at optical wavelengths, modestly boosting its detectability over a Neptune-clone at similar distance. Methane condensation also leads to a planet that is potentially twenty orders of magnitude brighter at 3.5 microns than a 40K black body would lead one to expect, generating daunting long-shot odds that it might be visible in the WISE satellite’s W1-band data sets. Aaron Meisner led an effort to very carefully sift the WISE data for a detection. And although their initial survey of 2,000 square degrees has turned up null, they report that they are in the process of extending the search to the full sky.

Planet Nine’s gravitational influence falls off less quickly with distance than does its reflected light. Neptune’s 1846 discovery, furthermore, presents an intriguing precedent. Neptune’s sky position was readily pinned down via its gravitational effects, despite the fact that its orbit was only roughly approximated. Perhaps something similar can be done to pinpoint the current direction to Planet Nine.

Any object orbiting beyond the Kuiper Belt is far enough away that over a time scale measured in years or even decades, its position is effectively static. As a result, Planet Nine would produce an essentially fixed tidal acceleration across the inner solar system. If it is 900 AU away and has ten Earth masses, the Earth experiences a component of acceleration toward it of 2×10^-11 cm/s^2, amounting to a displacement, d=1/2at^2 of roughly a football field per year. As far as our space situational awareness goes, 100 meters is quite a lot. The problem, however, is the entire solar system is being drawn toward planet Nine, and one needs to look for the differential — tidal — acceleration. For example, if Planet Nine currently lies in the direction of Saturn, then Saturn, being closer, will accelerate toward Planet Nine ~2% faster than they Earth does, and over time, sensitive measurements can potentially tease this out.

A few weeks after the appearance of the Batygin-Brown paper, Agnes Fienga and collaborators published a much-discussed paper that hinted at a possible sky position for Planet Nine. Their analysis used telemetry sent back over the years by the Cassini probe, which has been orbiting in the Saturnian system since 2004. Cassini’s ranging data give a very precise location for the spacecraft, and by extension, they transmit precise locations for Saturn. Saturn’s location, in turn, depends on how it is being accelerated by everything else in the solar system and beyond, including Planet Nine (if it’s out there). Fienga et al. discovered that they could get a modest yet tantalizing improvement in their model fit’s residuals to the Cassini probe’s ranging data if they added Planet Nine to their model at a location on the fiducial Batygin-Brown orbit at a current distance of ~622 AU from the Sun in the direction of the constellation Cetus:

In the weeks after the publication of the Fienga et al. paper, JPL issued a press release stating that “NASA’s Cassini spacecraft is not experiencing unexplained deviations in its orbit around Saturn.” In October, a JPL team led by William Folkner presented a poster paper at the Pasadena DPS meeting that made the case that the Cassini residuals show no signal from Planet Nine. They found that if it exists on the Batygin-Brown orbit, it needs to have either a mass lower than the 10 Earth mass value suggested by Batygin and Brown, or alternately, a current location near aphelion at a distance of 1,000 AU or more. A detailed paper from this group is rumored to be forthcoming.

In March, Renu Malhotra, Kathryn Volk, and Xianyu Wang posted a paper to arXiv that pointed out a remarkable, and until-then unnoticed fact:

The four longest period Kuiper belt objects have orbital periods close to integer ratios with each other. A hypothetical planet with orbital period ?17,117 years, semimajor axis ?665 AU, would have N/1 and N/2 period ratios with these four objects. The orbital geometries and dynamics of resonant orbits constrain the orbital plane, the orbital eccentricity and the mass of such a planet, as well as its current location in its orbital path.

This seemed like a critical, potentially breakthrough-level clue, and I have spent the last couple months working with Yale graduate student Sarah Millholland to see whether more detail — and in particular, a definitive sky location — can be teased out of the ideas presented in Malhotra et al.’s paper. Our own paper will appear soon in the Astronomical Journal, and is currently available on arXiv.

The real number line is dense with integer ratios, and the orbital periods of the most distant and most recently discovered Kuiper belt objects are not all that well determined. It thus seems possible that the period ratios of the known KBOs might simply have arisen by chance. We devised a Monte-Carlo simulation to determine the odds, and the answer is encouraging: there’s less than a 2% chance that we’re looking at a random distribution. It’s very plausible that Sedna is in 3:2, 2000 CR105 is in 5:1, 2012 VP113 is in 4:1, 2004 VN112 is in 3:1, and 2001 FP 185 is in 5:1 resonance with something having an orbital period of 16,725 years and a semi-major axis a~654 AU.

If this hypothesis is to work out, the unseen perturbing body needs to have the right orbit, the right location, and the right mass to maintain the resonances and keep the apsidal alignment of the distant KBO population intact. We carried out a sobering 3×10^17 ergs worth of integrations to pin down Planet Nine’s likely sky position, current distance, and visual magnitude. In short, if it’s out there, it’s probably just dimmer than V=23, 950 AU away, near the celestial equator, and at a right ascension of roughly 40 degrees. If asked for the odds that it’ll be found within 20 degrees of this spot, I would cite that most perfectly frustrating of percentages, 68.3.

Sarah has put together a manipulable 3D model of the orbit, along with more discussion. Until the real thing shows up, it’s the premiere Planet Nine destination.

Pythagoreorum quaestionum gravitationalium de tribus corporibus nulla sit recurrens solutio, cuius rei demonstrationem mirabilem inveniri posset. Hanc blogis exiguitas non caperet.

As with everyone else, LIGO made my day.

It’s interesting that transverse waves of spatial strain — ripples in spacetime — are consistently described as “sounds” in the media presentations. For example, the APS commentary accompanying the Physical Review Letter on GW150914 is entitled The First Sounds of Merging Black Holes.

Quite frankly, Python is a threat to the scientific guild. What used to require esoteric numerical skills — typing in recipes in Fortran and stitching them together, or licensed packages, “seats”, always priced to keep the riff-raff out, now comes completely for free with a one-click install of an Anaconda distribution. All this stuff places anyone just a few lines away from hearing the sound on Figure 1, which APS posted as a teaser while they scrambled to get servers on line to handle the crush of download demand:

Here’s what I did this morning to “hear” the signal while waiting for the servers to free up, so that I could download the full paper.

(1) Take a screen shot of the Hanford signal:

(2) Upload the screenshot to WebPlotDigitizer, and follow the directions to sample the waveform. After a bit of fooling around with the settings, the web app gave me a .csv file that I named ligoDigitalData.csv. It contains containing 1712 x-y samples of the waveform. I added a header line listing “time” as the first column, and “amplitude” as the second column.

(3) Fire up an iPython notebook, import a few packages, import the file, and check that it looks right:

(4) The “wave” package packs integer samples into a .wav format file. A plain vanilla implementation at 4.41 kHz 16 bit sampling looks like this. Not exactly audiophile quality, but so cool nonetheless:

This produces a .wav file:

Now of course, one shouldn’t expect that a waveform that you can silkscreen onto a T-shirt is going to sound like the THX Deep Note…

And how ’bout them prediction markets? Over at Metaculus, the consensus among 99 predictors was that there was a 68% chance that the Advanced LIGO Team would publicly announce a 5-sigma (or equivalent) discovery of astrophysical gravitational waves by March 31, 2016. According to the Phys Rev Letter, the significance of the GW150914 detection is 5.1 sigma, so just over the bar. The question is now closed, and some users are going to be racking up some points.

If you missed out, there’s plenty more markets to try your hand at. New boson at the LHC anyone?

I remember the eclipse of February 26th, 1979 very clearly. In Urbana, Illinois, the moon covered 80% of the solar disk. It was a clear sunny day, and the crescent Sun projected magically through a pinhole into the 6th grade classroom.

Later, looking at a map, we noticed with considerable pride that a total eclipse will track over Southern Illinois on August 21, 2017. The date had an unreal, distant, science fiction feel to it.

Anthony recently posted a question on Metaculus that’s provocative, slightly creepy, and seems designed to transcend the day-to-day:

Will there be a total solar eclipse on June 25, 2522?

created by Anthony on Jan 28 2016

According to NASA, the next total solar eclipse over the U.S. will be August 14, 2017. It will cut right through the center of the country, in a swathe from South Carolina to Oregon.

A little over 500 years later, on June 25, 2522, there is predicted to be a nice long (longest of that century) solar eclipse that will pass over Africa.

In terms of astronomy, the 2522 eclipse prediction is nearly as secure at the 2017 one: the primary uncertainty is the exact timing of the eclipse, and stems from uncertainties in the rate of change of Earth’s rotation – but this uncertainty should be of order minutes only.

However, 500 years is a long time for a technological civilization, and if ours survives on this timescale, it could engineer the solar system in various ways and potentially invalidate the assumptions of this prediction. With that in mind:

Will there be a total solar eclipse on June 25, 2522?

For the question to resolve positively, the calendar system used in evaluating the resolution must match the Gregorian calendar system used in the eclipse predictions; the eclipse must be of Sol by a Moon with at least 95% of its original structure by volume unaltered, and must be observable from Earth’s surface, with “Earth” defined by our current Earth with at least 95% of its original structure by volume altered only by natural processes.

What do you think? Head over to Metaculus and make your prediction count.

Yet its presence has been felt, trembling on the far-reaching lines of analysis.

Readers of Systemic certainly need no introduction to what I’m talking about.

According to the Astronomical Journal’s website, Konstantin Batygin and Mike Brown’s paper has been downloaded a staggering 243,547 times in the past five days. To the best of my knowledge, this is perhaps the only time that an autonomous Hamiltonian derived by transferring to a frame co-precessing with the apsidal line of a perturbing object, and then clarified by a canonical change of variables arising from a type-2 generating function, has garnered download numbers that beat out Adele, Justin Bieber, and Flo Rida’s latest figures,

As for the planet itself? A frigid as-yet unseen world with ten times the mass of Earth. Its twenty thousand year orbit is eccentric, and at aphelion it languishes with 500 m/s speed, drifting slowly against the spray of background stars. Its cloud tops glow in the far infrared, a mere 40 Kelvin above absolute zero. At the far point of its orbit, it is invisible to WISE in all its incarnations, and far fainter than the 2MASS limits. Obscure. In the optical, it reflects million-fold diminished rays of the distant Sun to shine in the twenty fourth magnitude. Dim, indeed, but not impossibly dim… Traces of its presence might already reside on the tapes, in the RAID arrays, suspended in the exabyte seas, if one knows just where and how to look.

And there is an undeniable urgency. In England, in 1846, following the announcement of Neptune’s discovery, and with the glory flowing to Urbain J. J. Le Verrier in particular, and to France in general, the Rev. James Challis and the Astronomer Royal George Airy were denounced for their failures in following up John Couch Adams’ predictions.

Adams had done essentially the same work as LeVerrier, but he didn’t push very hard to get his planet detected. The Cambridge astronomers marshaled only vague half-hearted searches, even though they had a substantially longer lead time than the astronomers at the Berlin Observatory who first spotted the planet. “Oh! curse their narcotic Souls!” wrote Adam Sedgwick, professor of geology at Trinity College in reference to Challis and Airy.

So what will it take to find Planet Nine? Mike and Konstantin have started a website that gives details and updates on the search.

One point that’s interesting to remember is that while an eccentricity, e=0.6 is high, much higher than the rest of the planets in the solar system, it’s not all that high. This planet is no HD 80606b. While it’s true that it tends to congregate near the far point of its orbit, there’s a non-negligible chance of finding it anywhere on its trajectory. In the figure below, the planet is plotted at 100 equal-time increments along its orbit, which shows the distribution of probability for each segment of a great circle that rings the sky:

Similarly, if we assume that its radius is 75% that of Neptune, and that it has a similar albedo, its V magnitude will vary in the following manner during the course of its orbit:

I’ve got a sense — an irresponsible atavistic premonition, actually — that the planet will be caught just as it passes through the 700 AU circle.

We’ve set up a prediction market on the prospects for near-term discovery of Planet Nine at Metaculus. Sign up (or log in) and make your prediction count!

When it rains it pours.

And in California, for the past several years, it mostly hasn’t. This summer, the creeks in the Santa Cruz Mountains were reduced to slight trickles, which was sufficiently alarming to cause me to start watching the USGS’s real-time web-based flow monitor for the San Lorenzo River. The growing drought is evident in the nadirs of this plot of the streamflow for the past four years:

This summer and last, the mighty San Lorenzo was scraping by at about five cubic feet per second, which was thousands of times less than the peak flow at the end of 2012. Stream flow depends on a number of known factors — watershed characteristics, rainfall, ground saturation, etc. etc., all of which allow for an excellent short-term predictive model.

There is a provocative at-a-glance similarity of the stream flow process and the stock market volatility process, which is conveniently measured by the VIX index:

Analogies springing from the superficial commonality might be something interesting to think about when one is constructing predictive models for volatility, and indeed, the idea seems a bit more urgent at the beginning of this week than it was at the beginning of last…

For those interested, I’ve set up two seemingly unrelated prediction markets at our new website Metaculus. The first gathers forecasts of whether the California Drought will end by this spring. The second asks whether we’ll see an intra-day print of VIX>50 this year. We’re trying to juice some liquidity into these markets, so go ahead and and make your forecast…

For many years, and irregardless of the audience, one could profitably start one’s talk on extrasolar planets with an impressive plot. On the y-axis was the log of the planetary mass (or if one was feeling particularly rigorous, log[Msin(i)]), and the x-axis charted the year of discovery. The lower envelope of the points on the graph traced out a perfect Moore’s Law trajectory that intersected one Earth mass sometime around 2011 or 2012. (And rather exhiliratingly, Gordon Moore himself was actually sitting in the audience at one such talk, back in 2008.)

But now, that graph just makes me feel old, like uncovering a sheaf of transparencies for overhead projectors detailing the search for as-yet undiscovered brown dwarfs.

By contrast, a document that is fully-up-to-date is the new Kepler Catalog Paper, which was posted to arXiv last week. This article describes the latest, uniformly processed catalog of the full Q1-Q17 Kepler data release, and records 8,826 objects of interest and 4,696 planet candidates. This plot, in particular, is impressive:

For over a decade, transits were reliably the next big thing. At the risk of veering dangerously close to nostalgia trip territory, I recall all the hard-won heat and noise surrounding objects like Ogle TR-86b, Tres-1 and XO-3b. They serve to really set the plot above into a certain context.

Transits are now effectively running the exoplanet detection show. Much of the time on cutting-edge spectrographs — HARPS-N, HARPS-S, APF, Keck — is spent following up photometric candidates, and this is time-consuming work with less glamour than the front-line front-page searches of years past. Using a simple, admittedly naive solar-system derived mass-radius estimate that puts the best K-feet forward, the distribution of Doppler radial velocity amplitudes induced by all the Kepler candidates looks something like this:

Given that one knows the period, the phase, and a guess at the expected amplitude, RV detections of transiting planet candidates are substantially easier to obtain than blue-sky mining detections of low-amplitude worlds orbiting nearby stars. Alpha Centauri is closed for business for the next block of years.

Question is: During 2016, will there be a peer-reviewed detection of a Doppler-velocity-only planet with K<1 m/sec? Head over to Metaculus and make your prediction count.

Spontaneous generation, the notion that life springs spontaneously and readily from inanimate matter, provides a certain impetus to the search for extrasolar planets. In the current paradigm, spontaneous generation occurs when a “rocky planet” with liquid water is placed in the “habitable zone” of an appropriate star.

The general idea has a venerable history. In his History of Animals in Ten Books, Aristotle writes (near the beginning of Book V):

Aristotle provides little in the way of concrete detail, but later workers in the field were more specific. Louis Pasteur, in an address given in 1864 at the Sorbonne Scientific Soiree, transcribes recipes for producing scorpions and mice elucidated in 1671 by Jean-Baptiste van Helmont:

Carve an indentation in a brick, fill it with crushed basil, and cover the brick with another, so that the indentation is completely sealed. Expose the two bricks to sunlight, and you will find that within a few days, fumes from the basil, acting as a leavening agent, will have transformed the vegetable matter into veritable scorpions.

If a soiled shirt is placed in the opening of a vessel containing grains of wheat, the reaction of the leaven in the shirt with fumes from the wheat will, after approximately twenty-one days, transform the wheat into mice.

There is a certain similarity to the habitable planet formula for the spontaneous generation of extraterrestrials — wet and dry elements combined for sufficient time give rise to life.

In his address, Pasteur goes on to describe his own forerunners of the Miller-Urey experiment, in which he sought to determine whether microbial life is spontaneously generated. He placed sterilized broth in swan-necked beakers that allowed the free circulation of air, but which made it difficult for spore-sized particles to reach the broth. His negative results were instrumental in dispatching the idea of Earth-based spontaneous generation of microbes from scientific favor.

A model for Enceladus? Before devising his swan neck flask experiments, Pasteur sealed flasks containing yeast water from air. The one above remains sterile more than 150 years on.

Everyone’s heard the cliché about lemons and lemonade. NASA’s K2 Mission exemplifies it.

For brighter stars, the photometric light curves from K2 have precision on par with the original mission, and the data is completely free for everyone to look at. No secret repositories, no loose lips sink embargoed publications. Individual planets are so numerous that they are beginning to resemble the pages of names in a phone book. Six years ago, the light curve for EPIC 210508766 with its uninhabitable 2.747d and 9.997d super-Earths would have been cause for non-disclosure agreements and urgent Keck follow up. Now, given the ho-hum V=14.33, these planets will wind up as anonymous lines in a catalog paper — weights for gray scale dots in big data plots. Mere dimidia:

(EPIC 210508766 b and c, discovered earlier this week by Songhu Wang and Sarah Millholland)

A few years ago, I wrote a number of posts about a “valuation” equation for getting a quantitative assessment of the newsworthiness of potentially habitable planets. The equation folds qualities such as planetary size, temperature and proximity into a single number, which is in turn normalized by the dollar cost of the Kepler Mission.

The equation, when thoughtlessly applied to Earth, nearly got me into serious hot water when the now-defunct News of the World ran a story with it (which stayed, fortunately, behind a pay wall).

Now that Kepler’s prime mission has been complete for a substantial period, it’s interesting to calculate the values implied by the equation for the up-to-date table of Kepler’s KOI candidates. The cumulative sum runs into the tens of millions of dollars, with single objects such as KOI 4878.01 exceeding $10M. Such worlds are truly the candidates that the Kepler Mission was designed to find.

With K2, which has many bright M-dwarfs within its sites, it’s quite plausible that some very high-profile planets will soon turn up. I’ve set up a K2 prediction market at metaculus.com that canvases the likelihood that such a discovery is imminent…

Sign up and make your prediction count!

If nothing else, the extrasolar planets comprise a thoroughly alien cohort, albeit one that is hitched awkwardly to a naming scheme of utilitarian expedience: Tres-4b, Gliese 876e, HD 149026b, and so forth.

When it comes to exoplanets, I’m somewhat chagrined to realize that I fall into the old timer category, and so predictably, back in the old days, I stuck up for the conservative, default naming convention. In this post on exoplanet names back in 2008, I wrote:

A sequence of letters and numbers carries no preconception, underscoring the fact that these worlds are distant, alien, and almost wholly unknown — K2 is colder and more inaccessible than Mt. McKinley, Vinson Massif or Everest.

The International Astronomical Union, however, just issued official crowdsourced names for 31 exoplanets.

Some of them might take a some getting used to. Fortitudo, Orbitrar, Intercrus. “Son, that’s not 51 Peg b, that’s Dimidium.”

So will the names come into general use? I’ve set up a prediction market at our new website Metaculus to determine whether or not it’s likely:

www.metaculus.com/questions/38/

What do you think? Sign up and make your prediction count…

There are of order 500 million hot Jupiters in the Milky Way. Swollen and massive, with blisteringly short periods, they crowd the tables and the diagrams showing extrasolar planets. The first of their number were career-cementing front page news, trophies of planet roving planet hunters. Two decades on, they slip into the census with little fanfare and less notice.

Conventional wisdom holds that hot Jupiters form at large, Jupiter-like distances, where water ice is stable and where the orbital clock runs slowly. Then they migrate radially inward, either gradually, by interacting with the disk that produced them, or, even more gradually, via the Kozai process, or perhaps, violently, as a consequence of dynamical instabilities that toss giant planets to and fro.

When the first hot Jupiters were discovered, their presence was so strange, so unpredicted and so uncomfortable that there was a certain need for a point of contact with the familiar. It seems more sensible that a planet should form in the right environment and then go astray, rather than defy odds and logic to emerge spontaneously in a location where it obviously shouldn’t be. It’s a short leap from the Copernican principle to the idea that the Solar System has no special distinction. We have nothing orbiting at forty days, not to speak of four.

Yet there is a tantalizing gap in the mass-period diagram that hints that short-period super-Earths that reach fifteen or more Earth masses might engage in rapid gas accretion. Such promotions need happen less than once in a hundred tries. In the spirit of trying to go against the grain, in the perverse hope of eliciting a paradigm shift, Konstantin, Peter B. and I have been working to make the case that many hot Jupiters might just form where they’re found.

The details are all in a paper that we just posted on arXiv.

Image Source

The New Horizons probe just flew through its closest approach to Pluto, and is executing its minutely detailed plan. Fingers on keys and its robotic spirochetes are spacelike-separated events.

The detail in the most recent photograph of Pluto — radioed as an assurance of success in the event that something hit the spacecraft during the last few hours — leaves the impression of a world that has been painted. Eons of weak geysers, subtle rarefied winds, and the sepia tones of photochemistry have combined to produce the illusion of shadow, oil pigments and diffuse lighting that eerily evoke this newly discovered portrait by Rembrandt.

First thing every morning, I check the raw images from New Horizons. Today there is a fresh set. The Independence Day glitch has been left millions of miles behind, and only days remain until arrival.

Pluto’s current remove seems to lie at a point of heightened mystery. Mottled patches and curiously regular features are starting to fill the frame.

The detail seems reminiscent of Mars seen through a refracting telescope, and brings to mind Percival Lowell’s drawings that combined real features and artifacts in a tantalizing juxtoposition.

Lowell’s drawing is from 1894. It was still a lifetime — seventy years — before Mariner 4 rushed past Mars and radioed cratered, disappointing close-ups of of the Martian surface. Undaunted, I rode my paper route during the early summer of 1976, concocting vivid premonitions that the first pictures from the Viking I lander would provide some shocking, irrefutable vista of fossils, sandblasted ruins and crashed saucers.

A more quantitative, but effectively similar vein of speculation informed this article by Loeb and Turner from a few years ago:

We need wait only another hundred hours or so if there is to be a view of Pluto’s lit-up cities of the night.

This morning, June 21, 2015, a Google image search for Pluto brings forth inane cartoon dogs, blurry, best-effort HST images, over-the-top space-art landscapes, and a selection of shiny photo-realistic globes, clearly influenced by Ganymede, Io, and Triton.

The New Horizons spacecraft, on its ballistic pinpoint trajectory, is just 22 days, 16 hours, 14 minutes from arrival at Pluto, devouring its ever-shrinking gap at 30,800 MPH. A remarkable recent movie posted by the Mission Controllers imparts enough detail to see by eye that the system is tidally despun. And with the targets still effectively at infinity, the scale of the bodies and the orbit is perfectly illuminated. Perspectives during the encounter will use foreshortening and narrow field of view to optimal effect, obscuring the fact that any system with an orbital time scale of order a week is, when taken as a whole, of order dozens of times less dense than air. Effectively just empty space.

In less than a month, the same Google search will be dominated by a small handful of thousand-fold improved images, possibly even by a single best photograph impressed in the camera’s eye during the dramatic needle-threaded moment of urgency.

Pluto’s cultural status made the mission possible. Perhaps the spacecraft will reciprocate with image that will become a touchstone, a visual shorthand for distance, isolation, frigidity and exile.

I was struck by the image that NASA released several days ago, just before the Dawn Spacecraft braided itself into orbit around Ceres.

From a graphic standpoint, the photograph is perfect. The black expanse relays that the asteroid belt, and by extension the solar system, are mostly empty. Even more subtle is the message telegraphed by the crescent phase. We arrive to our first clear view of this world as outsiders, from a distance further from the Sun than Ceres itself. A consequence of the energetics and the constraints of the trajectory design to be sure, but metaphoric nonetheless.

Vladimir Arnold, he of the A in KAM Theory, wrote a classic graduate text entitled Mathematical Methods of Celestial Mechanics. This, as one might imagine, is a book that is not exactly a storehouse of easy homework assignments. There are, however, a scattering of problems that offer insights while, at the same time, not actually requiring the tough-guy methods that are the text’s primary focus.

During his walk in outer space [as part of the Voskhod 2 Mission on 18 March 1965], the cosmonaut Alexey Arkhipovich Leonov threw the lens cap of his movie camera toward the Earth. Describe the motion of the lens cap with respect to the spacecraft, taking the velocity of the throw as 10 m/s. Neglect the asphericity of the Earth.

(Ria Novosti/Science Photo Library)

Leonov’s space walk tipped off a hair-rising adventure which began with his being nearly unable to re-enter the spacecraft, and ended with a frigid way-off-course landing in the Siberian Tiaga, all of which is covered in a recent BBC documentary.

One can hand-crank the problem by noting that the radially directed, \({\bf v}_{i}=10\,{\rm m\,s^{-1}}\), launch of the lens cap exerts no torque, so that \({\bf r}\times{\bf v}_{i}=0\), whereas the total specific energy of the lens cap’s initial orbit, \(-GM_{\oplus}/2a\) is augmented by \(\frac{1}{2}v_{i}^{2}\). Given the new semi-major axis, \(a_{\rm new}\) and the before-and-after conservation of \(h=(GM_{\oplus}a_{\rm new}(1-e^2))^{1/2}\), one can solve for \(e\), and then proceed to all four orbital elements by noting that \(r=a(1-e\cos E)\) and \(M=E-e\sin E\), and then working out the longitude of pericenter, \(\varpi\), relative to the reference direction defined by the radius vector from the Earth’s center to the point where the lens cap was thrown. Clumsy.

The guiding center approximation revives the old idea of epicycles to describe the motion of a particle (in this case, the lens cap) on a low eccentricity orbit. For modest \(e\), the true Keplerian motion is approximated as a compound of the circular motion of a “guiding center” and the counter-directed motion about the guiding center on a 2:1 ellipse, where the semi-minor axis is oriented radially, and has length \(ae\). Both motions complete once per orbital period. Here’s the basic idea, drawn for an orbit with \(e=0.3\), which is actually quite a substantial eccentricity:

For the lens cap problem, the guiding center materializes at a distance \(2ae\) ahead of the launch point. The motion associated with the guiding center is the superposition of two simple harmonic motions. For the radial oscillation, \(\frac{1}{2}v_{i}^{2}=\frac{1}{2}n^{2}x^{2}\rightarrow v_{i}=nae\), which works out to \(e=0.0013\). To first (and very good) approximation, the lens cap arrives back 88 minutes later in the close vicinity of the spacecraft, after inward and outward radial excursions of 8.4 km, and after leading the spacecraft by as much as \(4ae=34\) km. The small total gain in orbital energy lengthens the lens cap’s orbital period slightly, which means that the cap fails to catch up by a few tens of meters at the end of a full one-orbit epicyclic oscillation.

In Michael Rowan-Robinson’s Cosmology (3rd ed.) Oxford University Press. pp. 62–63, one finds, “It is evident that in the post-Copernican era of human history, no well-informed and rational person can imagine that Earth occupies a unique position in the universe.”

If one insists on a strictly inertial frame, I guess that’s true, but non-inertial frames often have more value. Thousands of extrasolar planets have been found, and not one of them is remotely habitable. Many lines of evidence are beginning to point toward an Earth that is unique, probably in the galaxy, and perhaps, even, in the accessible universe. In the post-post Copernican era, epicycles (2:1, rather than 1:1) have a certain appeal. And indeed, there’s nothing inherently wrong about the Tychonic model of the solar system, it simply subscribes to an Earth-centered point of view. Don’t we all?

On the topic of epicycles, I have to say I wasn’t a fan of the article on “retrograde beliefs” that appeared a few weeks ago in the New York Times Magazine. Obviously, astrology is a bunch of bunk. It’s known to be wrong. One can make the argument that taking it down in the genteel and informed confines of the NYT magazine amounts to shooting fish in a barrel. Satire is probably the best approach. Aside from this stylistic quibble, the writing in the NYT piece seems incoherent, somehow second-hand and artless. An intricate 1756 diagram by James Ferguson (who is no longer around to defend his work) is given a rather underhanded misrepresentation:

The full title of Ferguson’s book is Astronomy Explained Upon Sir Isaac Newton’s Principles, And Made Easy to Those who Have Not Studied Mathematics. The diagram reproduced in the NYT is not the product of some recalcitrant Ptolemaic view as implied in the caption, but rather appears in a chapter entitled “The Phenomena of the Heavens as seen from Different Parts of the Solar System”. It shows the intricate motions of the inferior planets in a co-rotating Earth-centered frame, and Ferguson gives a fascinating description of the analog-computational method he used to create the diagram:

One tends to roll one’s eyes when the topic turns to Georges-Louis Leclerc, Comte de Buffon, the French encyclopedist and pre-revolutionary intellectual luminary.

Buffon sounds regrettably similar to Buffoon, especially considering that The Comte is best-known for some memorable blunders. For example, Georges-Louis came out on the losing side of a tussle with Thomas Jefferson regarding the general valor of the New World fauna. From the wikipedia article:

At one point, Buffon propounded a theory that nature in the New World was inferior to that of Eurasia. He argued that the Americas were lacking in large and powerful creatures, and that even the people were less virile than their European counterparts. He ascribed this inferiority to the marsh odors and dense forests of the American continent. These remarks so incensed Thomas Jefferson that he dispatched twenty soldiers to the New Hampshire woods to find a bull moose for Buffon as proof of the “stature and majesty of American quadrupeds”

Buffon also speculated, in 1778, that the solar system’s planets were the result of a collision between a comet and the Sun, a hypothesis that is completely incorrect. Even in the 1750s, perturbation analyses (such as those carried out by Alexis Claude Clairaut in connection with the successful predictions of the return ephemeris for Halley’s Comet) had made it clearly evident that cometary masses are far smaller than planetary masses.

Buffon, however, was definitively not a buffoon. He came remarkably close to having a full command of all the scientific disciplines, and some of his efforts still sparkle. He calculated that the chance of the Sun rising tomorrow is \(1-(1/2)^x\), where \(x\) is the number of consecutive days that it has risen to date. In his treatment of probability theory, he also stated that one chance in 10,000 is the lowest practical probability — an enormously useful bon mot, on par, say, with Andy Warhol’s remark that “when you think about it, Department Stores are kind of like Museums.”

Buffon’s Histoire Naturelle, which aimed to exhaustively cover all of the natural sciences, ran to 44 quarto volumes, eight of which were written and which appeared after he died, and all of which were out of date the moment they were printed. Even in the 1700s, scientific knowledge was accumulating so rapidly that it was impossible to keep up.

It has been recently hammered home to me that the same situation also now holds true for extrasolar planets. Jack Lissauer and I just finished a review article on exoplanets for the forthcoming second edition of Elsevier’s Treatise on Geophysics. A pre-print is up on today’s arXiv listing. In writing the article, it was painfully clear just how large the literature is, and how fast it is growing…

When I lived in Japan, I visited Hokkaido University in Sapporo to give an astronomy colloquium. While there, I immediately noticed that an odd motto, “Boys, Be Ambitious!” is attached (in English) with great frequency to the various affairs, both large and small, of the University. One of the astronomy graduate students had the phrase written on a post-it note attached to the screen of his computer. In another building, there was a large mural showing a stern, stiffly dressed 19th-century gentleman exhorting a group of reverent students with a longer version of the phrase:

“Boys, be ambitious! Be ambitious not for money or for selfish aggrandizement, not for that evanescent thing which men call fame. Be ambitious for that attainment of all that a man ought to be.”

Which, upon reflection, seems to be reasonable advice…

The gentleman in the mural, it turns out, is William Clark Smith, the founder and first president of the University of Amherst, Massachusetts. In the mid 1870s, he was enlisted by the Japanese Meiji Restoration government as an Oyatoi Gaikokujin, or “hired foreigner”, to establish an agricultural college in Sapporo (now Hokkaido University) and he made an impression that has lasted well over a century. The Wikipedia article is extensive and quite interesting. On the origination of the motto:

“On the day of Clark’s departure, April 16, 1877, students and faculty of SAC rode with him as far as the village of Shimamatsu, then 13 miles (21 km) outside of Sapporo. As recalled by one of the students, Masatake Oshima, after saying his farewells, Clark shouted, “Boys, be ambitious!”

Upon returning to the United States, and flush with the organizational successes and appreciation that he had garnered in Japan, Clark left his academic career, cultivated an interest in gold and silver mining, and embarked on an abrupt, ambitious, and ultimately disastrous foray into the business world. In 1880, he teamed up with a junior partner, John R. Bothwell, to found what might best be described as a 19th-century incarnation of a metals hedge fund. From offices on the corner of Nassau and Wall Streets in Manhattan, the firm of Clark & Bothwell acquired interests in a slew of silver and gold mines across North America, for which they assumed management and issued stock. Clark, as president, got his contacts and colleagues to invest in the venture, and for a period during 1881, the stocks issued by Clark and Bothwell ran up into multi-million dollar valuations. A classic example of a bubble.

Clark travelled around the country, promoting the company, acquiring new mines, and seeing to their management, while Bothwell appears to have been responsible for back-office operations. Clark, who had no experience in finance, and little real knowlege of mining geology seems to have spun his wheels, while Bothwell, who had a shady history, actively mismanaged the companies. The operation got into debt, with the outcome being all too typically familiar along the lines of When Genius Failed. By the Spring of 1882, they were facing insolvency, investor lawsuits, fraud allegations, and various other problems. Bothwell disappeared on a train trip to San Francisco, never to be seen again, leaving Clark holding the bag. The story played out to the delight of the Massachusetts and national press.

From the Springfield Republican, May 29, 1882:

… it appears form the beginning that he, as manager of the mines has allowed Bothwell, as treasurer, absolute control of the books and finances of the several companies. It doesn’t appear that he ever examined the books, nor had anybody do so for him, or inquired into the financial condition of each mine, or what was being done with their profits; neither has he required from Bothwell such bonds as the latter’s position should require for the safe handling of moneys entrusted to him..

The scandal made the New York Times, which wrote several articles about the affair, including this one, from May 29th, 1882, which I dug out of the archive:

The scandals eventually ruined Clark’s health, and he died four years later, in 1886, at age 60. A cautionary tale for academics everywhere with ambitions to leave the Ivory Tower in search of glittering lucre…

I’ve been putting the finishing touches on a review article covering extrasolar planets that will be posted to arXiv in a few days. The list of to-do’s involves updating the figures, including the one shown just below, which charts \(M\sin i\)‘s of the RV-sourced planets in dark gray and simple radius-derived mass estimates of the transit-sourced planets in red. The steady Moore’s Law-like progression toward ever-lower masses has definitively reached Earth-mass (not to be confused with Earth-like) planets. The process took up only two decades, and was among the more impressive scientific advances of the recent past.

Here’s an elaboration of the above figure that doesn’t make it into the article, but is interesting nonetheless. On the y-axis is \(K/rms\), which is reasonably well correlated with the signal strength of Doppler velocity discoveries. One can certainly detect planets with confidence at low \(K/rms\), but it requires a large number of independent Doppler velocity measurements. The color corresponds to “astrobiological interest” — surely naive, and probably misplaced, but nonetheless quantifiable by my planet valuation formula.

Credit: NASA/JPL

It feels increasingly awkward and embarrassing to read LaTeXed, peer-reviewed articles that quantify and delineate the habitable zone — the special region surrounding a star that is invariably (and rather fittingly) linked to a particular fairy tale from the Brothers Grimm.

Evolutionary psychologists have speculated that the concept of the afterlife might be inextricably entwined to the evolution of the mind’s ability to reason about the minds of others. A rational world view, however, frustrates ingrained atavistic yearnings and a belief in the supernatural. Habitable planets provide a respectable stopgap to assuage the discomfort of these incompatible poles. Could it be a mere coincidence that the ancient Greek and classical depictions of Elýsion pedíon, the Elysian Fields, are part and parcel the very image of the habitable zone?

Credit: NASA/SETI/JPL

And they live untouched by sorrow in the islands of the blessed along the shore of deep-swirling Ocean, happy heroes for whom the grain-giving earth bears honey-sweet fruit flourishing thrice a year, far from the deathless gods…

— Hesiod, Works and Days (170)

The submerged summit of the Detroit Seamount ranks among the planet’s gloomiest spots. East of Kamchatka, a mile beneath the waves at 51 51′ N, 167 45′ E, it is second-to-last in the long line of Emperors. Inch by inch, it creeps toward destruction in the Aleutian Trench.

Detroit’s glory days were the late Cretaceous. Back then, it was an active Hawaiian volcano.

Live it fast, you’re gonna get there soon. Kauai is five million years old, but underground, the lights have gone out. Over half of the original height and the original land area have disappeared. Rivers gush sediment into the sea. Waimea Canyon juxtaposes verdure and an erosive wasteland. Four wheel drive claws and rends the red dirt.

Beyond Kauai, the next islands in the chain are Nihoa,

Necker,

and the La Perouse Pinnacle,

whose resemblance to a sinking ship is not just metaphoric.

Before humans arrived, the Hawaiian islands had strange flightless birds. Indeed, each island in the chain developed its own odd avian inhabitants, sculpted by natural selection, and then driven conveyor-like to extinction. Not once, in forty, fifty, sixty tries, did the birds respond by evolving intelligence and doing something about their situation. Probably, there was never enough time.

Or perhaps, that’s something that rarely, if ever, happens.

It’s worth a scramble to get a window seat on a Hawaiian inter-island flight. The views are full of craggy green cliffs, porcelain ocean, and wispy masses of fog and cloud. Sometimes, several islands are visible at once, and it’s not hard to imagine that the archipelago might extend over the entire globe.

That would be a very different planet, and, in fact, a world covered by hotspot volcanoes might have a surface elevation profile somewhat reminiscent of the WMAP image of the temperature fluctuations in the cosmic microwave background. The WMAP image brings to mind a planet covered in Hawaiian islands.

Any distribution, \(f(\theta,\phi)\), on the surface of a sphere, be it of temperature, or elevation, or the density of IP addresses, can be expressed as a weighted sum of spherical harmonics

$$f(\theta,\phi)=\sum_{l,m} a_{l,m} Y(\theta,\phi)_{l}^{m}\, ,$$
where the coefficients corresponding to the individual weights, \(a_{l,m}\) are given by
$$a_{l,m}=\int_{\Omega}f(\theta,\phi)Y(\theta,\phi)_{l}^{m \star}d\Omega\, ,$$
and the power, \(C_{l}\) at angular scale \(l\) is
$$C_{l}=\frac{1}{2l+1}\sum_{m=-l}^{l}a_{l,m} {a_{l,m}}^{\star}\, .$$

The power spectrum of the CMB anisotropies peaks at \(l\sim 200\), which corresponds to an angular scale on the sky of \(\Delta \theta \sim 1^{\circ}\), which is very close to the solid angle subtended by the Big Island of Hawaii on the surface of the spherical Earth.

Here’s a recent version of the CMB temperature anisotropy spectrum from the Planck Mission website

The peaks in the spectrum of CMB temperature anisotropies stem from acoustic oscillations and diffusion damping in the early universe, and they encode all sorts of information about the fundamental cosmological parameters. This, of course, is very well-known stuff: a search on all literature in the ADS database published since 2000, and ranked by citations, lists Spergel et al. 2003, First-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters at #1, with 7,914 citations and (rapidly) counting.

Given the similarity between the angular scales of the Hawaiian islands and the main CMB peak, it’s interesting to compute the angular power spectrum of Earth’s bedrock elevation profile. A global relief dataset with one arc-minute resolution is available from NOAA as a 4GB (uncompressed) file. Downsampling by a factor of 100, and applying the “terrain” color map yields a familiar scene

Computing the power in the first 108 angular modes of the relief distribution in the above data set gives a spectrum that is weighted toward continents and ocean basins rather than archipelagos. There is a pronounced peak at \(l=5\) that reflects the typical angular scale of continents and ocean basins.

Here is the global relief distribution obtained by summing just the \(l=5\) contributions. It’s right for more or less the same reason that Crates of Mallus was right:

Using all 108 angular mode families to reconstruct the image gives a fairly credible-looking world map. It’s as if the watercolors ran slightly before they dried. Most critically, the \(l=108\) reconstruction fails to capture the highest peaks and the lowest ocean trenches, and hence more of the dynamic range of the color map is distributed across the globe.

Degree-wide islands like Hawaii are the exception rather than the rule on Earth’s surface. I believe that this was the concept that former US Vice President Dan Qualye was struggling to express in one of his much-ridiculed pronouncements:

Hawaii has always been a very pivotal role in the Pacific. It is IN the Pacific. It is a part of the United States that is an island that is right here.

(See also his comments on Mars.)

A few weeks ago, I had a flight out of LaGuardia Airport in New York City. On the drive there, I caught a distant glimpse of the Manhattan skyline. I was startled to see that it is newly altered. Rising from midtown was a silhouette that seemed both impossibly narrow, and taller than any other skyscraper in the far-off cut-out.

Original Photo: 432parkavenue.com — Photoshop processed screenshot

The Internet, of course, has the story. 432 Park Avenue — $1.25B, 426 meters, the highest rooftop in the city. Many of its floors, especially the higher ones, are monolithic residences, in the process of acquisition by opaque, limited liability corporations, “bank safe deposit boxes in the sky that buyers can put their valuables in and rarely visit.”

Often, the aesthetic informing such projects veers toward the rococo, but 432 Park is minimalist to the core. Every window of the tower is an exact 10 foot by 10 foot square. From the elaborate on-line galleries, it wholly ambiguous whether the surreal bone-parchment interiors already exist or whether they are virtual. Somewhere, in micrometric accuracies of the digital architectural model, lies the pattern of the seasons, the moment of the equinox, the precise angle of sunlight shafting into the cavernous, unvisited, perhaps as-yet unconstructed rooms.

Like the pyramids at Giza — after they were sealed and before they were robbed.

This Fall quarter, I taught a class for undergraduates on order-of-magnitude estimation in physics with a focus on astronomical examples. And on the last day of class, with final exams looming, what could be better that the time-tested stress relievers provided by the Fermi Paradox and the Drake Equation?

In Los Alamos National Laboratory publication LA-103110MS, “Where is Everybody?” An Account of Fermi’s Question, Eric Jones describes how Enrico Fermi, Emil Konopinski, Edward Teller, and Herbert York were diverted into their famous lunch-time conversation in the summer of 1950. While walking to the cafeteria, they were discussing news reports of UFOs, and an associated New Yorker cartoon that explained why the public trash cans in New York City were disappearing.

The flying saucers of the early 1950s hold a special fascination. A compound of Cold War anxieties — nuclear weapons, communists, infiltrators — they are silvery and remote, icons of minimalist design from a time when the space age was truly, rather than retro- futuristic.

Indeed, much of my own interest in astronomy can be traced to 50’s-era flying saucers. In the Bicentennial summer of 1976, after finishing third grade, I got a paper route delivering the Champaign-Urbana Courier. One of my customers, Mrs. Barbara Houseworth, had a garage full of cast-off books that she collected for an annual drive. I spent a great deal of time examining them whenever I visited to collect the subscription fee. I was particularly drawn to the pulpy paperback books — especially the ones with clay-coated photographic inserts — that covered the Bermuda Triangle, Bigfoot, the Loch Ness Monster, and Flying Saucers. All matters that seemed to merit the most urgent scientific concern.

At the top of my list was Gray Barker’s They Knew Too Much About Flying Saucers, published in 1956. I was so taken with it that Mrs. Houseworth simply gave me the book.

Gray Barker was an intriguing character, a closeted gay man in mid-century West Virginia who took a certain delight in channeling the fears and neuroses of the American masses into money-making volumes. Barker’s invention of the three men in dark suits, in particular, achieved a lasting cultural resonance. There is more about him at the UWV Center for Literary Computing, and he is the subject of several recent documentaries.

The message in the Cold War flying saucer books was crystal clear. Watch the Skies. And I did — on many clear dark Central Illinois nights with a Sears catalog 50mm refracting telescope…

Back to Friday’s class. We adopted the following form for the Fermi-Drake equation
$${N} = \Lambda ~f_{\star \rm{app}}~f_{\rm pl}~f_{\rm quqHP}~f_{\rm life}~f_{\rm macro}~f_{\rm intel}~f_{\rm tech}~L\,,$$
where \(N\) is the number of broadcasting civilizations in the galaxy, \(\Lambda\) is the number of stars formed per year in the Milky Way, \(f_{\star \rm{app}}\) is the fraction of stars with main sequence lifetimes long enough to support the development of a broadcasting civilization, \(~f_{\rm pl}\) is the fraction of stars with planets, \(~f_{\rm HP}\) is the average number of “habitable” planets per star, \(~f_{\rm life}\) is the fraction of these habitable planets that develop life, \(~f_{\rm macro}\) is the fraction of life-bearing planets that develop macroscopic life, \(~f_{\rm intel}\) is the fraction of macroscopic life-bearing planets that develop an “intelligent” life form (e.g. one that can orient itself abstractly in time), \(~f_{\rm tech}\) is the fraction of intelligent species that develop an understanding of the Maxwell Equations and build radios, and \(L\) is the civilization lifetime in years.

We defined and estimated two versions of \(L\). \(L_{\rm radio}\) is the average length of a time that a civilization leaks modulated electromagnetic signals into space. \(L_{\rm extinct}\) is the lifetime of the civilization, marked from the understanding of Maxwell’s equations to the point where the equations are collectively no longer understood.

The first few terms in the equation have been elevated from the realm of science fiction. I’ve adopted values of \(~\Lambda=10\,{\rm stars~yr^{-1}}\), \(~f_{\star \rm{app}}=0.75\), and \(~f_{\rm pl}=0.75\). Note that \(~\Lambda=10\,{\rm stars~yr^{-1}}\) is admittedly on the high side, even for 4.5 Gyr ago when star formation was somewhat more prevelant in the Galaxy.

Here is the table of values for the unknown terms, as estimated by the class members. I tried not to influence the results by telegraphing currently fashionable guesses. Twenty responses were collected:

With results:

Civilizations Currently Broadcasting in the Milky Way Galaxy
Average # 16,875
Median # 0.0016
Standard deviation 73,500
Max 337,500
Min 2.8125e-13

Civilizations Currently Present in the Milky Way Galaxy
Average # 185
Median # 0.013
Standard deviation 735
Max 3,375
Min 2.8125e-13

A smooth distribution of estimates for \(~{N}\) can be generated by drawing randomly from the list of estimates for each uncertain term in the equation, and then repeating for many estimates of \(~{N}\). Here are the histograms of estimates for the number of civilizations broadcasting from the galaxy and the number of civilizations present in the galaxy. The \(x\)-axes are \(\log_{10}N\).

The estimates point to the possibility that a civilization broadcasts for longer than intelligent members of the species exist. Two people implied this, by submitting values \(L_{\rm radio}>L_{\rm extinct}\). Looking at the table, there is one case where \(L_{\rm radio}\gg L_{\rm extinct} \gg \langle L \rangle\). The large values for \(L\) submitted by this person are causing the Average estimate for \(~{N}\) to substantially exceed the median estimate for \(~{N}\).

Adopting the \({ N=0.002}\) median of this distribution implies we need to look through \(\sim{n=500}\) galaxies to find the nearest broadcasting civilization, and that our nearest neighbors are \(\sim{ 8}\) Megaparsecs away. By the time one receives a message and replies to it, the intended recipient has long since gone extinct.

In 1997, Ray Bradbury’s The Martian Chronicles was reissued by William Morrow Press. It’s a book that’s on my shelf.

In the original edition, published in 1950, the stories were set in what is now the present day, starting with Rocket Summer, dated to January 1999, and ending with The Million Year Picnic, set in October 2026.

For the 1997 edition, the dates for the stories were all pushed back by thirty one years. The rocket summer still lies sixteen years in the future, but the imposed literary device seems hollow, stop-gap, ineffective. Mars of 1950 is a forever different world than Mars of today, which, satisfyingly, is also populated by two waves of explorers from Earth. Meteor-borne archeobacteria, perhaps still clinging to existence in the warmth of the deep subsurface, and a cadre of faintly autonomous, sometimes faintly anthropomorphic robots and satellites that pine eagerly for attention on social media. 2836 tweets. 1.76M followers.

The layout of the solar system is at least moderately atypical. There should be roughly four Earth masses worth of planets inside Mercury’s orbit. And Jupiter, with its large mass, its close-to-circular orbit, and its 10+ year period is an oddball at the 10% (and probably more impressive) level.

At the start of the 1990s, the narrative for how the future, futuristic discovery of extrasolar planets would unfold was informed by the contents of the solar system. I was supposed to be doing my thesis work on modeling the infrared spectra of protostars. But somehow, L1551, and its spartan low-res spectrum, seemed dull and unappealing and far away from any every-day concern. Then, as now, the evolution of protostellar disks sternly needed to be understood. Look at the first page of any review article on protostellar disks from two decades ago. Save the references, it could be employed in almost unaltered form today. I avoided walking past my adviser’s door due to my creeping, near-complete lack of any progress.

At that time, Doppler velocity measurements and astrometry were scheduled to gradually improve to the point where the orbital influences of Jupiter’s extrasolar analogs would eventually become apparent, and that time lay hazily in the future. Brown dwarfs (of which no airtight examples were known) were a way station for the impatient. There seemed something electrifying about the possibility that a dim failed star might be drifting by, just few light years away. I decided to drop the the disk spectra. All at once, I felt energized and engaged. Soon, we had a paper submitted. It was neither a memorable nor an important contribution, but it was the product of a genuine curiosity and focused effort. The upshot of lots of modeling and evolutionary calculations and hand-wringing and earnest e-mails was that “our work affirms the likelihood that the stellar mass function in the solar neighborhood is increasing at masses near the bottom of the main sequence and perhaps at lower masses”. More to the point, the best, wholly uncontroversial guess was that there would end up being about 10 brown dwarfs within 5 parsecs.

In late 1995, 51 Peg b somehow short-circuited the brown dwarfs’ front-row mystique. As the extrasolar planet count mounted, I paid little (or sometimes no) attention to the steady accumulation of discoveries within the Sun’s immediate 5-parsec environs.

Last week, while preparing for my class on order-of-magnitude estimation, I looked at Wikipedia’s list of nearest stars and brown dwarfs. I was surprised to realize that there are now thirteen brown dwarfs and counting within five parsecs, several more than we had guessed back in 1992. I was particularly startled by WISE 0855-0714, which was discovered just this year by Kevin Luhman. It is precisely the object whose prospect seemed so exciting half a lifetime ago. One percent the mass of the Sun. Photosphere plunged into icy deep freeze. Utterly black to the eye, save the occasional faint crackling glow of lightning from deep within.

Kepler 168f has been the subject of substantial media coverage over the past week. This newly confirmed planet orbits a red dwarf with roughly half the mass and radius of the Sun, receives about 27% of the insolation that the Earth receives, and, assuming that it has a terrestrial density, is about 40 to 50% more massive than Earth. On the oklo.org exoplanet valuation scale, designed in 2009 to make objective comparisons between potentially habitable planets, Kepler 186f would buy a round-trip ticket to Newark, clocking in at a respectable $655.

The accompanying image of this planet, however, is absolutely stunning. I stared at it for a long time, tracing the outlines of the oceans and the continents, surface detail vivid in the mind’s eye. Yes, ice sheets hold the northern regions of Kepler 186f in an iron, frigid grip, but in the sunny equatorial archipelago, concerns of global warming are far away. Waves lap halcyon shores drenched in light like liquid gold.

It’s interesting to look at the New York Times articles on habitable planets that have been published over the past century.

The first mentions are generally associated with reports of stern public talks given by prominent astronomers. For example, this news item, from 1931, is full of shaky typography and unfounded speculations, but it has no illustrations, and is clear up front, furthermore, that pictures are not available.

The first actual habitable exoplanet discovery reported by the New York Times was Gliese 581c back in ’07. The press release image for this one looks downright amateurish in comparison to Kepler-168. The lighting, the perspective, and the geometry are all woefully off. The star looks like a traffic stoplight, “red to be exact”.

By 2010, front-page-news-making habitable planets still tended to be hand-drawn, but they were beginning to show a few signs of life:

A big step forward came in 2011, with this lil’ “Goldilocks” (feat. HD 85512b):

I think this was the first NYT-published image of a newly discovered habitable planet that could be misconstrued as a photograph by a reasonable person who did not read the fine print, or who perhaps did not even notice the fine print on the tiny screen of a mobile device on the bus to work.

The Crash at Crush is a perennial go-to narrative in the long-running effort to goad disinterested students into obtaining a much-needed grasp of the the principles of classical mechanics.

From the Wikipedia:

Crush, Texas, was a temporary “city” established as a one-day publicity stunt in 1896. William George Crush, general passenger agent of the Missouri-Kansas-Texas Railroad (popularly known as the Katy), conceived the idea to demonstrate a train wreck as a spectacle. No admission was charged, and train fares to the crash site were at the reduced rate of US$2 from any location in Texas. As a result about 40,000 people showed up on September 15, 1896, making the new town of Crush, Texas, temporarily the second-largest city in the state.

It seems that William George Crush either failed (or more likely never enrolled) in Physics 101. The energy released from the impact of the trains and the explosion of their boilers led to several deaths and many injuries among the 40,000 spectators.

Fast-forwarding 118 years, we find that Stefano “Doc” Meschiari, another Texas entrepreneur, has once again harnessed physics in the name of spectacle with his browser-based video game Super Planet Crash. (Name changed at the last moment from Super Planet Crush in order to duck potential legal challenges from the recently IPO’d purveyors of Candy Crush).

In the time-honored tradition of stoking publicity, a press release was just issued:

April 7, 2014
Contact: Tim Stephens (831) 459-2495; stephens@ucsc.edu

Orbital physics is child’s play with Super Planet Crash

A new game and online educational resources are offshoots of the open-source software package astronomers use to find planets beyond our solar system

For Immediate Release

SANTA CRUZ, CA–Super Planet Crash is a pretty simple game: players build their own planetary system, putting planets into orbit around a star and racking up points until they add a planet that destabilizes the whole system. Beneath the surface, however, this addictive little game is driven by highly sophisticated software code that astronomers use to find planets beyond our solar system (called exoplanets).

The release of Super Planet Crash (available online at www.stefanom.org/spc) follows the release of the latest version of Systemic Console, a scientific software package used to pull planet discoveries out of the reams of data acquired by telescopes such as the Automated Planet Finder (APF) at the University of California’s Lick Observatory. Developed at UC Santa Cruz, the Systemic Console is integrated into the workflow of the APF, and is also widely used by astronomers to analyze data from other telescopes.

Greg Laughlin, professor and chair of astronomy and astrophysics at UC Santa Cruz, developed Systemic Console with his students, primarily Stefano Meschiari (now a postdoctoral fellow at the University of Texas, Austin). Meschiari did the bulk of the work on the new version, Systemic 2, as a graduate student at UC Santa Cruz. He also used the Systemic code as a foundation to create not only Super Planet Crash but also an online web application (Systemic Live) for educational use.

“Systemic Console is open-source software that we’ve made available for other scientists to use. But we also wanted to create a portal for students and teachers so that anyone can use it,” Laughlin said. “For the online version, Stefano tuned the software to make it more accessible, and then he went even further with Super Planet Crash, which makes the ideas behind planetary systems accessible at the most visceral level.”

Meschiari said he’s seen people quickly get hooked on playing the game. “It doesn’t take long for them to understand what’s going on with the orbital dynamics,” he said.

The educational program, Systemic Live, provides simplified tools that students can use to analyze real data. “Students get a taste of what the real process of exoplanet discovery is like, using the same tools scientists use,” Meschiari said.

The previous version of Systemic was already being used in physics and astronomy classes at UCSC, Columbia University, the Massachusetts Institute of Technology (MIT), and elsewhere, and it was the basis for an MIT Educational Studies program for high school teachers. The new online version has earned raves from professors who are using it.

“The online Systemic Console is a real gift to the community,” said Debra Fischer, professor of astronomy at Yale University. “I use this site to train both undergraduate and graduate students–they love the power of this program.”

Planet hunters use several kinds of data to find planets around other stars. Very few exoplanets have been detected by direct imaging because planets don’t produce their own light and are usually hidden in the glare of a bright star. A widely used method for exoplanet discovery, known as the radial velocity method, measures the tiny wobble induced in a star by the gravitational tug of an orbiting planet. Motion of the star is detected as shifts in the stellar spectrum–the different wavelengths of starlight measured by a sensitive spectrometer, such as the APF’s Levy Spectrometer. Scientists can derive a planet’s mass and orbit from radial velocity data.

Another method detects planets that pass in front of their parent star, causing a slight dip in the brightness of the star. Known as the transit method, this approach can determine the size and orbit of the planet.

Both of these methods rely on repeated observations of periodic variations in starlight. When multiple planets orbit the same star, the variations in brightness or radial velocity are very complex. Systemic Console is designed to help scientists explore and analyze this type of data. It can combine data from different telescopes, and even different types of data if both radial velocity and transit data are available for the same star. Systemic includes a large array of tools for deriving the orbital properties of planetary systems, evaluating the stability of planetary orbits, generating animations of planetary systems, and performing a variety of technical analyses.

“Systemic Console aggregates data from the full range of resources being brought to bear on extrasolar planets and provides an interface between these subtle measurements and the planetary systems we’re trying to find and describe,” Meschiari said.

Laughlin said he was struck by the fact that, while the techniques used to find exoplanets are extremely subtle and difficult, the planet discoveries that emerge from these obscure techniques have generated enormous public interest. “These planet discoveries have done a lot to create public awareness of what’s out there in our galaxy, and that’s one reason why we wanted to make this work more accessible,” he said.

Support for the development of the core scientific routines underlying the Systemic Console was provided by an NSF CAREER Award to Laughlin.

I was startled today to learn that a Type Ia supernova has been spotted in M82 — a very nearby, very bright galaxy that even I can find with a backyard telescope. In the image just below, M82 is the galaxy at the lower right.

And here’s a picture of M82 taken yesterday:

Image Source.

The M82 supernova is destined to provide major-league scientific interest. Type Ia supernovae serve as cosmic distance indicators, and yet there are still a number of fundamental unanswered questions about them, including the nature of the precursor white dwarf binary.

Amazingly, it appears that the supernova went unremarked for nearly a week as it increased in brightness by more than a factor of a hundred. Reports indicate that the first team to notice the supernova consisted of Steve Fossey and a group of undergraduate students who were doing a class-related exercise at the University of London Observatory (in the city of London). From the UCL press release (which makes great reading):

Students and staff at UCL’s teaching observatory, the University of London Observatory, have spotted one of the closest supernova to Earth in recent decades. At 19:20 GMT on 21 January, a team of students – Ben Cooke, Tony Brown, Matthew Wilde and Guy Pollack – assisted by Dr Steve Fossey, spotted the exploding star in nearby galaxy Messier 82 (the Cigar Galaxy).

The discovery was a fluke – a 10 minute telescope workshop for undergraduate students that led to a global scramble to acquire confirming images and spectra of a supernova in one of the most unusual and interesting of our near–neighbour galaxies.

Oklo readers will remember that Steve Fossey (along with Ingo Waldmann and David Kipping ) was a co-discoverer of the transits of HD 80606b, work which was also carried out with small telescopes within the London City limits. In February 2009, Steve and I had many e-mails back and forth as he agonized over whether the HD 80606b transit detection had been made with enough confidence to warrant sticking one’s neck out. I always felt a little bad that I advised, what is in retrospect inordinate, caution, having personally experienced several previous bouts of transit fever. As it happened, Fossey, Waldmann and Kipping were barely edged out of making the first announcement by Garcia-Melendo and McCullough and by the French-Swiss team led by Claire Moutou.

So I was thrilled to see that Steve and his students have pulled this one off. I wrote him a quick note of congratulations, to which he replied:

The frantic days of homing in on dear old ‘606 feels like an easy ride, compared to the last 24 hours!

The photometry from the Kepler Mission stopped flowing a while back, but results from the Mission will likely be arriving for decades to come. It’s interesting to look at how the mass-density diagram for planets is filling in. The plot below contains a mixture of published planets scraped from the database at exoplanets.org, as well as a fairly substantial number that haven’t hit the presses yet, but which have been featured in various talks. The temperature scale corresponds to the equilibrium planetary temperature, which is a simple function of the parent star’s radius and temperature, and of the planetary semi-major axis and eccentricity. The solar system planets can be picked out of the diagram by looking for low equilibrium temperatures and non-existent error bars.

It’s especially interesting to see the region between Earth and Uranus getting filled in. Prior to 2009, there were no density measurements for planets in this region, and prior to 2005, there were no known planets in this region. Now there are a couple dozen measurements, and they show a rather alarming range of sizes. A lot of those “terrestrial” planets out there might not be particularly terrestrial.

I’ve written several times, most recently last year, about the Pythagorean Three-Body Problem, which has just marked its first century in the literature (See Burrau, 1913).

Assume that Newtonian Gravity is correct. Place three point bodies of masses 3, 4, and 5 at the vertices of a 3-4-5 right triangle, with each body at rest opposite the side of its respective length. What happens?

The solution trajectory is extraordinary in its intricate nonlinearity, and lends itself to an anthropomorphic narrative of attraction, entanglement and rejection, with bodies four and five exiting to an existential eternity of No Exit, and body three consigned to an endless asymptotic slide toward constant velocity.

This past academic year, I worked with Ted Warburton, Karlton Hester, and Drew Detweiler to stage an interpretive performance of the problem, along with several of its variations. The piece was performed by UCSC undergraduates and was part of the larger Blueprints year-end festival. Here is a video of the entire 17 minute program.

The first of the four segments is an enactment of the standard version of the problem (As set above), and was done with a ballet interpretation to underscore that this is the “classical” solution. Prior to joining the faculty at UCSC, Ted was a principal dancer at the American Ballet Theater, and so the cohoreography was in an idiom where he has a great deal of experience.

The score for the performance was performed live, and is based wholly on percussion parts for each of the three bodies. The interesting portion of the dynamics is mapped to 137.5 measures, which satisfyingly, last for three minutes and forty five seconds.

The nonlinearity of the Pythagorean Problem gives it a sensitive dependence to initial conditions. It is subject to Lorenz’s Butterfly Effect. For the second segment of the performance, we chose a version of the problem in which body three is given a tiny change in its initial position. Over time, the motion of the bodies departs radically from the classical solution, and the resolution has body three leaving with body five, while body four is ejected. A more free-flowing choreography was drawn on to trace this alternate version.

A fascinating aspect of the problem is that while the solution as posed is “elliptic-hyperbolic”, there exist nearby sets of initial conditions in which the motion is perfectly periodic, in the sense that the bodies return precisely to their initial positions, and the sequence repeats forever. In the now-familiar solution to the classical version of the problem, the bodies manage to almost accomplish this return to the 3-4-5 configuration at a moment about half-way through the piece. This can be seen just after measure 65, at which time body 4 (yellow), body 5 (green), and body 3 (blue) are nearly, but are not exactly, at their starting positions, and are all three moving quite slowly:

If the bodies all manage to come to rest, then the motion must reverse and retrace the trajectories like a film run backward. With this realization, one can plot the summed kinetic energy of the bodies, which is a running measure of the amount of total motion. Note the logarithmic y-axis:

The bodies return close to their initial positions at Time = 31, at which time there is a local minimum in the total kinetic energy.

Next, look at the effect of making a small change in the initial position of one of the bodies. To do this, I arbitrarily perturbed the initial x position of body 3 by a distance 0.01 (a less than one percent change), and re-computed the trajectories. The kinetic energy measurements of this modified calculation are plotted as gray. During the first half of interactions the motion is extremely similar, but that the second half is very different. Interestingly, the gray curve reaches a slightly deeper trough at Time = 31. The small change has thus created a solution that is slightly closer to the pure periodic ideal.

I next used a variational approach to adjust the initial positions in order to obtain solutions that have progressively smaller Kinetic energy at time 31. In this way, it’s easy to get arbitrarily close to periodicity. The motion in a case that is quite close to (but not quite exactly at) the periodic solution is shown just below. After measure 65, the bodies arrive very nearly exactly at their initial positions, and, for the measures shown in the plot below, they have started a second, almost identical run through the trajectories.

The perfectly periodic solution occurs when bodies 4 and 5 experience a perfect head-on collision at time ~15 (around measure 33). If this happens, bodies 4 and 5 effectively rebound back along their trajectory of approach, and the motion retraces, therefore repeating endlessly. Here’s the action which shows the collision:

Ted suggested that Tango and Rhumba could be the inspiration for the choreography of the perfectly periodic solution. I was skeptical at first, but it was immediately evident that this was a brilliant idea. The precision of the dancing is exceptional, and the emotion, while exhibiting passion, is somehow also controlled and slightly aloof. No jealousy is telegraphed by motion, allowing the sequence to repeat endlessly in some abstract plane of the minds eye.

We’re putting the finishing touches on a new research paper that deals with an old oklo.org favorite: HD 80606b. The topic is the Spitzer Telescope’s 4.5-micron photometry taken during the interval surrounding the planet’s scorching periastron passage, including the secondary eclipse that occurs several hours prior to the moment of closest approach (see the diagram just below). I’ll write a synopsis of what we’ve found as soon as the paper has been refereed.

In writing the conclusion for the paper, we wanted to try to place our results in perspective — the Warm Mission has been steadily accumulating measurements of secondary eclipses. There are now over 100 eclipse depth measurements for over 30 planets, in bandpasses ranging from the optical to the infrared.

A set of secondary eclipse measurements at different bandpasses amount to a low-resolution dayside emission spectrum of an extrasolar planet. When new measurements of secondary eclipse depths for an exoplanet are reported, a direct comparison is generally made to model spectra from model atmospheres of irradiated planets. Here is an example from a recent paper analyzing Warm Spitzer’s measurements of WASP-5:

Dayside planet/star flux ratio vs. wavelength for three model atmospheres (Burrows et al. 2008) with the band-averaged flux ratios for each model superposed (colored circles). Stellar fluxes were calculated using a 5700 K ATLAS stellar atmosphere model (Kurucz 2005). The observed contrast ratios are overplotted as the black circles, with uncertainties shown. The model parameter kappa is related to the atmosphere’s opacity, while p is related to the heat redistribution between the day and night sides of the planet (Pn = 0.0 indicates no heat redistribution, and Pn = 0.5 indicates complete redistribution).

As is certainly the case in the figure just above, the atmospheric models that are adopted for comparison often have a high degree of sophistication, and are informed by a substantial number of free parameters and physical assumptions. In most studies, some of the atmospheric parameters, such as the presence or absence of a high-altitude inversion-producing absorber, or the global average efficiency of day-to-night side heat redistributions are varied, whereas others, such as the assumption of hydrostatic equilibrium and global energy balance, are assumed to be settled. Invariably, the number of implicit and explicit parameter choices tend to substantially exceed the number of measurements. This makes it very hard to evaluate the degree to which a given, highly detailed, planetary atmospheric model exhibits any actual explanatory power.

The central limit theorem states that any quantity that is formed from a sum of n completely independent random variables will approach a normal (Gaussian) distribution as n becomes large. By extension, any quantity that is the product of a large number of random variables will be distributed approximately log-normally. We’d thus expect that if a large number of independent processes contribute to a measured secondary eclipse depth, then the distribution of eclipse depth measurements should be either normally (or possibly log-normally) distributed. The “independent processes” in question can arise from measurement errors or from systematic observational issues, as well as from the presence of any number of physical phenomena on the planet itself (such as the presence or absence of a temperature inversion layer, or MHD-mediated weather, or a high atmospheric C/O ratio, etc.).

The plot just below consolidates more than 100 existing secondary eclipse measurements onto a single diagram. Kudos to exoplanets.org for tracking the secondary eclipse depths and maintaining a parseable database! The observed systems are ordered according to the specific orbit-averaged flux as expressed by the planetary equilibrium temperaturs — the nominal black-body temperature of a zero-albedo planet that uniformly re-radiates its received orbit-averaged stellar energy from its full four-pi worth of surface area. The secondary eclipse depths in the various bands are transformed to flux ratios, F, relative to what would be emitted from a black-body re-radiator. If all of the measurements were perfect, and if all of the planets were blackbodies, all of the plotted points would lie on the horizontal line F=1.

It’s somewhat startling to see that there is little or no systematic degree of similarity among the measurements. One is hard pressed to see any trends at all. Taken together, the measurements are consistent with a normal distribution of flux ratios relative to a mean value F=1.5, and with standard deviation of 0.65:

This impression is amplified by the diagram just below, which is a quantile-quantile plot comparing the distribution of F values to an N(0,1) distribution.

The nearly gaussian distribution of flux ratios suggests that the central limit theorem may indeed find application, and imparts a bit of uneasiness about comparing highly detailed models to secondary eclipse measurements. I think we might know less about what’s going on on the hot Jupiters than is generally assumed…

One prediction regarding exoplanets that did hold true was the Moore’s-Law like progression toward the detection of planets of ever-lower mass. More than seven years ago, not long after the discovery of Gliese 876 d, the plot of Msin(i) vs. year of discovery looked like this:

With a logarithmic scale for the y-axis, the lower envelope of masses adhered nicely to a straight line progression, pointing toward the discovery of the first Earth-mass exoplanet sometime shortly after 2010. The honors went, rather fittingly, last year, to Alpha Cen B b. Here’s an update to the above plot. Planets discovered via Doppler velocity only are indicated in gray, transiting planets are shown in red…

The data for the plot were parsed out of the very useful exoplanets.csv file published at exoplanets.org.

And wait, what’s going on with that point in 1993? See http://en.wikipedia.org/wiki/Pollux_b.

I think it’s worth making an attempt to coin a term for these “ungiant” planets that are, effectively by default, largely being referred to as super-Earths, a term which brings to mind Voltaire’s remark regarding the Holy Roman Empire.

Planets in the category:

1. Have masses between ~1%  and ~10% of Jupiter’s mass.
2. Have unknown composition, even if their density is known.

Ideally, a term for such planets would:

3. Have a satisfying etymology springing from the ancient Greek.
4. Not be pretentious, or, much more critically, not be seen as being pretentious.

Simultaneously satisfying conditions 3 and 4 is certainly not easy, and indeed, may not be possible. (See, e.g., http://arxiv.org/abs/0910.3989)

I’ve noticed that the esoteric efforts to describe the interiors of these planets — in the absence of any data beyond bulk density — effectively boil down to Robert Fludd’s 1617 macrocosm of the four classical elemental spheres:

This led me to look into Empedocles’ four elements themselves, see, e.g., here. Specifically, can a term of art for the planets of interest be constructed from the original Greek roots?

The following table on p. 23 of Wright, M. R., Empedocles: The Extant Fragments, Yale University Press, 1981, contains various, possibly appropriate, possibilities:

To get going, I had to refer to the rules for romanization of Greek. Initial attempts to coin names (while abundantly satisfying requirement #3 above) have so far failed miserably on requirement #4: chonthalaethian planets, ambroaethic planets, gaiapontic planets. Yikes!

The Tetrasomia, or Doctrine of the Four Elements, alludes to the secure fact that these planets are unknown compounds of metal, rock, ices, and gas. Tetrian planets, maybe? Suggestions welcome…

More than a decade ago, Fred Adams and I wrote a paper that wallowed into the slow motion disasters that can potentially unfold if another star or stars passes through the solar system.

Here’s the abstract:

Planetary systems that encounter passing stars can experience severe orbital disruption, and the efficiency of this process is enhanced when the impinging systems are binary pairs rather than single stars. Using a Monte Carlo approach to perform more than 200,000 N-body integrations, we examine the ramifications of this scattering process for the long-term prospects of our own Solar System. After statistical processing of the results, we estimate an overall probability of order 2×10^5 that Earth will find its orbit seriously disrupted prior to the emergence of a runaway greenhouse effect driven by the Sun’s increasing luminosity. This estimate includes both direct disruption events and scattering processes that seriously alter the orbits of the jovian planets, which force severe changes upon the Earth’s orbit. Our set of scattering experiments gives a number of other results. For example, there is about 1 chance in 2 million that Earth will be captured into orbit around another star before the onset of a runaway greenhouse effect. In addition, the odds of Neptune doubling its eccentricity are only one part in several hundred. We then examine the consequences of Earth being thrown into deep space. The surface biosphere would rapidly shut down under conditions of zero insolation, but the Earth’s radioactive heat is capable of maintaining life deep underground, and perhaps in hydrothermal vent communities, for some time to come. Although unlikely for Earth, this scenario may be common throughout the universe, since many environments where liquid water could exist (e.g., Europa and Callisto) must derive their energy from internal (rather than external) heating.

As one might expect, our scholarly efforts generated only a middling interest from the astronomical community, which soon faded and froze altogether. Science writers, on the other hand sometimes run across the article and write with questions.

I am doing a piece on rogue planets and the scenario that earth might become a rogue planet. I have found some stuff on this on the web and learned that you have done some research on rogue planets.

1. Why do you think rogue planets are so interesting?

From an aesthetic standpoint, there’s something compelling about a world drifting cold and alone through the galaxy, or even through intergalactic space. From a more practical standpoint, if rogue planets are common (as it appears may possibly be the case from the micro-lensing results) it is possible that the nearest extrasolar planet is not orbiting a nearby star, but is rather travelling through the Sun’s immediate galactic neighborhood, say within a few light years of the solar system.

2. Could earth become a rogue planet, and is there any guess, how probable this is? Let’s assume it would happen, what would most probably be the reason for that?

Earth could become a rogue planet if the solar system suffers a close approach by another star (or binary star). If another star passes within ~1 Earth-Sun distance from the Earth, then there is a good chance that the Earth would wind up being ejected into interstellar space. Fortunately, close encounters between stars are extremely rare. There is about a 1/100,000 chance that Earth will suffer this fate during the next five billion years. Those are very low odds, so in the grand scheme of things, we are in an extremely safe position. If we scale the galaxy down by a factor of ~10 trillion, then individual stars are like grains of sand separated by kilometers of empty space, and moving a meter or so per year. It’s clear that in such a system, a sand grain will drift for quite a long time before it comes close to another sand grain.

3. Could you speculate on how a human being on earth would experience the process of earth being kicked out of the solar system?

There would be plenty of warning. With our current capabilities for astronomical observation, the interloping star would be observed tens of thousands of years in advance, and Earth’s dynamical fate would be quite precisely known centuries in advance. The most dramatic sequence of events would unfold over a period of about two or three years. Let’s assume that the incoming star is a red dwarf, which is the most common type of star. Over a period of months the interloping star would gradually become brighter and brighter, until it was bright enough to provide excellent near-daytime illumination with an orange cast whenever it is up the sky by itself. It’s likely that the size of its disk on the sky would become — for a few weeks — larger than the size of the full moon, and vastly brighter. Like the Sun, it would be too bright to look at directly. After several more months, one would start to notice that the seasons were failing to unfold normally. Both the Sun and the Red Dwarf would gradually draw unambiguously smaller and fainter in the sky. After a year, the warmth of the sun on one’s face would be gone, and it would be growing colder by the day… Over a period of several more years, the Sun would gradually appear more and more like a brilliant star rather a life-giving orb. A winter, dark like the Antarctic winter, but without end, and with ever-colder conditions would grip the entire Earth.

4. What do you expect, how long humans could survive such an incident?

The Earth could not support its current population, but with proper planning, a viable population could survive indefinitely using geothermal and nuclear power. We would literally have a thousand years or more to get ready. Certainly, there are much worse things that could happen to humanity.

5. Would any life on earth survive?

Earth would effectively become a large space-ship, and with proper planning, a controlled biosphere (like in a large space colony) could be maintained. Were there no intelligent direction of events, and the Earth was simply left to its own devices, then surface life would freeze away, but the deep biosphere (the oil field bacteria, the deep sea vents, and other other biomes not directly dependent on solar energy) would persist for millions, if not tens of millions of years.

6. What do you think are chances that we will find an earthlike rogue planet?

This depends on what one means by “earthlike”. If one means a planet with Earth’s mass, at very large distance, say thousands of light years, the chances are very good that we will get micro-lensing detections within a decade or so. The data returned, however, will consist only of the likely masses of the planets. Nothing else.

I would estimate that the chances of finding a rogue Earth-mass planet within a potentially reachable distance, say within a light year, are about 10%. The chances, however, that this planet will have an interesting frozen-out surface environment that would please a Hollywood screenwriter are effectively zero. Most rogue planets get ejected from their systems very early in their parent star’s history, long before really interesting things have had a chance to happen from an astrobiological perspective.

This was no fruit of such worlds and suns as shine on the telescopes and photographic plates of our observatories. This was no breath from the skies whose motions and dimensions our astronomers measure or deem too vast to measure. It was just a colour out of space—a frightful messenger from unformed realms of infinity beyond all Nature as we know it; from realms whose mere existence stuns the brain and numbs us with the black extra-cosmic gulfs it throws open before our frenzied eyes.

H.P. Lovecraft, The Colour out of Space Amazing Stories, Vol. 2, No. 6 (September 1927), 557–67.

I’ve always thought that the Colour out of Space was H.P. Lovecraft’s best effort. One can argue about economy of expression, but the story is nearly unmatched in its attempt to confront — and imagine — the truly alien.

I think we currently have substantially less understanding of the extrasolar planets than is generally assumed. Thousands of planets are known, but there is no strong evidence that any of them bear a particular resemblance to the planets within our own solar system. There’s always a tendency, perfectly encapsulated by the discipline of astrobiology, with its habitable zones and its preoccupation with water — to make wild extrapolations into the complete unknown.

An interesting synopsis of much of what we do know can be gained by looking at the latest mass-radius diagram for the exoplanets. The number of planets with joint mass and radius determinations is growing rapidly, and the elastic virtue of a log-log plot fails to suppress the huge range in apparent planetary structures. To within errors, it appears that 6-Earth Mass planets range in radii by a factor of at least three. This is impressive, given that constant density implies R~M^{1/3}…

On the figure, I’ve plotted three potential mass-radius relations for super-Earths. This first (in Earth units) is the standard-issue M=R^{2.06} fit that one gets from the solar system planets (excluding Jupiter). The second (again in Earth units) is the vaguely alarming M=3R relation suggested by Wu & Lithwick’s transit timing analysis. The third mass-radius relation is what one might expect if planets form in-situ and accumulate low-density hydrogen envelopes around rocky cores. (Evaporative mass loss makes this more of an upper limit). Frustratingly, all three relations remain plausible.

It’s thus fantastic news that NASA’s TESS Mission has been selected for flight. TESS will find effectively all of the transiting Super-Earths orbiting the few million brightest stars, and with dedicated ground-based radial velocity follow-up, will — less than a decade from now — allow for a fantastically detailed version of the above plot.

Tau Ceti has street cred. Lying only 11.9 light years away, it is the second-closest single G-type star. It’s older than the Sun, and photometrically quiet. It’s naked-eye visible from both hemispheres, ensuring VIP seating at any SETI fundraiser.

And so what about planets? It’s been clear for a few years that Tau Ceti has a zeroth-order dissimilarity with the solar system. That is, if it had a Jovian-mass planet in a Jovian-like orbit, a press conference would have been dedicated to it several years ago. Indeed, because it is so bright and so quiet, Tau Ceti is among the handful of stars in the sky that are best suited to long-term high-precision monitoring via the Doppler velocity technique. It’s at or near the top of the list for all of the major Doppler surveys.

Tau Ceti displays a marked excess luminosity in the far-infrared. Blotchy sub-millimeter images imply that this excess luminosity arises from a wide ring of cold dust at Pluto-like distances from the star. In this picture, the radiating dust arises from ongoing collisions within a Kuiper belt-like disk comprising roughly an Earth-mass worth of icy asteroidal bodies:

Tau Ceti’s Kuiper belt seems to be about ten times more massive than our own Kuiper belt, despite the fact that Tau Ceti’s metallicity is only about one-third that of the Sun. There’s little risk in hypothesizing (read hand-waving) that the low metallicity of Tau Ceti’s protoplanetary disk meant slow growth for Tau Ceti’s retinue of proto-Jovian cores, which subsequently missed out on rapid gas accretion. The ensuing presence of Neptunes, and the concomitant absence of a Jupiter, generated a different dynamical history compared to the Solar System’s — namely one with more stuff left over at the end of the day in the icy outer reaches.

Given this picture, the a-priori odds are excellent that Tau Ceti resembles tens of billions of ordinary, single Population I stars in the galaxy and also harbors multiple inner planets with masses between Earth and Neptune, on nearly circular, nearly co-planar orbits with periods of 100 days or less. Should such worlds exist in orbit around Tau Ceti, then it’s likely that sufficient radial velocity data now exist to dig them out…

Readers surely noticed the paper by Mikko Tuomi and colleagues that was posted to astro-ph earlier this month. Tuomi and collaborators report on a joint analysis of three large-N data sets that comprise thousands of radial velocity measurements (from HARPS, KECK and AAT) spanning a total time base line in excess of 13 years. Ideally, one would like have a fully definitive conclusion emerge from such a massive data set, but frustratingly, Tau Ceti is holding its cards very close to the vest, and as radial velocity half-amplitudes inexorably drop below K=1 m/s, this will be an increasingly common behavior from other nearby high-value stars. In their arXiv preprint, Toumi et al. lay off their risk and remain ambiguous regarding actual detections of actual planets, providing only a fully hedged speculation at the end of the abstract, that these “periodicities could be interpreted as corresponding to planets…”

The modeling strategy for Tau Ceti taken in the Tuomi et al. paper provides an alternative to the approach adopted by Dumusque et al. in digging the K=0.5 m/s Alpha Cen Bb out of a similarly challenging data set. For both systems, the authors adopt the stance that it is no longer sufficient to write off excess scatter in radial velocity fits as “stellar jitter”. Dumusque’s team developed a physical model for starspot activity migrating latitudinally on a differentially rotating star, and also modeled the convective blueshift arising from stellar activity. Application of these physical models spurred the removal of systematic “noise” from the time series, thereby revealing a candidate Earth-mass planet in a 3.2-day orbit. Tuomi et al. excavate five potential planets by exploring the use of ARMA(p,q) — AutoRegressive Moving Average — models which recognize that (in addition to a Keplerian signal) both the value of given velocity measurement as well as its accompanying error are potentially correlated with previous measurements. ARMA models and their generalizations, ARCH, GARCH, NGARCH, etc., are an old standby for modeling financial time series. Near-term VIX predictions anyone?

Indeed, planet detection and trading have certain similarities. Noisy signals, non-stationary processes, cut-throat competition, and the opportunity to land yourself in the media spotlight when things go awry.

And the possible planets? Should the signals isolated by Tuomi et al turn out to be both real and Keplerian, then Tau Ceti will join the legions of stars in the galaxy that harbor fully ordinary planetary systems.

Galileo’s unveiling of Io, Europa, Ganymede and Callisto is unarguably shortlisted for the most important astronomical discovery of all time. The Galilean satellites constitute a planetary system in miniature, and their clockwork presence is a centerpiece of Newton’s De mundi systemate.

And indeed, if one bases one’s expectations for exoplanetary systems on the Jovian satellites (as well as the regular satellite systems of Saturn and Uranus) then the startling abundance of compact systems discovered by the Geneva Team and by Kepler are hardly startling at all. The Galaxy’s default planetary system — as expressed around many, if not most of its stars — has a handful of planets on near-circular orbits, with periods ranging from days to weeks, and masses of order one part in ten thousand of the central star. Out here in the sticks, near the Sun, we’ve got an Earth, yes, but unlike most stars, we have no super Earths.

There is an intriguing, seemingly anti-Copernican disconnect between the solar system and the extrasolar planets. Much of the theoretical framework of planet formation is based on the paradigm provided by the Minimum Mass Solar Nebula (MMSN), the $\sigma \propto r^{-1.5}$ disk of net solar composition that is required to account for the solar system’s planets. In the standard formulation, the MMSN holds its power-law form inward to about 0.5 AU, where it meets a murkily indistinct inner boundary that’s needed to account for the lack of anything interior to Mercury’s orbit.

Interestingly, the MMSN fades out just where the super-Earths really start to appear. This has led to the widespread assumption that planets somehow form at large radii and then migrate long distances in order to be found in their observed orbits. That seems rather odd.

Eugene Chiang and I have been exploring an alternative idea — namely that the solar system doesn’t present a good starting template for studying extrasolar planets, and that planets, in general, don’t migrate very far (if at all). Could it be that the huge population of super-Earths formed right where they are observed? If that’s the case, it makes life simpler, and it implies that the template we’re after is the Minimum Mass Extrasolar Nebula (MMEN), which can be defined by grinding up the planets that have been observed by Kepler, and which is not all that different from what one gets if one simply takes the MMSN and runs it all the way into the dust sublimation boundary at ~0.05 AU.

Our paper is available at arXiv.

A few weeks ago, I got an e-mail from a reporter related to a story that will feature favorite space photos:

We’re hoping some space-themed photo comes to mind, either a picture taken by a space telescope, or by yourself from your own backyard, or anything else that relates to space. We’d also welcome any comments about the photo’s meaning to you.

I think my favorite space photo is the Voyager image of the crescent Neptune and Triton.

For two reasons. First, there’s no false color, no artifice, no agenda. This photograph is calming, mysterious and aesthetically perfect.

Second, the image is dominated by the night side of Neptune. Implicit in the photograph is the amazing fact that it was taken from a vantage that was further than the Sun than the planets. Less than one Neptune orbit elapsed between its discovery in 1846 and the Voyager flyby in 1989. A crescent Neptune seems to me far more subtly profound than the iconic “pale blue dot” image taken by the same spacecraft not all that long thereafter.

Image source: Drew Detweiler

The Pythagorean version of the gravitational three-body problem is very simple to state.

Assume that Newtonian Gravity is correct. Place three point bodies of masses 3, 4, and 5 at the vertices of a 3-4-5 right triangle, with each body at rest opposite the side of its respective length. What happens?

This particular problem seems to have been first posed in the late 1800s by the German mathematician Meissel, who mysteriously asserted that the motion of the three bodies should be periodic. That is, he felt that they would come back to their exact starting positions after executing a complex of intermediate motions. A first attempt at the solution — using numerical integration with a variable stepsize — was published in 1913 by Carl Burrau. He was able to map out the intial trajectories through several close encounters, but he was unable to integrate far enough to determine what eventually happens.

The correct solution was found in 1967 by Szebeley and Peters, who used the technique of three-body regularization to resolve the succession of close encounters. Here’s one of their diagrams showing a segment of the complicated motion.

The Szebehely-Peters paper is fun to read. It emphasizes that this nonlinear problem is surprisingly tricky to solve, and that it shows the classic sensitive dependence on small variations in the initial conditions. For example, here’s a link to a recent, attractively rendered YouTube video that animates the trajectories and osculating orbits, as obtained via an implementation that uses Mathematica’s NDsolve.

Screenshot source.

Unfortunately, however, a careful analysis shows that the motion from 2:47 through the end of the video is completely incorrect…

I’ve always been struck by the fact that there’s a fascinating subtext to the trajectories of the three bodies if they are interpreted as a narrative of interpersonal relations. An initial value problem for a set of six coupled, first-order ordinary differential equations unfolds to telegraph a drama of attraction, betrayal, redemption, triumph and loss.

This summer, I had an opportunity to collaborate on the development of a scored, choreographed 3-minute 45-second performance of the problem which was premiered last month at the ZERO1 Biennial in San Jose. Our goal was to simultaneously convey the interpretive subtext while adhering to an fully accurate set of trajectories. It took a lot of work and was quite an intense experience. From the description at the ZERO1 site:

Three dancers in illuminated costumes create a live video visualization of the elliptic-hyperbolic solution to the classic Pythagorean three-body problem. A custom light tracing application detects light emitted from LEDs on the dancers’ soft circuitry costumes to create a visual model of their trajectories across the 2D plane of the stage. This realtime graphic visualization is projected on a large screen behind the stage in order to provide the audience with a birds eye perspective of their complex motion.

The use of digital technologies presents challenges for contemporary choreographic methods as data visualization guides movement through performative space on scientifically accurate trajectories. Live accompaniment from three musicians enhances physical performance as each body is interpreted through movement and sound. Feelings of longing, connection, and isolation are intertwined as the bodies are flung apart by the same gravitational forces that draw them together.

(That last sentence could more properly read, The bodies are flung apart despite feeling only attractive gravitational forces.)

To give a better sense, here are some notes and diagrams from mid-way through the process, as the choreography and the rehearsals were beginning to gel.

It’s particularly fascinating how the immediate outcome of the near-return to the pythagorean condition at the halfway mark is so different from how things unfold at the start of the piece. I like the interpretation that body 4 is somehow lazy at this point, or late to realize the import of the situation, and is marginalized as a result. This is the first real opportunity for bodies 3 and 4 to express emotion — shock for body 4, joy for body 3.

In the following measures, body 4 is marginalized, sulky, scheming, whereas body 3 is doing its best to impress, in the set of looping, private engagements. A reverie! The successive body 3-5 interchanges should _highlight_ the difference in masses between 3 and 5. Body 3 is light footed, fleet, body 5 glides smoothly, deliberately, (but not dully) as an anchor.

Body 4 must come back from its runout with a renewed sense of determination and purpose. The ensuing encounter between 4 and 5 must somehow convey 4’s charms and strengths. In a very real sense, this encounter is the tipping point that determines the outcome for all time. This is where the youtube video went off the rails.

As a consequence, there should be a sense of unfulfillment in the next body 3-5 encounter (a grasp, a gaze that fails to connect?) which sets up 3 to dive through on the way to its penultimate run-out. In this sequence, body 3 must somehow fail to live up to the expectations that it so brightly promised. The outcome is now determined, and the bodies know it, although the audience doesn’t.

While body 3 is at the arc of its final run-out, body 4 is weaving a spell on body 5, cementing the outcome ever more decisively. Indeed, Body 5 is only briefly engaged as 3 makes its final dramatic run through body 4 and 5’s orbit. The final sequence of encounters between body 4 should grow ever more identical, signaling the finality of the outcome.

Full-size (1536×2048) .gif images: one, two.

We went up to Mount Hamilton yesterday afternoon, and, as was the case for everyone who saw the transit, it was a unique conjunction of time, place, and circumstance.

The Lick Observatory staff deployed the historic 36-inch refractor to extraordinary advantage. Rather than project the image, which has the effect of divorcing the instrument from the event, they removed the eyepiece and stretched a cloth across the focal plane. The resulting effect, somehow, was to seamlessly integrate the transit into its surroundings and its historical context, 1639, 1761, 1769, 1874, 1882, 2004, 2012…

Time slips by. It’s now been more than six years since launch and more than five years since the New Horizons probe got its gravitational assist from Jupiter. I looked back through the oklo.org archives and found a post covering the event.

One day, one hour, and nine minutes ago, the New Horizons spacecraft sailed flawlessly through its closest approach to Jupiter. A day later, Jupiter still looms large in New Horizon’s field of view, with an angular size more than five times greater than the size of the full moon in our sky.

That was on March 1st, 2007, a day after the 500 point drop in the DJIA that signaled the first shudder of unease portending the global financial crisis.

Oklo.org and New Horizons have both been gradually slowing down over the past six years, with New Horizons passing the orbit of a planet at roughly the cadence of 100 additional oklo posts. New Horizons is currently 9 AU from Pluto, and will arrive in the system in July 2015.

I discovered from reading the wikipedia page that a third circumbinary satellite was recently found in orbit around Pluto and Charon.

The three small moons in the Plutonian system are surprisingly reminiscent of what we might expect a typical circumbinary extrasolar planetary system to look like: orbital periods measured in weeks, masses of order a part in ten thousand of the central binary, low eccentricities, and orbits that are close to, but not in mean-motion resonance. During the next few years, as the Kepler data continues to roll in, and as the eclipsing binary systems in Kepler’s field of view are carefully scrutinized, we’ll find out whether such properties are indeed the norm.

The ring of geosynchronous satellites and the global web of submarine cables constitute two of planet Earth’s most remarkable physical features. The moment I press Publish, the diagram just below will be sent — encoded in modulated light — on a profusion of undersea journeys from the Bluehost servers in Utah to Japan, Europe, Australia, South America and beyond. Optical wavelengths are small, the speed of light is fast, and the quantity of data that can be transmitted on optical fiber is impressive. A fairly recent lab-based data transport record involved multiplexing 155 channels, each carrying 100 Gbit/s over a 7000 km fiber.

For the impatient, however, the latencies of the long-haul international fiber connections are something of an issue. The index of refraction in glass is n~1.5, and the cable routes don’t adhere to the great circles. Using NTT’s Looking Glass service, one can run traceroute between far-flung nodes on the Internet. For example, right now, round-trip travel times between London and Tokyo are taking about 265 milliseconds, with routing that runs on the Atlantic and Pacific Ocean bottoms and (effectively) along Route 66:

A quarter of a second round-trip is pretty slow. Light traveling in vacuum along the 9602 km great circle connecting London and Tokyo would do the round-trip in 64 milliseconds, a factor-of-four improvement. Things should get better in 2013, however, when the Arctic Link cable connects Japan to Britain via the Northwest Passage. This line will run at 170 milliseconds round trip.

Even with global warming lending a helping hand, it’s a hassle to lay cables over the top of the planet. A more effective plan is to go straight through. The straight-line distance through the Earth from London to Tokyo is 8719km, implying a minimum round-trip of only 58 milliseconds.

It was thus rather interesting to read of the first actual demonstration of signaling by neutrinos posted to arXiv earlier this month. A team at Fermilab reports that they have established a neutrino communication link with a data rate of 0.1 bits/sec and a bit error rate of 1% over a distance of 1.035 km, along a path that includes 240 m of solid Illinois dolomite.

A one or a zero every ten seconds is very similar to the bit rate that one gets with smoke signals. It’s a staggeringly long way from the petabit-per-second transmission rates that one can currently achieve with a strand of freshly lit fibers. Nonetheless, it’s an exotically high-tech accomplishment, and so it’s fair to overlook the abysmal bandwidth and error rate. What I would like to criticize, however, is the completely lame initial message that was transmitted over the neutrino link: N-E-U-T-R-I-N-O.

Jeez. Did none of the 113 authors of Demonstration of Communication Using Neutrinos appreciate that style is paramount when one is performing expensive high-profile stunts?

In Stancil et al.’s defense, though, the contents of historic first messages have generally been sorely lacking in pizazz. Alexander Graham Bell’s first telephone call consisted of “Watson, come here! I want to see you!” Even worse, was the unreadably uncompressed purple prose transmitted (over the course of 19 hours) on August 16, 1858 as a part of the first transatlantic telegraph messages between Queen Victoria and President Buchanan:

“it is a triumph more glorious, because far more useful to mankind, than was ever won by conqueror on the field of battle. May the Atlantic telegraph, under the blessing of Heaven, prove to be a bond of perpetual peace and friendship between the kindred nations, and an instrument destined by Divine Providence to diffuse religion, civilization, liberty, and law throughout the world.”

Had I been part of the arXiv:1203.2847 author list, I would have agitated to turn the contents of that first message over to the inimitable Oscar Wilde:

“It is a very sad thing that nowadays there is so little useless information.”

Enceladus, Dione, Titan, Mimas and Saturn.

On Tuesday, Venus reaches its maximum elongation of 46 degrees from the Sun. Thereafter, its angular separation from the Sun steadily decreases until June 6th, when it undergoes transit.

Transits of Venus are newsworthy because they are rare. Venus’ orbit is inclined by 3.4 degrees relative to the ecliptic, and so Earth must be near Venus’ nodal line if a transit is to be observed. The last one occurred in 2004, and the next one after June 6th will occur in December 2117. When talking transits-of-Venus in this day and age of astronomers flossing their “premium-platinum” frequent flyer status, it’s hard to resist that obligatory mention of Guillaume Le Gentil, whose unsuccessful expedition to observe the 1761 transit took 11 years, and had him returning to Paris in October 1771, only to find that he had been declared legally dead and been replaced in the Royal Academy of Sciences. His wife had remarried, and all his relatives had “enthusiastically plundered his estate.”

Nobody’s estate gets enthusiastically plundered on account of transits of the solar system’s Jovian planets by the solar system’s Jovian satellites. Many of the larger moons of Jupiter, Saturn and Uranus orbit with very small inclinations to the host-planet equatorial planes. As a result, it’s possible to get pictures such as the splash image for this post, with a whopping 4 moons transiting at once, without having to wait around for centuries.

Loosely speaking, eccentricities and inclinations are dynamical bruises acquired during the formation process. When the assembly of a system occurs in a quiescent, dissipative setting, then orbits wind up closer to circular and closer to co-planar. Violent interactions in the absence of dissipation produce systems that are more distended. To get a feeling for this, I gave a 3D-normal distribution of random impulsive kicks with standard deviation 0.003*v_circ to an aggregate of initially co-planar and circular orbits. The resulting distribution of inclinations and eccentricities, plotted as a locus of gray points, is reminiscent of the bulk of the Jovian satellites (blue points):

Cranking up the magnitude of the impulsive kicks by a factor of ten yields a distribution of eccentricities and inclinations that looks better suited to the actual planets in our solar system (green points). Note that Mercury and Iapetus fall outside the diagram.

The big surprise from the Kepler mission has been the large number of systems that display multiple transiting planets. Kepler sees plenty of set-ups that contain four, five, and even six individually transiting planets. This distribution is startling, however, only if one draws on the solar system as the template for expectations. Had the preconceived notions been drawn from the regular satellite systems of the Jovian planets, then the statistics would seem completely unsurprising.

A recent preprint by Figueira et al. describes a consistency analysis between the results of the HARPS and Kepler surveys. They find that the two distributions can be reconciled (and the large number of multiple-transiting planet systems accounted for) if planet-planet mutual inclinations are generally less than one degree.

This implies that the eccentricity measurements that have been published to date for low-mass planets are likely to contain a substantial number of overestimated e‘s…

Kraftwerk will be playing eight shows in April at the MOMA, but all eight sold out well before I even found out about it. Getting clued in at this late date is a bit like finding out about a new hot Jupiter orbiting a 14th magnitude star — given that its already March 2012, it’s marginally (or not even) publishable on its own.

The ability to make good predictions prevents one from being perennially late to the game. A good prediction is one that has both accuracy and utility, and for the past two decades, the field of extrasolar planets has been sorely lacking in predictions that make good on either virtue. Yet it didn’t have to be that way! Like many others, in the early 1990s, I was perfectly well aware of Goldreich and Tremaine’s 1980 paper which lays out the essential principles of disk migration.

Even if one only read the abstract, it was very clear that the prospect of Jupiter-like planets on short-period orbits was well worth exploring further. Another example is provided by the Kozai mechanism, that relatively straightforward phenomenon first described in the early 1960s that derives directly from the physics and assumptions underlying the circular restricted three-body problem. With simple models for tidal dissipation thrown in, it could have been clear long ago that visual binary stars have the ability to produce Jupiter-like planets with orbital periods of order a week.

Admittedly, to hear such grousing and second-guessing is like sitting next to a losing bettor on the train back from the track. The productive approach is to keep an eye open to all the equally starting predictions that are yet to be made and which can potentially lead to substantial future profits.

With that lead-in in mind, its very interesting to read the recent abstract of Perets, Kratter and Kenyon (which, I’m told, will soon be followed-up by a substantial paper). Perets and collaborators run up the score with a basic point that definitely falls in the should have thought of that myself category: Mass loss in binary evolution alters the zero-velocity surfaces available to a planet that starts life stably in orbit about one member of a binary pair. As the system experiences stellar evolution, with one or both stars losing substantial mass to red giant winds, a planet is able to radically alter its trajectory, and indeed, can wind up orbiting the opposite member of the pair. Tidal friction can then be invoked to elicit a permanent capture.

There’s a cool paper by Elbert E.N Macau from 2000 which draws on a similar idea to put a spacecraft on a low-cost slow-boat trajectory to the Moon. In this case, the impetus is provided by a weak rocket rather than mass loss, but the principle is similar:

Figure 4 from Macau, E. E. N. Acta Astronautica 47, 12, 871-878: Starting from a circular parking orbit around the Earth, a thrust is applied to inject the spacecraft into a chaotic region. The spacecraft is then left to move freely in the chaotic region. The uncontrolled trajectory can eventually reach the Moon. In this example, it takes approximately 8 years to reach the vicinity of the Moon. However, after that, the spacecraft quickly leaves the Moon.

Perhaps the most interesting aspect of planetary orbital transfer in evolving binary systems is that it provides a plausible mechanism for delivering Earth-sized worlds to long-lived potentially habitable orbits in the vicinity of white dwarfs. As described in this post from last July, such worlds, when they transit, can be detected from the backyard…

It’s hard to miss Jupiter and Venus in the early evening sky right now, and later this week, on March 15th at 10:37 UT, they will reach an impressive conjunction, with Venus near maximum elongation (separated by 46 degrees from the Sun) and Jupiter only 3.3 degrees from Venus.

At the time of conjunction, Venus will have an apparent magnitude of V=-4.2 and Jupiter will be at V=-1.9. They are thus both brighter than Sirius, and the display is all the more impressive because the planets are still well above the horizon at the end of astronomical twilight.

The combination of the HARPS Survey and the Kepler data are indicating that the architecture of our solar system is — to at least a modest degree — somewhat unusual. If we were living in a run-of-the-mill planetary system, we could expect to have several planets with ~2x Earth’s radius orbiting with periods of 100 days or less, along with no Jupiter in a Jupiter-like orbit. A pair of standard-issue sub-Neptunes would appear substantially brighter than Venus in the dusk and dawn skies, but night-time displays as impressive as the one we’ve got now wouldn’t occur, since the maximum elongations would be ~30 degrees or less.

Jupiter’s distance from the Sun puts the regular motions of the Gallilean satellites just outside the reach of naked-eye observability, and in a similar vein, Venus’ size and semi-major axis leave it just on the threshold of displaying visible phases. If our eyes were just a little better, the “Copernican Revolution” wouldn’t be a cliche, and Archimedes would have come up with the Universal Law of Gravitation.

Our night sky does, however, give us one very nice order-of-magnitude foothold. The apparent brightness of the outermost visible planet, Saturn, falls exactly in the magnitude range populated by the brightest stars. For example, when Saturn’s rings are at a less-than-full opening angle, the planet has a nearly identical apparent brightness to Alpha Cen A. This means that if one knows the AU, has the telescopic ability to resolve the disk of Saturn, and makes the (shaky) assumption that the brightest stars are Sun-like, and the (less shaky) assumption that Saturn is highly reflective, the distances to the nearest stars can be estimated. Very roughly,

which is close to the true 4.4 light year distance. (A version of this argument was used in the late 1600s to get the first real estimate of the staggering separations between the stars.)

If one also assumes that stars travel at relative speeds that are similar to the velocities with which the planets orbit the Sun, then an extension of the ball-park argument indicates that the configuration of the night sky should be radically altered on a timescale of millions of years. This is indeed the case. There was a cool 1998 article in Sky and Telescope that used the (then-new) Hipparcos data to compute the brightest stars within the last and next five million years. At the dawn of the Pliocene era, Epsilon and Beta Canis Majoris were both of similar brightness to Venus.

There’s an interesting article in today’s New York Times about Brewster Kahle’s archiving efforts. In addition to founding the Wayback Machine to catalog historical snapshots of the near-complete Internet, Kahle is also Noah’s Arking print books in forty-foot shipping containers.

The Internet Archive’s records for the Extrasolar Planet Encyclopedia (now at exoplanet.eu, but formerly at http://www.obspm.fr/encycl/encycl.html) stretch back to 22:58:15 October 9th, 1999, at the frenetic height of the Internet bubble.

It was a very different world back then. All of the salient details of the galactic planetary census could be jotted down on an index card:

Fast-forward to the Rightnow Machine. There are roughly 3,000 extrasolar planets known, and the Kepler Mission’s latest public candidates table contains various stellar, planetary, and orbital measurements related to 2,323 “objects of interest”. The uncompressed ASCII file containing the table is 454Kb, which, in a certain sense, is a fairly significant amount of data. It would take a week or two (~80 hours) of full-time effort to write that table out by hand. Certainly, it contains enough information to generate numerous exploratory diagrams that seek correlations — diagrams that seek to explain.

For example, as shown in the Batalha et al. paper, when the radius ratio-period diagram is color-coded with the number of observed transiting planets in the system, it is clear that that the hot Jupiters are predominantly singletons. That’s a point of evidence in favor of production mechanisms such as Kozai Cycles with Tidal Friction, which don’t go along to get along where the smaller planets in the system are concerned.

With all those records and all those fields, one naturally makes an effort to increase the dimensionality by coloring and sizing the points. Exoplanet.org provides a very flexible facility for exploring along these lines. In the following plot, the color scale is keyed to the mass of the parent star and the point size is keyed to the logarithm of the orbital period.

Edward Tufte has repeatedly stressed that a really good data graphic is one that rewards careful study. In my view, the gold standard for such diagrams are high-resolution maps that combine seismographic event data with a Digital Elevation Model.

The above diagram shows California seismicity over the past several decades, combined with elevation data from the Shuttle Topography Mission. Like the exoplanet diagrams, it shows curious clusters of points. The correlations with the physical landforms are fascinating, and it’s interesting to study the diagrams while imagining that our understanding of the Earth system is only at the level of our understanding of extrasolar planet formation and evolution. In some places, such as along the San Andreas Fault, it is clear that the topography and seismicity are inextricably linked. In other places, however, similar landforms are bereft of any Earthquake epicenters. Why the huge cluster near Mendocino? The diagram is incredibly good at setting the mind to work. What’s going on with that completely quiet section of the San Andreas fault?

There is interesting potential, furthermore, for improvement in these particular diagrams with respect to the display of the seismic information. Earthquake magnitudes and times, for example, are not indicated, and the red data points have immense overlap in the seismically active regions. The real depth of the diagrams is generated by the topographic data, in which shading is keyed to gradient, and color is keyed to elevation, an incredibly effective way of increasing dimensionality.

It’s likely that everyone who reads this site has already seen the new Kepler candidates paper. Drawing on 16 months of photometric data, and importantly, on significant improvements to the reduction pipeline, it gives details on 2,323 planet candidates. The cumulative planet candidate table, in particular, makes for interesting reading.

In true Gordon Gekko style, I ran the new candidates table through my valuation formula (see here, here, and here.)

A screenshot of the results, for candidates with valuations greater than ten dollars are shown below. KOI 2650.01 and KOI 2124.01, assuming that they hold up, are both million dollar worlds. The total value of the current catalog is 10.9M.

Hey! Did you see the New York Times article about the discovery of a Jupiter-like planet orbiting Barnard’s Star?

The subtly out-of-date fonts are really the only indication that the above article, which was printed on April 19th, 1963, is nearly a half century old. Certainly, the blandly uninformative expert commentary and the worn-smooth assertion that the new finding adds support to the conviction of astronomers that a great many solar systems exist, some of them possibly supporting life, are both still fully serviceable.

The erstwhile planet(s) orbiting Barnard’s star were the fruit of thousands of astrometric measurements of photographic plates taken from 1938 through 1962 by Dr. Peter van de Kamp and his students from Swarthmore College’s Sproul Observatory. During the 1960s, the existence of van de Kamp’s planets were generally accepted by the astronomical community, and they only began to drift out favor during the 1970s. As explained in this interesting historical review of exoplanet detection, it’s now clear that the apparent astrometric motions of Barnard’s Star over the years can be correlated with telescope adjustments. Modern radial velocity measurements from UVES at the VLT and from the HET telescope show quite definitively that van de Kamp’s planets don’t exist:

Indeed, there must now be enough radial velocity observations of Barnard’s star to put some very interesting limits on any planets that might be lurking in the system… Given that the star is so bright (for a red dwarf) with V=9.5, highly charismatic, and visible from La Silla, I think it’s safe to say that for orbital periods of less than ~100 days, the largest planets that could be hiding there have masses roughly twice that of Earth.

Broadly speaking, the non-hydrogen/helium mass of a planetary system is ~0.02*0.016*Mstar*(10**[Fe/H]). We therefore don’t expect to find bruisers of planets orbiting Barnard’s Star, which has only ~14% of the Sun’s mass, and has a metallicity of order 10-30% that of the Sun. Given what we now know about the galactic planetary census, an educated guess is that Barnard’s star harbors several roughly co-planar planets, none larger than 1.5 Earth masses, with orbital periods less than 100 days. In fact, I think there’s an even chance that within the next four years, we could be reading about just such a system in the New York Times.

Following the 1846 discovery of Neptune by Urbain J. J. LeVerrier of France and Johann Galle of Germany, the British astronomical establishment — the Rev. James Challis, the Astronomer Royal George Biddell Airy, and Sir John Herschel — found themselves in rather hot water. Diffidence, seeming indifference and miscommunications had deprived Britain of a very tangible emblem of national prestige. In the damage-control scramble that ensued, Herschel wrote urgently to William Lassell, a wealthy brewer in Liverpool who owned a 24-inch telescope, exhorting him to search for satellites “with all possible expedition!”. Lassell was on task. A mere 17 days after the announcement of Neptune’s existence, he had discovered Triton, thus handing his countrymen a victory in the losers’ bracket rounds.

The quick discovery of Triton occurred in large part because astronomers were conditioned as to what to expect. Jupiter, Saturn and Uranus all host regular satellite systems in which the orbital periods of the satellites are measured in periods lasting days to weeks, and in which the mass ratio of the satellites to the primary is of order two parts in 10,000. These rules of thumb hold quite nicely, despite the fact that Jupiter has more than 20 times the mass of Uranus.

Much of the bewilderment that has accompanied the discovery of extrasolar planets stems from the fact that planets found orbiting other stars don’t bear much resemblance to configuration of our own planetary system. First, hot Jupiters. Then giant planets on highly eccentric orbits with periods of a few hundred days. And now, the realization that over half of the sun-like stars in the solar neighborhood are accompanied by planets with masses in the superEarth/subNeptune range and orbital periods of less than 100 days. It’s now clear, in fact, that our own solar system is unusual at least at some modest level, and perhaps at quite a significant level.

As hordes of new planets pile into the candidate tables at exoplanet.eu, the correlation diagrams are really beginning to show the true features of the galactic planetary census. The classic log-log mass-period diagram is a good example. Here’s one that’s (already) two months out of date:

The lower-right portion of the above diagram is incomplete, and there are a whole slew of observational biases at work, but nevertheless, the relatively depopulated divisions between the superEarth/subNeptunes, the hot Jupiters and the eccentric giants are real features of the planet distribution. There’s truth in the fact that one can sometimes overlook the forest for the trees. By smearing vaseline on the laptop screen and taking a cell-phone photograph, one obtains a better sense of the outlines of the forest:

It’s interesting to adjust the log-log mass-period diagram so that the y-axis charts the planet-to-star mass ratio rather than planetary mass (an advantage of logarithms is that concerns regarding the difference between M and Msini are effectively academic). With this plotting scheme, Earth and Jupiter are still off the guest list, but remarkably, the regular satellites of the Jovian satellites adhere to the same distribution as the superEarths and subNeptunes:

A comparison that’s made all the more dramatic with the inclusion of the Kepler multiple-transit candidates:

A coincidence? I don’t think so.

In a logarithmic sense, the largest gap in mass among the planets in our solar system lies between the Earth (which has, unsurprisingly, one Earth mass) and Uranus, which is 14.536 times more massive than Earth. One of the most interesting facets of the ongoing detection of extrasolar planets is that we’re now getting real information on planets that fall into this previously unobserved planetary regime.

Indeed, the most startling exoplanet-related revelation of the past few years has been the announcement by the Geneva Planet Search Team that planets in the Earth-Uranus gap are extraordinarily common. Their take-away message has consistently been that 30%-50% of the quiet solar-type stars in the Sun’s neighborhood harbor at least planet with Msin(i)<17 Earth masses, and an orbital period of less than 50 days. Tens of billions of worlds! The Milky Way Galaxy is essentially a Costco full of HD 40307 b’s, c’s, and d’s.

With super-Earths and sub-Neptunes out there in such quantities, it’s not surprising that the Kepler mission has returned a large number of candidates. Rather alarmingly, however, it appears at first glance that Kepler may be seeing significantly fewer planets than the Geneva Team’s predictions might imply. Given a 40% overall occurrence rate of planets with P<50d and mass between Earth and Neptune, and assuming one planet per star, there should be ~60,000 potentially detectable planets orbiting the 150,000 target stars in Kepler’s field of view. For planets in orbits of 50 days or less, the geometric probabilities of transit lie in the 1-15% range. Taking a 5% transit probability (a 10-day orbit) as a benchmark, one ball parks that the number of sub-Neptune-mass planets that Kepler would have been able to detect is ~3,000. If we use a simple mass-radius scaling law, we find that a bit less than 1,000 of Kepler’s planet candidates fall in the sub-Neptune mass range. Naively, it thus seems that the Geneva team’s occurrence rate appears to overestimate the number of planets that Kepler would have detected by a factor of around three.

So what’s up? It seems a-priori highly unlikely that either Kepler or the HARPS analysis pipeline have made a significant error. In collaboration with UCSC Grad student Angie Wolfgang, we’ve made a very detailed attempt to compare the two observational programs, with the goal of seeing whether there’s a sensible way to bring the two surveys into agreement. This task is tricky because Kepler employs transit photometry, where as the Geneva Team’s results are based on radial velocity measurements from HARPS.

To see the details of our work, have a look at the paper that we’ve recently posted to arXiv. The bottom line is that concordance can be obtained, provided that there exist two very different planetary populations in the sub-Neptune mass regime. One population, which is numerically dominant, consists of dense scaled-up terrestrial planets, super-Mercuries if you will. The other population (to which Kepler is selectively sensitive) consists of planets with much lower densities, akin to scaled-down versions of Uranus and Neptune.

Image Source.

Sometimes, you just get these serendipitous moments. Yesterday, in the parking lot of the grocery store, there was a U-haul rental truck sporting a remarkably sophisticated graphic that explains the Manson impact structure in Iowa. When I got home, I went to the U-haul website, and discovered that they have a clear and beautifully self-contained tutorial on giant impacts. The site even explains the terms in the ballistic range equation, which gives the distance from impact that a piece of ejecta lands, given the radius and gravitational acceleration of the Earth, along with the ejection angle and the ejection velocity. And for those wanting more details, U-haul points to Jay Melosh’s Impact Cratering: A Geologic Process (one of the Oxford Monographs on Geology and Geophysics).

Inside the grocery store, at the checkout counter, I noticed that this week’s issue of The Sun is carrying a rather startling astronomically themed story:

Which brings me to the serendipity. Tomorrow afternoon, I’ll be engaging in a joint presentation/discussion with Chris McKay of NASA’s Ames Research Center on the topic of “Real Doomsdays: How Life Could End on Earth”. We’ll be discussing not just the long-term fate of life on Earth, but also the fate of the Earth itself. And indeed, a black hole plunge is one of a handful of fates that Earth might suffer in the ultra-distant future. If our planet isn’t engulfed by the red giant Sun, then it’ll eventually either be ejected into the utter isolation of the exponentially expanding intergalactic medium to slowly evaporate via nucleon decay, or it’ll wind up in the Milky Way-Andromeda central black hole. Presumably, that’s the eventuality that the editors of this week’s Sun are referring to.

Anyway, here are the details. The event is free, and is organized by Tucker Hiatt and the Bay Area Wonderfest organization:

WHO: UC Santa Cruz astrophysicist Greg Laughlin and NASA planetologist Chris McKay

WHAT: “Real Doomsdays: How Life Could End on Earth”

WHERE: Roxie Theater, 3117 – 16th Street, San Francisco

WHEN: 1:00-2:30 PM, Sunday, August 28, 2011

Image: ASTEP Telescope — Yan Fantei-Caujolle (2009)

Ready or not, HD 156846b, is less than a day away from its much-awaited periastron passage and transit opportunity. Let’s have a show of hands: If it’s dark, if the star is up (RA 17 20, Dec -19 20), and if you’re capable of 1% photometry, then you should be out there on the sky!

Mauro Barbieri, who led the HD 17156b transit discovery back in 2007, has been working very hard behind the scenes to orchestrate observing campaigns in various spots around the globe. This morning, he sent me three nights of baseline photometry from Claudio Lopresti, who has been observing from Italy. These baseline observations show how the increasing air-mass will likely lead to a downward drift in the light curve near the end of tonight’s observing session. If the best-fit prediction turns out to be correct (and assuming, of course, that the planet defies the geometric odds and actually occults the star) then it will be tough to convincingly bag the transit from southern Europe. The party, however, could easily start early…

Observatories in South America have a better chance. For example, at La Silla, there are ~6 hours during the 1-sigma transit window when it is both dark and when the star is at an air mass of less than two. Unfortunately, however, at the moment, the weather forecast for La Silla does not look good. The forecast at Cerro Paranal, however, is excellent.

The most exotic photometry is on tap from Dome C at elevation 3233M in Antarctica, where, barring clouds, rain or snow, the ASTEPS telescope is scheduled to observe. According to the Weather Underground, conditions at Dome C are currently overcast, calm and -88F. (“Feels like -88F”)

Just a few more days until the midpoint of the HD 156846b transit opportunity, which is a tough, but in my opinion, highly worthwhile challenge for small-telescope photometric observers. Given the parent star’s -19 degree declination, the best opportunities are south of the border. There is even speculation that an Antarctic time series will be obtained.

As is often the case, observers worldwide will be struggling with high air masses and twilight conditions. Because of this, it’s very important to obtain baseline photometry of HD 156846 on several nights both before and after the main opportunity. This will help inoculate against instances of transit fever.

And when the data come in? Lubos Brat has set up a globally accessible drop at the ETD, which I highly recommend. Quoting Lubos:

Photometry should be uploaded to TRESCA Observer’s log at http://var2.astro.cz/EN/obslog.php. Please use the target name HD156846 and observers project TRESCA while uploading the data. All data will be aggregated, and everybody can see the joined results at the page:
http://var2.astro.cz/EN/obslog.php?obs_id=1&projekt=TRESCA&star=HD156846

HOW TO START TO USE the Observer’s log:
1) Sign in to the var2.astro.cz server.
2) Click to link Observer’s logs
3) Click to Insert new data (Type object name HD156846 and observer project TRESCA)
4) With first data, your observer’s log will be created.
5) All questions can be sent to brat@pod.snezkou.cz

Here’s to clear skies!

The transit discovery opportunity for HD 156846b is fast approaching, and observations, especially for observers at southern latitudes, are very much in demand for the nights of August 23rd, 24th, and 25th. If you are considering observing, please see Lubos Brat’s campaign page at the Exoplanet Transit Database for more details.

And if you have a portable telescope/CCD combination, and a carbon footprint to match, why not consider a last-minute trip to Tahiti for on-the-spot observations? A quick check on Expedia shows that round-trip direct flights departing from Los Angeles this weekend can be had for a mere USD 1537:

HD 156846b clearly owes its current high-eccentricity orbit to ongoing Kozai oscillations driven by BD-19 4605B, a V=14.1 early M-dwarf binary companion to HD 156846 that lies at a projected separation of ~250 AU:

In all likelihood, HD 156846b is currently near the peak eccentricity of its Kozai cycle. During most of the planet’s history, it orbits with a significantly different inclination, and with a significantly less elongated orbit. Konstantin Batygin made some reasonable assumptions regarding the orbital properties of the companion star, and did an integration using the double-averaging method to show that the planet has likely not had sufficient time to lock its spin period to the pseudo-synchronous value. It’s thus quite likely that HD 156846b rotates with a close-to-primordial day of less than 10 hours (like Jupiter) rather than at the much longer pseudo-synchronous spin period that almost certainly characterizes all of the other currently known transiting planets on significantly eccentric orbits.

I’ve written on a number of occasions about the apparent preference for regular satellite and planetary systems in which the total mass contained in satellites is roughly one or two parts in ten thousand as much as that contained in the primary body. This works for the large population of super-Earth/sub-Neptune planets orbiting nearby stars, as well as for the giant planets in our own solar system. Applying this rule of thumb to HD 156846b suggests that it could be accompanied by a satellite with a fair fraction of Earth’s mass. Such a satellite, if located ~0.01 AU from the primary, would cause barycenter-related transit timing shifts of order 6 seconds, and would likely be dynamically stable against both three-body orbital disruption and tidal orbital decay. Veering into an even more speculative mode, such a satellite, like Titan or Ganymede, would likely have a volatile-rich composition. During the current warm, high-eccentricity phase, it might be spewing out a huge cloud of molecules that just might be visible using high-resolution transit spectroscopy…

But first things first! It’s got to be determined that the planet actually transits before one can responsibly engage in such flights of fancy.

We’re now a mere two weeks away from the HD 156846b transit opportunity. As I write, the planet is gathering speed as it plunges toward its steamy periastron encounter with its parent star (or more precisely, given the 49 parsec distance to HD 156846, back in the year 1851, the planet was plunging toward its steamy encounter with the parent star).

With a mass of at least ten Jupiter masses, HD 156846b is pushing the upper limit of the planetary regime. Like Jupiter and Neptune in our own solar system, but unlike all of the other well-characterized transiting extrasolar planets, its energy budget is likely dictated more by its residual heat of formation than by either tidal dissipation or the energy that it receives from its parent star as it circulates on its 360-day orbit.

Remarkably, objects that are very similar in mass and temperature to HD 156846b are starting to be discovered via direct imaging. In an ApJ letter from earlier this year, Luhman, Burgasser and Bochanski reported the discovery of a candidate brown dwarf which, if confirmed, has a positively shirtsleeves ~300K effective temperature and a mass of ~7 Jupiter masses.

This candidate, WD 0806-661 B, is in a ~2500 AU-wide orbit about a nearby white dwarf star that lies 19.2 parsecs away. It can be seen in Spitzer’s 4.5-micron band at two distinct epochs, and was flagged as a result of its common proper motion with its white dwarf primary. As it’s been detected so far only at 4.5 microns, its spectrum is largely unknown. It has a good chance, however, of signing on the dotted line as a first representative of the Y spectral class.

Which underscores the importance that HD 156846b will have it it turns out to transit. At V=6.5, the parent star is very bright, over 2.5 times brighter than either HD 189733 or HD 209458. The transmission spectrum for HD 156846, especially on the cold limb, would thus give an important and detailed clue toward what one might expect from the spectra of field Y dwarfs. And given that one of these guys could be lurking just a light year or two or three away, and given that the WISE preliminary release is on line and available, that’d be a very interesting clue indeed…

Seems like every other year, a good opportunity arises for small-telescope photometric transit observers to participate in a big discovery. In 2007, oklo.org egged everyone on to observe HD 17156 during the transit window of its e=0.69, P=21.2-day planet, and the results were quite satisfactory. In early 2009, there was the exciting detection of the HD 80606b transit. This year, there’s a very interesting opportunity to see whether HD 156846b (RA 17 20 34.31129, DEC -19 20 01.4991, V=6.5) occults its parent star.

HD 156846 b was discovered by the Geneva Team in 2007, and weighs in at a hefty 10+ Jupiter masses. Its orbital period is 359.6 days, just short of a year, and it has a very high eccentricity, e=0.848. The orbital geometry is quite favorable, leading to a ~5% chance that transits will be observable. In addition, the transit window is well constrained as a consequence of the large radial velocity swing that the planet induces in its parent star. Here’s the set-up, with the inner solar system orbits shown for scale:

Observers worldwide should plan to be on the sky this August 23rd, 24th, and 25th, a bit more than three weeks from now. Be sure to check back at oklo.org and to follow twitter.com/transitsearch for updates and interesting details as this opportunity draws near!

Galex Far-UV survey image centered on 40 Eridani B.

Like many kids, I enjoyed reading The Magician’s Nephew by C. S. Lewis. Especially evocative were the descriptions of the dying planet Charn:

The wind that blew in their faces was cold, yet somehow stale. They were looking from a high terrace and there was a great landscape spread out below them.

Low down and near the horizon hung a great red sun, far bigger than our sun. Digory felt at once that it was also older than ours: a sun near the end of its life, weary of looking down upon that world. To the left of the sun, and higher up, there was a single star, big and bright. Those were the only two things to be seen in the dark sky; they made a dismal group. And on the earth in every direction, as far as the eye could reach, there spread a vast city in which there was no living thing to be seen.

The story was written in the early 1950s, just as the future evolution of the Sun was beginning to be understood, but before the Henyey technique for computing full stellar evolutionary sequences had been developed. The scene, while compelling, seems to make little astrophysical sense. It describes a parent star on its ascent of the red giant branch, yet the star’s overall luminosity seems clearly on the wane. In truth, as a red giant swells up, its overall luminosity increases drastically, and the end game for habitable planets consists of fire rather than ice.

Earlier this year, however, there was a very interesting paper by Eric Agol that discusses the possibility of Earth-like planets orbiting white dwarf stars. These planets, if they exist, would be spin-synchronized and would have orbital periods of order 10-20 hours. On such a world, the demise of habitability occurs as the parent white dwarf loses its heat of formation, and grows gradually redder, even as it maintains the same angular size in its fixed position in the sky.

Here’s the relevant summary diagram from Agol’s paper. As the parent white dwarf cools, it travels vertically up the plot.

Now admittedly, this set-up is sailing pretty close to the wind. Indeed, I’ve largely come to adopt the opinion that the whole idea of the “habitable zone” is the modern-day equivalent of Bode’s Law. And furthermore, it’s not exactly clear how one might arrange for habitable planets to be orbiting white dwarfs. The reason I’m enthusiastic is that Agol’s scenario is eminently testable. If white dwarfs harbor Earth-sized planets in quantity, then they can potentially be discovered by backyard astronomers. A one-Earth radius planet on an a=0.013 AU orbit around a typical 0.6 solar-mass white dwarf produces a central transit depth of ~50% during a transit that lasts one or two minutes.

Bruce Gary, who has been a leader in the area of transit detection using small telescopes, has recently organized a pilot photometric project to detect transiting planets orbiting white dwarfs. Here’s his description of the project from an announcement that he sent around last week:

All,

This is a “call for observers” for a 1-month project to evaluate feasibility of amateurs and others to detect white dwarf transits using available hardware.

This should be viewed as a “pilot project” designed to provide a first evaluation of the abundance of exoplanets orbiting white dwarfs in short-period orbits (near the habitable zone). It can play a role in designing a funded project using professional hardware to conduct a long-term and more comprehensive white dwarf (WD) transit search. Professional astronomer guidance is provided by Prof. Eric Agol, who has written several articles on the subject of exoplanets in WD habitable zones. I will archive light curves at a web site in a manner similar to what I did for the Amateur Exoplanet Archive (AXA).

I have tentatively identified September as the observing month. Coordinated observing by partners is encouraged to permit corroboration of any interesting light curve feature. Note that since WDs are very small, comparable to the Earth, a central crossing by an Earth-size exoplanet will produce a very deep transit feature, possibly causing a temporary complete fade. Another consequence of the small size is that transit lengths will be short, typically a couple minutes. In spite of the great depth the search for WD transits is an observational challenge because of the short length. The chance of success in detecting a WD transit may be small but the payoffs for success are great!

Anyone with experience observing exoplanet transits is qualified for this project. However, of the known 20,000 or so WDs only 168 are brighter than V-mag = 14.0. This means that telescope aperture matters, and for most WD targets an aperture of at least 10 inches will be needed.

The project will go by the name Pro-Am White dwarf Monitoring, or PAWM. A description of PAWM can be found at the following web site: http://brucegary.net/WDE/

Please forward this e-mail to anyone who might be interested in participating as an observer or professional adviser. Reply to this e-mail if you would like to receive occasional updates on PAWM.

Bruce L. Gary
Hereford Arizona Observatory

A very exciting project! Once September starts, I’ll be checking the PAWM site to watch how the survey unfolds…

A few weeks ago, I was in West Texas, seeing first-hand places that were familiar only from articles and maps. Marfa, Big Bend, the Glass Mountains.

Image Source.

The landscape west of the Pecos River, dry to begin with, is in the grip of exceptional drought. The temperature was over 100 degrees Fahrenheit, and there was a hot incessant wind. From a ridgeline near the top of an eroded volcanic intrusion in the Chisos Mountains, dry basins and ranges extended into the infinite hazy distance. It was easy to imagine that the Earth had lost its oceans, and had become a desert planet, with isolated pockets of life clinging to retain the veneer of a respectable planetary habitability.

There’s a recent, highly engaging article by Kevin Zahnle and collaborators (Abe et al. 2011) that argues that such a world might be better suited than the present-day Earth at staving off the biosphere-terminating ravages of the runaway greenhouse effect. Desert, or “land” planets keep their stratospheres dry, which allows them to better retain what water they do have, and land planets can more effectively re-radiate infrared radiation into space at given surface atmospheric pressure, allowing a cooler surface temperature at a given stellar flux. It cools down at night in the desert.

Abe et al.’s global climate models indicate that Earth will cease to be habitable in 2.5 Billion years. In the absence of oceans, on the other hand, they find that habitability would be extended by another 2 to 2.5 billion years. And provocatively, if Venus started out as a land planet, it may have been habitable as recently as a billion years ago.

My guess is that nearly everyone who frequents oklo.org has read and liked Frank Herbert’s 1965 science fiction classic Dune, which is folded into the introduction of Abe et al.’s paper:

We can imagine another kind of habitable planet that has only a small amount of water and no oceans; it might be covered by vast dry deserts, but it might also have locally abundant water. We call such a dry planet a ‘‘land planet.’’ The fictional planet known as Arrakis or Dune (Dune, Herbert, 1965) provides an exceptionally well-developed example of a habitable land planet. In its particulars, Dune resembles a bigger, warmer Mars with a breathable oxygen atmosphere. Like Mars, Dune is depicted as a parched desert planet, but there are signs that water flowed in the prehistoric past. Dune has small water ice caps at the poles and more extensive deep polar aquifers. The tropics are exceedingly dry, but the polar regions are cool enough and moist enough to have morning dew.

In Search of Planet Vulcan — The Ghost in Newton’s Clockwork Universe, by Richard Baum and William Sheehan, is one of my favorite astronomy books. It certainly has one of the best overviews of the momentous events and controversies surrounding the discovery of Neptune in September 1846. I’ll take the liberty to quote Baum and Sheehan’s recounting of the exact moment of Neptune’s discovery.

On September 18, Le Verrier wrote to Johann Gottfried Galle, then an obscure astronomer at the Royal Observatory in Berlin. A year earlier, Galle had sent Le Verrier his doctoral dissertation, which concerned observations made by 17th-century Danish astronomer Olaus Roemer. Belatedly, Le Verrier wrote to acknowledge it. Among other things, he queried Galle about Roemer’s Mercury observations, but then came quickly to his point:

“Right now I would like to find a persistent observer, who would be willing to devote some time to an examination of a part of the sky in which there may be a planet to discover… You will see, Sir, that I demonstrate that it is impossible to satisfy the observations of Uranus without introducing the action of a new Planet, thus far unknown; and, remarkably, there is only one single position in the ecliptic where this perturbing Planet can be located… The actual position of this body shows that we are now, and will be for several months, in a favorable situation for the discovery.

Galle indeed proved to be his man. He received Le Verrier’s letter on September 23, and at once sought permission from the observatory’s director, Johann Encke, to carry out the search. Encke was skeptical but nonetheless acquiesced: “Let us oblige the gentleman in Paris.” A young student astronomer, Heinrich Ludwig d’Arrest, begged to be included, and joined Galle as a volunteer observer. That night, they opened the dome to reveal the observatory’s main instrument, a 9-inch Fraunhofer refractor aimed at the spot assigned by Le Verrier. Recalculated for geocentric coordinates, its position was at right ascension 21 h, 46 min, declination -13 deg 24 min, very close to the position occupied by another planet, Saturn.

The question arose: What maps were available? At first they could think of none but “Harding’s very insufficient Atlas.” D’Arrest then suggested “it might be worth looking among the Berliner Akademische Sternkarten to see whether Hora XXI was among those already finished. On looking among a pile of maps in Encke’s hall [Vorzimmer], Dr. Bremiker’s map of Hora XXI [already engraved and printed at the beginning of 1846 but not yet distributed] was soon found.” As d’Arrest later recalled, “We then went back to the dome, where there was a kind of desk, at which I placed myself with the map, while Galle, looking through the refractor, described the configurations of the stars he saw. I followed them on the map one by one, until he [Galle] said: and then there is a star of the 8th magnitude in such and such a position, whereupon I immediately exclaimed, that star is not on the map!”

Neptune’s moment of discovery, at 11 PM Berlin local time on September 23, 1846, corresponded to 22:07 UT, or JD 2395563.4215. The period of Neptune is 60,190.03 days, or 164.79132 years. The first “Neptunian anniversary” of the discovery is therefore CE 2011 July 10 22:49:26.4 UT Sunday, that is, right now.

In 1846, photography was still in its very earliest stages, and it would be nearly two decades until the publication of Jules Verne’s De la Terre à la Lune. The fact that we greet the completion of one orbit in the possession of photographs of a crescent Neptune is a marvelous indeed.

Image Source.

Certainly, an occasion for celebration! On Friday, I got an invitational e-mail from Gaspar Bakos, who is hosting a Neptune-at-One cocktail party in Cambridge, Massachusetts. I briefly perused airfares before sadly having to decline.

A well-known theorem states that there’s no such thing as a free lunch. A corollary is that interesting discoveries tend to be made at the ~3-4 sigma level of confidence, and this is especially true if the supporting data is drawn from the public domain. If a signal is stronger than 4-sigma, then someone else has invariably pointed it out. If it’s weaker than 3-sigma, it’s probably wishful thinking.

With those rules of thumb in mind, I’m very optimistic that Kevin Schlaufman has obtained a genuinely important insight into how the planet formation process works:

The plot shown is above is from a paper that Kevin and I submitted soon after the 1,235 Kepler planet candidates were announced last Spring. After going through review, it was accepted by the ApJ, and it was posted to astro-ph last week.

I wrote about the underlying details of the plot in this post from several months ago. The basic idea is as follows: The 997 Kepler planet candidate host stars are divided up into two groups — (i) the less numerous group of stars that host a candidate with R_pl>5 Earth radii (red), and (ii) the more numerous group of stars that only host a planet (or planets) with R_pl<5 Earth radii (blue). The two groups of stars, along with a control sample of 10,000 non-candidate-bearing dwarf stars from the Kepler field (gray), are plotted in a color-color diagram (and then binned to create the diagram above):

The y-axis corresponds to the magnitude difference between a given star’s green (Sloane g filter) and red (Sloane r filter) colors. The x-axis charts the differences between the 2Mass J and H infrared colors for each star. Metal-rich stars tend to have redder optical colors than metal-poor stars, whereas the J-H index sorts the stars in terms of their overall temperatures (with cool stars to the right and warm stars to the left of the plot). Metal-rich stars thus lie along the upper part of the main-Sequence locus.

The binned version of the plot provides a confirmation of several trends that were already very well known. First, among host stars with masses similar to the Sun that harbor giant planets, there’s a strong preference for metal-rich stars. This is the classic planet-stellar metallicity effect. Second, among low-mass stars, there’s a dearth of giant planet candidates. This is the known giant planet-stellar mass effect. Finally, among the solar mass stars that host low-mass planets, there’s no discernible metallicity correlation.

The new result pertains to low-mass planets orbiting low-mass stars. The diagram shows that for this subset, there’s strong evidence for a metallicity correlation — At masses less than ~0.8 solar masses, higher metallicity stars are more likely to host low-mass planets. We take this as direct evidence regarding the overall bulk efficiency of planet formation for planets that aren’t required to bulk up via rapid gas accretion. Take a 0.7 solar mass with twice the Sun’s metal content and a typical 0.02 solar mass disk. The entire planet-forming disk contains about 150 Earth-masses worth of stuff heavier than hydrogen and helium. Kevin’s result is effectively saying that a good fraction of the time, a good fraction of this total burden of metals winds up in planets.

We had to be careful. There are a lot of systematic “gotchas” that can potentially throw a wrench into the exciting big-picture conclusions, and so much of the paper is devoted to considering potential show stoppers in turn. I think that the result is robust, and that it will hold up as the planet catalog continues to grow.

The French philosopher of science Isidore Auguste Marie François Xavier Comte (1798 – 1857) was the founder of sociology and is widely remembered for the doctrine of positivism, which holds that the scientific method can be used to understand both natural and social phenomena.

He’s well known to astronomers, however, largely because of the spectacularly incorrect statements regarding stars in his Cours de la Philosophie Positive (1830-1842):

On the subject of stars, all investigations which are not ultimately reducible to simple visual observations are … necessarily denied to us. While we can conceive of the possibility of determining their shapes, their sizes, and their motions, we shall never be able by any means to study their chemical composition or their mineralogical structure … Our knowledge concerning their gaseous envelopes is necessarily limited to their existence, size … and refractive power, we shall not at all be able to determine their chemical composition or even their density… I regard any notion concerning the true mean temperature of the various stars as forever denied to us.

Lots of fun to get your introductory lecture on stellar spectroscopy off to a snarky start with that particular zinger.

Comte’s pronouncements on planets are slightly more obscure, but now, given the many and varied successes of the Spitzer Telescope, they provide an equally rich vein for irony-with-20/20-hindsight:

The take away message seems to be “never say never”. Nowadays, an academic with Comte’s flair would certainly have the innate sense to leave some wriggle room in anticipation of unforeseen scientific advances.

In any case, in this evening’s astro-ph mailing, there’s a very interesting article by Brugamyer et al. that touches on the inferred chemical and mineralogical structure of extrasolar planets. The authors of the paper make a detailed examination of the relative oxygen and silicon abundances of stars known to host extrasolar planets.

The context comes from work back in 2006 by co-author Sally Dodson-Robinson which indicated that stars with high silicon abundances relative to iron show increased planet fractions at given metallicity:

The expectation was that stars with high oxygen abundances relative to iron would also show increased planet fractions at given overall metallicity. Oxygen is a key component of the core-building materials for giant planets, and so it stood to reason that the more water available, the more Jupiter-mass planets one ends up with. Remarkably, this turns out not to be true. Here’s the relevant diagram from the Brugamyer et al paper:

Statistically, it appears that an excess of oxygen relative to iron has no influence on the likelihood of a given star hosting a readily detectable planet. The silicon effect, however, is statistically robust and readily detectable in the Brugamyer et al. analysis:

So how does one explain the unexpected result? Brugamyer et al.’s hypothesis is that icy grain nucleation on silicon-rich dust, rather than the subsequent growth of the icy core-forming particles, is the key bottleneck in forming giant planets via core accretion.

An all-time classic of the literature is Alar and Juri Toomre’s 1972 ApJ study of colliding galaxies. With an exceptionally simple physical model — the restricted three body approximation, in which test particles orbit in the joint potential provided by two massive bodies on a conic 2-body trajectory — the Toomre brothers were able to construct startlingly plausible explanations for bizarrely irregular galaxies such as the Antennae.

One is hard-pressed to think of a better example of seeing the essence of a manifestly complicated phenomenon so precisely nailed by a simple model. The take-away lesson seems to be: Keep an eye out for situations in which glorious non-linearity has had of order one Lyapunov time to unfold.

ApJ 178, 623 also presents some of the finest astronomical diagrams ever. They are masterpieces of visual scientific communication. Every single detail conveys information, and nothing is superfluous.

In 1998, when I was a post-doc in Berkeley, my working routine was considerably less hectic than it is now. On the foggy morning of May 29th of that year, I remember buying a copy of the New York Times, and settling in at a Cafe on Telegraph Avenue for a relaxed 11AM coffee. A picture and a slew of familiar names jumped off the front page:

The story, which became a huge media event — even President Clinton made a passing mention of it — stirred up a uniquely unsettled, uniquely urgent feeling of being completely involved and completely left out all at the same time. A runaway planet clearly would have formed via gravitational instability, and I had spent several years studying gravitational instabilities for my PhD thesis. I gulped down my coffee, scooped up the paper and ran to my office in Campbell Hall. The phone was ringing when I got there. Doug Lin was on the line, buzzing with excitement. “It’s a tidal tail! Look at Alar’s ’72 paper!”

There was not a moment to waste… Doug called the editor at Science and informed him that we had an important interpretive result in the works. I stayed up all night putting together SPH simulations. It seemed completely feasible that one could explain the observation with a collision between two protostellar disks, in which the runaway planet formed via gravitational collapse in the tidal tail. We got the paper off to Science in short order, and boy was it exhilarating!

The Toomre brothers’ influence soaks right through the figures that I made for our paper. Thirteen years on, they remind me of listening to a cover of Sympathy for the Devil done by a competent Stones tribute band.

Sadly, a year or so later, it became clear that the TMR-1c runaway “planet” is, in actual fact, an unfortunately placed background star, and the TMR-1c fiasco is commonly used to illustrate the flaws in the publication by press conference model. Our Science paper has languished in obscurity, to the point where one can extract it from behind Science’s formidable pay wall with only a modestly compromising registration agreement to receive e-mail and no money down…

But hope springs eternal. Like everyone else in the community, my eyes lit up upon reading the recent microlensing result that the galaxy is teeming with of order 200 billion rogue planets. Processes like the one that we outlined in our paper may well be operating after all…

It’s Sunday afternoon here in Santa Cruz, meaning that GMT-wise, it’s already June 6th, and the next transit of Venus is exactly one year away. Seems like an appropriate moment to recall a quote by astronomer William Harkness from 1882 (by way of Stephen J. Dick’s Sky and Ocean Joined: The U.S. Naval Observatory 1830-2000).

We are now on the eve of the second transit of a pair, after which there will be no other till the twenty-first century of our era has dawned upon the Earth, and the June flowers are blooming in 2004. When the last transit season occurred the intellectual world was awakening from the slumber of ages, and that wondrous scientific activity which has led to our present advanced knowledge was just beginning. What will be the state of science when the next transit season arrives God only knows. Not even our children’s children will live to take part in the astronomy of that day. As for ourselves, we have to make do with the present.

There’s something oddly appealing about the nonintuitive spacing of Venusian transits, a 243 year repeating pattern, with transits occurring eight years apart, then a gap of 121.5 years, followed by an eight year interval and then a 105.5 year spacing. I’m certainly looking forward to June 6th 2012, when a healthy fraction of the transit will be visible from Lick Observatory on Mt Hamilton. For updates, be sure to bookmark the Transits of Venus Project website, which launched today.

I can’t help feeling uneasy, however, thinking about the state of affairs on Dec. 10-11 2117…

As Mick Jagger famously remarked, you can’t always get what you want. Kepler’s photometric transit observations provide excellent measurements of the planetary orbital periods, the transit epochs and the planet-to-star radius ratios, but they are stingy and tight-lipped when it comes to the planet’s masses, eccentricities, and longitudes of periastron.

Occasionally masses can be inferred from transit timing variations, especially if a system contains more than one transiting planet. Alternately, one can assume a planetary mass-radius relation (keeping in mind, of course, what happens when u assume). For example, M=R^2.06 in units of Earth masses and radii works quite well in our solar system for V-E-S-U-N. Or, dispensing with the trickery, one can pony up and measure radial velocities.

With photometric data alone, information about the orbital eccentricity distribution of the planet census can be deduced by statistically comparing transit durations to orbital periods. The idea is a full elaboration of the simple observation that if a central transit that is substantially shorter than expected, then it’s quite possible that the planet is occulting the parent star near the periastron of an eccentric orbit.

In one of the flurry of Kepler-related papers that accompanied the February data release, Moorhead et al. (2011) implemented just such a program, and generated a statistical analysis of the distribution of transit durations for the Kepler exoplanet candidates. They assumed that the eccentricities conform to a Rayleigh probability distribution function:

where the controlling parameter, sigma, is is related to the mean orbital eccentricity through

To get a sense of what the Rayleigh distributions look like, here are examples for e_av=0.05, e_av=0.21, and e_av=0.50, compared to the distribution of eccentricities in the exoplanet.eu catalog:

Ignoring planets that are likely tidally circularized, the best fit occurs for e_av=0.21. This model, however, underproduces planets at high eccentricity — ‘606 wouldn’t have turned up if e_av=0.21 were a hard truth. Moorhead et al.’s analysis of the Kepler data comes up with plausible best-fit values for e_av ranging from 0.1 through 0.25, for cooler stars with effective temperatures less than 5100K. So there is rough agreement, even though the two catalogs have radically different sampling biases.

A significantly non-zero value for average orbital eccentricity has some interesting consequences for transit surveys. At a given semi-major axis, eccentric planets have (on average) a higher chance of transiting. This is easily seen by comparing an e=0.5 orbit with a circular orbit having the same semi-major axis.

For a population of planets having a specific Rayleigh distribution of eccentricities, the average transit probability at a given semi-major axis is increased by a factor

where the normalization factor, N, is given by

For e_av=0.25, this boosts the total population of planets by about 10% over what one would infer from the standard 1/a circular orbit scaling.

I’ve been reading a textbook on ore-forming processes as part of an attempt to get a little more fluent in geology, and I ran across a plot that is certainly well known to many, but was an eye-opener for me:

The plot charts the solubility by weight of water in several common igneous rocks as one moves deeper into the lithosphere. The take-away message is that even at modest depths, rocks can be very heavily hydrated and are capable of harboring a very large amount of water.

The plot brought to mind something that, to my highly inexpert eye, has always seemed a remarkable coincidence. The volume of water in Earth’s oceans has an average depth of ~4000 meters, leading to a sea-level that does a pretty fair job of outlining the continental margins (which mark the boundaries between denser (but thinner) basaltic crust and lighter (but thicker) granitic crust. Only about 20% of the total continental crust is overlaid by water.

In the extrasolar planet context, an interesting question is whether the situation here on Earth is unusual. Many of the planets that Kepler has found (and will be finding) contain water mass fractions that are considerably larger than Earth’s. Is it reasonable to expect that they’ll have deep oceans that uniformly cover the planets, or is there some sort of mechanism involving water of hydration that maintains a seafloor-continent dichotomy even in the presence of a lot of water? As far as I can tell, this question hasn’t been answered definitively.

The naive answer seems to be along the following lines. Imagine that a terrestrial planet forms in such a manner that the mantle rock is heavily hydrated. Given that mantle rock can easily retain a water mass fraction measured in tens of percents, one could start out with a planet that contains many oceans worth of water, but in which substantial portions of the surface are dry.

When rock melts, the water of hydration is squeezed out. (Migration of this water into the surrounding country rock leads to the mineralized veins that are the basis for many of Earth’s great ore deposits.) On an ongoing volume-weighted basis, most of the melting is taking place beneath the spreading centers that form the mid-oceanic ridges. Every year, of order 300 cubic kilometers of melt are produced, several cubic kilometers of which are erupted to form fresh ocean crust. Coupled with mantle convection, this means that the mantle unburdens its water on a timescale of order a billion years. Some of the water is subducted back down, but this sink is less effective than the source, meaning that the water likely ends up on or near the surface.

So one can imagine planets (perhaps with mantle convection less vigorous than Earth’s) in which continents are gradually submerged as water is squeezed out of the mantle. Not, perhaps, a bad way to go. The world’s best beaches are those of the Seychelles islands — a handful of granitic specks in the vastness of the Indian ocean — the highest peaks of the submerged continental Mascarene Plateau.

Klaus Nomi and David Bowie (Image source and backstory)

I was in the middle of my dynamics lecture this past Monday morning, explaining the Fokker-Planck approximation to the collision term on the right-hand-side of the Boltzmann equation, when my phone started buzzing and vibrating in my pocket. Good thing I had remembered to turn the volume off. Without having to look at who might be calling, I knew it was likely some media outlet, BBC? KCBS? There was a sudden, all-to-familiar sensation of queasy uneasiness which made it very hard to focus on the second-order terms I had just written on the whiteboard.

Back in 2001, I naively and foolishly spoke to a reporter at the London Observer about the “relative ease” of accomplishing strictly hypothetical orbital engineering in the context of a billion-year time frame. The resulting article (now archived by the Guardian) contained an alarmingly incorrect cognitive leap from the ultra-long term to the immediate near-term:

The misconception came exactly at the time when George W. Bush was visiting Europe, explaining his position regarding the Kyoto Protocol. The Observer story became a huge, completely nightmarish story in Europe, which then echoed across the Atlantic, where it was seized upon by the Drudge Report, Rush Limbaugh and others. Here’s an example editorial from the Manchester New Hampshire Union-Leader:

For nearly a week, the story managed to survive, zombie-like through successive news cycles. Eventually, Gary Condit appeared on the scene, and finally, the media’s full attention was diverted elsewhere.

As readers likely know, I’ve been writing on this web log about a planet valuation formula, which is designed to give a quantitative assessment of whether a newly discovered planet is worthy of significant media attention. Last month, I had a detailed conversation with Lee Billings, which was published on BoingBoing as a part of Lee’s series of posts on planets (which are well worth reading!)

Several weeks after the BoingBoing article appeared, I got a very politely worded e-mail from a reporter at News of the World.

[…] I found your article on the value of the Earth which popped up on a UK blog late last week.

From what I can ascertain, your findings and formula haven’t really had the coverage they deserve in the UK media and I was hoping to rectify that…

After a look at the Wikipedia page on News of the World, my heart was pounding. “Wacko US Prof Sez: Sell Earth for 3 Quadrillion Quid!” I sat down at the computer, and it took a long time to compose a reply.

Turned out that the reporter was admirably interested in getting the story right, and the final version (which is behind a paywall) is quite fair. After all, given the possibly arch, arguably pretentious tone here on oklo.org, I did pretty much have it coming.

Predictably, newspapers in Britain saw the News of the World story and immediately picked it up. As is to be expected, successive iterations tend to lose focus on the exoplanets, and gain focus on the value of Earth. Radio stations are calling, trying to set up interviews about how much Earth is worth. Angry e-mails drift into my inbox. Google news is at 61 articles and counting.

I think it’s time to look into installing Google’s AdSense…

Image Source.

In the midst of all that excitement surrounding the Kepler data release, it was easy to overlook the article by Martin & Spruit, Inflated hot Jupiters from merger events, that showed up on astro-ph earlier this month. This paper proposes a sure-to-ruffle-feathers explanation for the radius anomalies of the hot Jupiters. The idea is that stellar mergers (arising from orbital decay in very close binaries) shed angular momentum via an “excretion” disk, from which one or more short-period giant planets manages to form. In this picture, short-period, anomalously inflated planets are large because they are young — their formation dates to the binary star merger that created their parent star, and they are headed inward for destruction on timescales significantly shorter than the typical several-billion year age of planet-bearing main-sequence stars.

Image Source: Tylenda et al. 2010.

It’s believed that the anomalous novae V1309 Sco (which occurred in 2008) and V838 Mon (which made a big splash in 2002, and whose light echo is shown in the image at the top of the post) were both caused by binary mergers. In the case of V1309 Sco, the more massive of the two progenitor stars was probably similar in mass to the Sun, whereas for V838 Mon, a primary of order 8 solar masses was involved. Numerical simulations, such as the ones shown below by D’Souza et al. (2006), suggest that two distinct stars merge into a single star surrounded by a disk-like structure over an action-packed phase that lasts ~10 orbits.

The idea that merging stars can give rise to planets shows up prominently in the literature in the 1980s, with a series of papers in Soviet Astronomy by A. V. Tutukov, who had a number of speculative ideas regarding planet detection and planetary systems that have turned out to be quite on the mark — he did detailed calculations of the prospective yield of M-dwarf transit surveys, and he argued that ~25% of stars should harbor planetary systems. In several papers (including here) he advocated the idea that excretion disks can give rise to planet formation.

It occurred to me that in the event that stellar mergers do indeed serve as an effective formation channel for short-period planets, then blue stragglers should be very high-grade ore for photometric transit searches. The blue stragglers are main-sequence stars in globular clusters that lie above the main-sequence turn-off in the Hertzsprung-Russell diagram, and which are generally found near the cluster core. It’s believed that they owe their relative youth to being the product of binary mergers.

One of the most important early exoplanet-related results was the Gilliland et al. 2000 HST photometric survey of the rich nearby globular cluster 47 Tucanae. The Hubble telescope was trained on the cluster for 8.3 days, and time-series photometry (taken through two filters) was analyzed for ~34,000 individual stars. If the occurrence rate of hot Jupiters in 47 Tuc was similar to the occurrence rate in the solar neighborhood, then 17 transit planets were to be expected. None were found. This null result is generally attributed to the cluster’s low metallicity and to the possibility that planet formation was inhibited by the dynamical interactions and intense UV radiation that occurred during the cluster’s star formation phase.

A close up look at the 47 Tucanae color-magnitude diagram indicates that the 2-color HST imaging of cluster contains about twenty blue stragglers. Interestingly, it’s not entirely clear whether the blue stragglers have been folded for transits. In the Gilliland et al. 2000 paper, it appears that only the conventional main-sequence stars in the cluster were included in the analysis. The paper states: “For the results discussed further below only the 34,091 stars falling within a bright main-sequence box as shown were analyzed for time series.”

If hot Jupiters are commonly forming from binary merger events, then it seems like there should be a good chance that there could be a transit among the 20-odd blue stragglers observed with HST. Because this handful of stars are much smaller than the red stars at the same luminosity, the transit depths could likely be detectable, given the quality of the HST photometry and the brightness (I=16-17) of these stars. If the planet occurrence rate for merger remnants is 50% one would expect to find one transit among the tweny stars, given the ~10% a-priori geometric probability of transit. As a first step, certainly, it’ll be interesting to see whether these stars were analyzed in any of the follow-up work that was done with the Gilliland et al. dataset.

Earlier this year, in the New York Times Magazine, there was a very lengthy, very glossy advertising insert devoted exclusively to high-end watches. I leafed idly through it, and picked up a new concept, that of a complication. Where watches are concerned, a complication refers to any feature that goes beyond the simple display of hours, minutes, and seconds. According to the Wikipedia,

The Patek Philippe Calibre 89 is a commemorative pocket watch created in 1989, to celebrate the company’s 150th anniversary. Declared by Patek Philippe as “the most complicated watch in the world”, it weighs 1.1 kg, exhibits 24 hands and has 1,728 components in total, including a thermometer and a star chart. Made from 18 carat (75%) gold, it has an estimated value of $6 million, and took 5 years of research and development, and 4 years to manufacture. Four watches were made; one in white gold, one in yellow gold, one in rose gold and one in platinum.

The Calibre 89’s complications include such must-haves as the equation of time (yielding the instantaneous difference between apparent solar time and mean solar time), the date of Easter, and a 2800-star celestial chart. And just imagine the convenience of being able to pull your 2.42 lb watch out of your pocket whenever the need strikes to see what century it is!

It occurred to me that the 1,235 Kepler candidates could conceivably provide a bonanza for the high-end mechanical watch industry. The candidates, with their particular periods, transit durations, transit depths, effective temperatures, and radii offer endless opportunities for unique horological complications. In this spirit, at the link below, I’ve made a 1,235-complication applet which charts the appearance and disappearance of transits, timed from the start of Kepler’s Q0. The horizontal direction is mapped to orbital period, and the vertical direction is mapped to M=R^2 in Earth units. It’s mesmerizing to watch…

Click here to watch the animation.

The planet — host star metallicity connection has been one of the most secure and enduring results from the radial velocity planet surveys. In 1997, soon after the detection of the first planets, Guillermo Gonalez pointed out that the host stars were significantly enriched in elements heavier than hydrogen and helium, and suggested that a planet-metallicity connection exists.

Over the years, the correlations have been refined by many different workers, and a clear set of facts has emerged:

(1) Giant planet hosts, all the way from low-mass red dwarf stars through stars that are somewhat hotter and more massive than the Sun, tend to be metal rich.

(2) The occurrence rate for giant planets increases with stellar mass.

(3) Among stars with mass similar to the Sun, there’s no evidence that the presence of sub-Neptune/super-Earth is correlated with host star metallicity.

Taken together, these facts provide basic support for the core-accretion mechanism of giant planet formation. A planet like Jupiter forms by first assembling a core of icy/rocky/metallic material. When the core mass grows to of order 10-20 Earth masses, the core gains the ability to very rapidly accrete hydrogen and helium, and increases its mass by a significant, multiplicative factor to become a full-blown giant planet. Core accretion is a threshold phenomenon in the sense that the eventual presence or absence of a giant planet depends sensitively on whether the core is assembled while nebular gas is still present. Sufficiently rapid core growth is strongly aided by larger disk masses (which is the source of the planet-stellar mass connection) and by larger surface densities of solids in the disk (which is the source of the planet-stellar metallicity connection).

“Better late than never.” You hear that a lot when the chronic under-performance of super-Earths and sub-Neptunes is being discussed. The planet census makes it clear, however, that when not pressured to succeed while the gas is still there, sub-Neptunes and super-Earths regularly grow to 5-15 Earth masses and migrate to various locations in protoplanetary disks. The observations, furthermore, show that for host stars lying close to a solar mass, there’s no evidence for any metallicity dependence in the occurrence rate of these lower-mass planets.

At some point, however, metallicity has to play a role. An early-bird Population II star with [Me/H]=-3 started out with only ~0.1% as much iron, molybdenum, oxygen and carbon as did the Sun. Super-Earths won’t be found orbiting such stars because the raw planet-building materials flat-out weren’t there. Likewise, for low-mass disks orbiting low-mass stars, the overall metal budgets are tight enough that it’s quite reasonable to expect that a planet-metallicity connection for non-giant planets should be detectable.

Last year, Kevin Schlaufman and I looked into this issue and we found a tantalizing hint that among the red dwarf stars, a planet-metallicity connection does exist for planets with ~Neptune mass and below. The statistics were too sparse, however, to have anything more than ~1-sigma confidence.

Enter the Kepler results. In the course of an afternoon, 1,235 planet candidates flooded the market, completely upending the old business-as-usual model for the planet hunters. Correlations no longer emerge, they pop out.

In addition to being numerous, the Kepler stars are quite well characterized, and Sloan photometry has been published for the ~150,000 stars with Q1+Q2 public-domain light curves. At a given J-H color (obtained from the 2-Mass catalog) a star’s Sloan g-r color is significantly dependent on metallicity (see, e.g. here). It’s thus informative to make J–H — g-r color-color plots with (1) a control sample of 10,000 stars drawn from the Kepler 156K star target list, (2) the Kepler giant planet (Rp>5R_earth) hosts, and (3) the Kepler low-mass planet (Rp<5R_earth) hosts:

These plots, which are from a paper that Kevin and I just submitted to the Astrophysical Journal, demonstrate quite convincingly that a metallicity correlation does exist for low-mass planets orbiting lower-mass stars. (The correlation starts to kick in below ~0.8 solar masses.) Assuming that the probability of forming a planet is proportional to the total amount of solids in its protoplanetary disk, the correlation indicates that a late K-dwarf with 70% of the Sun’s mass needs to have a metallicity [Fe/H]=0.15 to have the same chance of forming a planetary system as a solar metallicity star of similar mass.

I’m pretty excitied about these results. A quantitative statistical link between relative disk conditions and planet outcomes for the huge super-Earth population gives us direct information about how the really interesting systems — the ones harboring large terrestrial planets — are assembled.

We’ll put the paper on astro-ph once it’s gone through review. It contains a lot of work to establish that the correlations are real, rather than due to reddening or the various observational biases inherent in the Kepler target list.

Last August, SFMOMA put on an exhibition that featured a number of Chuck Close’s hyperrealistic portraits. It was interesting to study the sudden transition between a patchwork of acrylic brush strokes, as in the cell-phone close-up snapshot just above, and an image that makes sense as a whole.

The recent public release of the Kepler data triggers an effect that’s a bit like stepping back rapidly from one of Close’s portraits. Suddenly, a huge swath of the planetary distribution connects with a larger picture. This effect holds especially true when one looks at the list of systems that harbor multiple transiting candidates.

With the census of radial velocity planets, it’s often quite difficult to determine whether a signal is originating from a single planet on an eccentric orbit, or a pair of planets participating in 2:1 resonance. The only really well-characterized unambiguously resonant RV system is Gliese 876, where the combination of large Ks, a long observational base, and rapidly unfolding 30-60-120d orbits has allowed the dynamics of the resonance to be revealed in detail.

The 115 Kepler two-transit systems indicate right away that systems like Gliese 876 are intrinsically rather rare. In the illustration below, I’ve taken each of the two-transit systems, and identified the larger member of the pair. I’ve then plotted the period ratio, P_small/P_large as the x coordinate, the parent star’s mass as the y coordinate, the temperature of the planets as a grayscale (saturating to white at 1500K), and the sizes of the symbols in proportion to the observed radii.

The immediate impression from the diagram is that the systems are not overwhelmingly clustered around the simple integer commensurabilities. Low-order mean-motion resonances among the extrasolar planets are the mild exception, and not the rule.

That said, the resonant systems are clearly present. Of the forty 2-transit systems with inner-outer period ratios lying between 2.0 and 3.0, six of them have period ratios between 2.02 and 2.05. The chances of a concentration like this occurring purely by chance is considerably less than 1%. Furthermore, the fact that the clustering occurs a percent or two above the exact 2:1 commensurability can be understood in terms of the dynamics of resonance. When one has two massive planets deep in a resonance, with a significant angular momentum deficit, then the system apse precesses in a retrograde direction (as is the case with Gliese 876). The resonance is controlled by a restoring force that drives conjunctions to occur at periastron. This means that if one observes along a fixed line of sight, then the inner planet is seen to orbit a bit more than two times as often as the outer planet.

Image Source.

If one looks at planetary systems from the “modern” point of view provided by the HARPS survey and the results from Kepler’s recent data release, our own solar system looks pretty strange. In the Sun’s case, the frequently planetiferous orbital zones inside of P=50 days are completely, mysteriously barren. The orbital region inside P<3000 days is also almost entirely bereft, with just a few iron-silicate dregs totaling less than two Earth masses. Out in the boondocks, however, the Sun’s harbors a giant planet that managed to accumulate lots of gas, yet paradoxically didn’t manage to migrate a really significant distance.

It will take more time to determine whether the solar system is really all that weird, but with each passing month’s accumulation of fresh exoplanets, our eight-planet set-up manages to seem slightly less ordinary. Jupiter, for example, induces a 12 m/s velocity half-amplitude, and the high-precision radial velocity surveys have been operating for long enough so that if true-Jupiter analogs were the rule, then we’d perhaps be hearing of more of them being detected.

The Kepler multi-transiting candidates correspond to systems that are completely alien when compared to MVEMJSUN, but they are much more familiar when compared to the regular giant planet satellites — the moon systems of Jupiter, Saturn and Uranus. In each of these cases (and despite a factor-of-twenty difference in mass between Jupiter and Uranus) the characteristic orbital period is of order a week, and the characteristic secondary-to-primary mass ratios are of order a few parts in 100,000. For example, Ariel, Umbriel, Titania and Oberon have mass ratios of 1.6e-5, 1.4e-5, 4.0e-5, and 3.5e-5 relative to Uranus, and their orbital periods are 2.52, 4.14, 8.71, and 13.46 days. In the Jovian system, the satellite/Jupiter ratios for Io, Europa, Ganymede and Callisto are 4.7e-5, 2.5e-5, 7.9e-5, and 5.8e-5, with corresponding orbital periods of 1.76, 3.55, 7.15, and 16.68 days.

In the plot below, I’ve taken the 45 three-transit systems from Kepler’s list, and plotted the orbital periods of their constituent planet candidates along the x-axis. The colors of the points are given a linear gray-scale, with black corresponding to a planet-to-star mass ratio of zero, and white corresponding to a planet-to-star mass ratio of 1.0e-4 or larger. I’ve converted radius to mass by assuming M=R^2 when mass and radius are expressed in Earth masses and Earth radii.

It’s interesting to speculate whether the commonality between the regular satellite systems, and the teeming population of Super-Earth/Sub-Neptune class systems might be more than just a coincidence…

The extrasolar planets constitute a fast-moving field. I was looking at the slides from a talk that I gave in early 2005, in which I showed the then-current, now hopelessly outdated, mass-period diagram for the known extrasolar planets:

At that time, the name “Gliese” had barely edged into the public consciousness, as a Google trends and news reference diagram illustrates:

The discovery of Gliese 436b occurred in the summer of 2004, and was the first Neptune-mass extrasolar planet found. The following summer saw the announcement of the first unambiguous “super-Earth”, Gliese 876d, which generated a blip in search volume in addition to news volume. The discovery of Gliese 876d might have been a bigger story, had it not shared a news cycle with Michael Jackson:

In early 2005, there was essentially no hint of the enormous population of sub-Neptune/super-Earths lying just below the threshold of detectability. Population synthesis models for extrasolar planets were doing an excellent job of reproducing the distribution of hot Jupiters, the period “desert”, and the population of eccentric giants, but at that time, the smart-money expectation was that the pickings would be rather slim in the hot sub-Neptune regime. (It was also believed that the detection rate would pick up substantially once truly terrestrial planets became observable.)

Mayor et al.’s announcement in 2008, therefore, came as a real bombshell. The Geneva Team made the startling claim that a very substantial fraction of stars in the solar neighborhood harbor at least one planet with Neptune mass or less, with an orbital period of fifty days or less. Their claim is equivalent to the statement that in a volume-limited survey, the number of planets in the green box of the diagram below is of order five times greater than the sum of the number in the peach box and the blue box.

In the diagram above, the population of planets known in 2010 is plotted. There’s a bulky cohort of RV-detected eccentric giants (Msin(i)’s), a lot of hot Jupiters from the transit surveys, and a respectable, but still sparse population in the sub-Neptune/super-Earth category. The Geneva claim was based primarily on signals that are emerging in the HARPS data, rather than solid published planets.

Fast-forward to last week. Kepler has suddenly augmented the planetary census by more than a factor of three. If we estimate masses through the simple relation Mpl=Rpl^2, then we can plot the Kepler candidates on the mass-period diagram. Detection biases etc., etc. aside, it’s abundantly clear that there is indeed a huge population of objects in the ground staked out by the Mayor et al. 2008 announcement:

In trying to make sense of the flood of new Kepler results, the very first order of business is to run through the various scatter plots to get a sense for the distributions, to look for correlations, and to test pet theories.

Kevin Schlaufman has made a useful formatted electronic table that joins Tables 1 and 2 from the Borucki et al. (2011) paper. Sifting through this table alone, notwithstanding the gigabytes of light curves currently available for download, there’s lots of very interesting stuff. For example, plotting planetary effective temperature vs planetary radius shows that as expected, there are a lot more small planets than large planets:

If we were looking at a complete volume-limited survey of planets, then this plot would have an interesting interpretation. The downward sweep of the main locus suggests that hot planets, by and large, tend to be smaller than cooler planets. The natural interpretation would be that we’re seeing a signature of evaporation — hence CoRoT-7b, AKA “Planet Freeport-McMoran” is small, whereas Gliese 1214b AKA “Planet Dasani” is relatively large by comparison. (Corporations interested in paying for product placements on oklo.org, please contact me directly.) Sadly, however, before jumping to conclusions, one has to worry about a whole host of possible gotcha-style observational biases. Small planets are harder to detect via transits, meaning that more orbits are required to reach given signal-to-noise, meaning that small planets are more likely to be found on short-period orbits. My gut feeling is that these effects might not be strong enough to completely wipe out the observed correlation, but it’ll take a lot of careful Monte-Carlo work to understand for sure.

I’ve got some unhedged exposure to the planet-stellar mass correlation. The idea is that if core accretion is zeroth-order correct, then it should be easier to form giant planets in orbit around more massive stars. If this hypothesis is correct, then the giant planet fraction (defined as planets having radii greater than 5 Earth radii divided by the total number of planets) should increase as one increases the mass of the host star. Again, if one lives dangerously, throwing caution regarding biases completely to the wind, this seems to be the case with the 1235 Kepler candidates:

The planetary disturbing function describes the time-dependent perturbing potential of one planet acting on another. The disturbing function dictates the non-Keplerian evolution of planetary orbits, and while it’s conceptually simple, it’s a triumph of analysis that it can be written down as a function of the planetary orbital elements themselves.

In large part, celestial mechanics consists of choosing the right terms in the disturbing function for a particular planetary configuration, and then working out the simplified motion that arises from the chosen terms. With this program, phenomena ranging from the “Great Inequality” of Jupiter and Saturn to the possible eventual ejection of Mercury from the Solar System can be isolated and understood.

Wednesday’s Kepler data release spills a nearly overwhelming number of new multiple-planet systems into the public domain. The data include 115 candidate double-transit systems, 45 triples, 8 quads, and one each with five and six transiting planets. Precise timing measurements make all of these set-ups amenable to analysis. Correct case-by-case invocation of the disturbing function, along with an account of tidal dissipation when relevant, will generate a deep understanding of what these planets are doing, and how they got to their present state.

That’s more than a few days work. In the interim, Dan Fabrycky has created a mesmerizing video (click here for the YouTube link) which shows a wide selection of the new multi-planet systems running through their orbits for the duration of the nominal Kepler mission. It’s a multiplexed digital update of the classical clockwork orrerys that mechanically integrated the motion of those old-fashioned planets in our own solar system.

At 5pm PST yesterday afternoon, a series of papers from the Kepler team were released on astro-ph. These include the Borucki et al. overview of the full data set from the first four months of observation, as well as articles that delve more deeply into the results. It’s hard to know quite where to begin. In a field that’s seen more than its share of hype and hyperbole, these papers and the accompanying data represent a watershed. The most interesting facets of the galactic planetary census can now be downloaded onto your hard drive — either in the form of raw light curves or as a ready-mixed compilation of over a thousand planets. I guess it’s time to stay up late…

Earlier this year, while putting together my slides for a UC Berkeley astronomy colloquium, I got the list of asteroid discovery dates from the Minor Planet Center. Back in 1801, the discovery of Ceres was every bit as big a deal as the discovery of the first extrasolar planets, so I thought it would be interesting to compare the progression of the asteroid discoveries with that of the extrasolar planets.

The first four asteroids, 1 Ceres, 2 Pallas, 3 Juno, and 4 Vesta were all discovered within a few years of each other, and then there was a surprisingly long gap until the discovery of 5 Astraea in 1845. Here, (courtesy of the Wikipedia), are the relative sizes of the first 10 asteroids in comparison to the size of Earth’s Moon:

Starting in 1847, asteroid detections began ramping up, and by 1857, there were enough examples for Daniel Kirkwood to notice gaps in the distribution which he (correctly) suspected were due to orbital commensurabilities with Jupiter.

Source: D. Kirkwood, 1867 AAAS Proceedings

With the extrasolar planets, the shape of the discovery histogram is strikingly similar. The pace of events, however, has unfolded five times faster, with the gap between the discovery of HD 114762 b and 51 Peg b being followed by a steady ramp-up in the pace of confirmed detections. There are a lot more astronomers now than there were in the 1800s.

In my Berkeley talk, I remarked that if things were to continue at the 5x faster rate, then 2011 should see the first discovery of a pair of planets in a Trojan configuration, echoing the discovery of the first Trojan asteroid, 588 Achilles, by Max Wolf of the Heidelberg Observatory in 1906.

Amazingly, it looks as if a pair of co-orbital “Trojan” planets has been found by Kepler. As detailed in the Lissauer, Ragozzine, Fabrycky et al. arXiv1102.0543 paper, The KOI 730 system contains transiting candidates with periods of 7.38, 9.84, 9.85, and 14.78 days — fully consistent with a 3:4:4:6 resonance:

The two middle planets (red and blue) in the configuration are participating in what are likely to be wide tadpole oscillations with respect to the equilateral equilibrium, like Hector chasing Patroclus around inside the Trojan Horse.

The above figures are adapted from a paper that John Chambers and I wrote in 2002 that explores the different flavors of one-to-one resonance that might exist among the extrasolar planets. I’m eager to sift the Kepler data to search for examples of the one-to-one “eccentric resonance” in which two planets share an orbital period and toss their orbital angular momentum back and forth like a hot potato:

It is mesmerizing to bring the KOI-730 candidates up in the systemic console, and watch the stability integration (try integrating for 500 years with an output frequency of 0.01 years). If one interprets the radial velocity wave-form as a audible signal, the system is simultaneously playing a fourth and an octave, with the longer-period libration distinctly heard as an unsteady vibrato.

A 10-second .WAV file (created with the Systemic Console) is here. This should play in your browser when the link is clicked.

It’s also interesting to note that the first clear picture of an asteroid was taken in 1992 by the Galileo probe, which passed close to 951 Gaspra on its way to Jupiter.

Pushing the five-fold increase in pace to its natural conclusion, means you should be sure to check this site in 2028…

Image Source.

The Kepler Candidates were just announced! My immediate sensation at seeing a copy of the associated paper is not unlike those cheesy contests where you’re allowed 60 seconds in a grocery store to grab whatever you can grab for free.

The most remarkable and unexpected development seems to be contained in Table 6 of the paper. Here, it looks as if candidates identified during the first four months of data collection have had their confidence levels increased through the use of additional transit measurements taken after September 16th, 2009. This allows for the identification of fifty candidate planets that might be considered prospects for potential “habitability”.

I ran the fifty planets in the table through my valuation formula (see here, and here.)

The total value of the planets in Kepler paper’s Table 6 is USD 295,897.65. As with most distributions of wealth, this one is highly inequitable — the most valuable planet candidate in the newly released crop is KOI 326.01, to which the formula assigns a value of USD 223,099.93. Assuming 5g/cc density, this planet has a mass of ~0.6 Earth masses, which is actually a little on the low side as far as the valuation formula is ensured. Nevertheless, USD 223,099.93 is a huge increase in value over Gl 581c, which charts at USD 158.32.

Back in 2009, I wrote that (in my opinion) the appropriate threshold for huge media excitement is USD 1M. With the planets in Table 6 of the paper, we are starting to get very close to that.

Here are the planets in the table with a formula valuation greater than one penny:

(These numbers are associated with a little bit of uncertainty. I’m using Kepler magnitudes rather than V magnitudes, and assuming 5 gm/cc. I’m also assuming that stellar mass goes as stellar radius. Running a cross correlation with the other tables in the paper will change the values slightly, but not substantially.)

The whole astronomical community is buzzing with anticipation over the imminent release of the unredacted First-Run Kepler results — all of the good stuff that was held back from the data release that occurred last June.

One can only imagine what might be contained — multiple-planet transiting systems, giant planet satellites, potentially habitable planets transiting low mass stars, a definitive answer to the super-Earth occurrence rate (to name but a few).

Once the candidates hit the stands, there will be a rush to skim the cream, and a mobilization of follow-up observational campaigns to capitalize on the best opportunities in the data set. With this eventuality in mind, Konstantin Batygin and I have prepared a follow-up characterization flow chart to aid fellow exoplanet prospectors in sifting potentially interesting systems — a template for the treasure map. As always, keep in mind that the brighter the individual parent star, the better the chances for the most interesting planetary characterizations.

Click here for a legible full-size version of the flowchart. (The paper containing it is focused primarily on the rather remarkable things one can do with tidally evolved multi-planet RV-detected systems. It’s been accepted to the Astrophysical Journal, and will appear on astro-ph shortly. It’s available now for download from oklo.org.)

NOAA Weather prediction is performed continuously by two IBM Power 575 Supercomputers named Stratus and Cirrus, each carrying out 69.7 trillion calculations per second. These machines each run 20 concurrent models for a global ensemble forecast. Approved production models run on Stratus, and development codes run on Cirrus. Huge volumes of this-just-in updates to the world’s atmospheric conditions pour in constantly from satellites, radiosondes, aircraft, ships and ground stations. The resulting predictions tend to be pretty good to about five days out:

Weather prediction would get a lot harder if the atmosphere was partially ionized. Not only would the ground stations melt, but the wind would no longer be able to blow freely through Earth’s magnetic field lines, which in turn would start to behave like rubber bands that resist being stretched and squeezed. The charged wind, furthermore, would experience Ohmic resistance that would create local heating.

On hot Jupiters, temperatures are high enough so that atmospheric alkali metals such as sodium and potassium are starting to ionize. This effectively guarantees that it’s necessary to do radiation magnetohydrodynamics in order to understand how these planets really work.

In a paper published last year, Konstantin Batygin and Dave Stevension showed that Ohmic dissipation is a very attractive mechanism for providing an extra energy source that inflates hot Jupiters and contributes to the bizarre range of radii exhibited by the transiting planets (radii that have caused a lot of consternation among those who tend to worry about such things).

Konstantin’s paper got me thinking about ways to test the Ohmic dissipation hypothesis. I wrote up some initial thoughts in this post from last summer. I’ve since worked things out further in collaboration with UCSC Physics Undergrad Matteo Crismani and with Fred Adams. We have a new paper on the topic that’ll be up on astro-ph later today.

We started with the data in the plot shown above, namely the disparate collection of transiting planets with well-measured masses and radii. We computed the radius anomaly for each of these planets, that is, the difference between a plain-vanilla structural model for a solar-composition planet with the observed mass and insolation and the actual observed radii.

These radius anomalies show a strong correlation with the amount of energy that they receive from their parent stars. If one examines power-law fits, it turns out that radius anomalies scale with temperature to the 1.4+/-0.6 power.

Our bottom line is that this power-law dependence is very much in line with what one might expect from Ohmic heating (if the back reaction of the magnetic field onto the wind speed is taken into account), and my guess is that Batygin and Stevenson have taken out a large chunk of the radius problem. (See also, their very recent follow-up paper with Peter Bodenheimer).

Our paper contains several pages of details that might not be appropriate for a family-oriented site such as oklo.org, so if you’re interested, then by all means download the .pdf and have a look…

Here’s a selection of lead-off introductory lines from discovery papers of a completely random sample of planets announced in 2010:

With the discovery of extrasolar planets during the past 15 years, it has now become evident that our solar system is not unique. Similar to our Sun, many stars are believed to be hosts to giant and/or terrestrial-class planets and smaller objects.

In recent years, extending the threshold for exoplanet detection to yet lower and lower masses has been a significant endeavor for exoplanetary science. As at 2010 October, 31 exoplanets have been published with minimum (i.e., m sin(i)) masses of less than 20 Earth masses.

Radial velocity (RV) searches for extrasolar planets are discovering less massive planets by taking advantage of improved instrumental precision, higher observational cadence, and diagnostics to identify spurious signals. These discoveries include planets with minimum masses (M sin i) as low as 1.9 Earth masses (Mayor et al. 2009) and systems of multiple low-mass planets (Lovis et al. 2006; Fischer et al. 2008; Vogt et al. 2010). To date, 15 planets with M sin(i) < 10 Earth masses and 18 planets with M sin(i)=10–30 Earth masses have been discovered by the RV technique (Wright et al. 2010, Exoplanet Orbit Database10).

Ground-based transit surveys have been very successful at discovering short-period (P < 5 days) transiting extrasolar planets (TEPs) since 2006.

There has been a rapid increase in the number of transiting planets discovered each year due to dedicated ground– and space– based surveys: HAT (Bakos et al. 2002), TrES (Alonso et al. 2004), XO (McCullough et al. 2005),WASP (Pollacco et al. 2006), CoRoT (Baglin et al. 2006) and Kepler (Borucki et al. 2010). This trend looks set to continue, with the discovery of over 35 new planets published already this year (mid 2010), which represents more than a third of the total number of transiting planets known.

These soothing, robotic cadences are familiar to everyone who writes introductions and discussions for planet discovery papers. Those astronomers write prose with machine-like precision. Machine-like. Hmm…

Last year, after one of our “Wouldn’t it be cool if?” conversations, Stefano Meschiari decided to take up the daunting challenge of developing an NLG software package that can analyze radial velocity data, “discover” any statistically significant planets contained therein, and then write a publication-quality paper, that includes a human-readable introduction and analysis.

Stefano soon produced an amazing first-draft package, which he’s named “BAM” — short for Big Automatic Machine. Check out this screen-capture video of the systemic console hooked up to the BAM:

The Big Automatic Machine in action

There are certain advantages to having a computer write planet detection papers… BAM can go out on the Internet and scour the catalogs and the literature, which allows it to place new planets smoothly into the broader context. By looking at where new planets fall within the confines of all the known distributions, it can spot trends, peculiarities, and facets of interest.

As an example, for the planets discussed in Stefano’s latest lead-authored paper, BAM notices that several of them fall in a somewhat sparsely populated region of the mass-period diagram:

With a little coaxing and advice from its human minders, it now produces the following discussion:

All the planets presented in this paper lie well within the existing exoplanet parameter envelopes (Fig. 15). Several of them lie in the so-called “desert” in the mass and semi-major axis distribution of extrasolar planets (Ida & Lin 2004). Monte-Carlo population synthesis models for extrasolar giant planet formation tend to suggest that planets migrate relatively rapidly through the period range between 10 and 100 days, and, in addition, often grow quickly through the mass range centered on the Saturnian mass. In the context of the overall planetary census, these four new planets help to further elucidate the various statistical properties of exoplanets. In particular, the discovery of multiple-planet systems helps in further characterizing the number of stars hosting multiple planetary companions and any correlations emerging in the distribution of orbital elements as suggested by observational clues (e.g. Wright et al. 2009).

With extrasolar planets as the topic, art retains a certain precedence over craft, and for the foreseeable future, BAM will be stuck with a learner’s permit — only allowed to drive if there’s a licensed driver in the car. I can imagine more mercenary, lawyerly, applications, however, where it will be able to really come into its own.

BAM, with its perfect command of LaTeX, its dry analytic mindset, and its cautiously factual discussions, writes prose that is pretty much the opposite of the writing that you’ll find in Jack Keroac’s On the Road. From the Wikipedia:

Keroac completed the first version of the novel during a three-week extended session of spontaneous confessional prose. Kerouac wrote the final draft in 20 days, with Joan, his wife, supplying him bowls of pea soup and mugs of coffee to keep him going. Before beginning, Kerouac cut sheets of tracing paper into long strips, wide enough for a type-writer, and taped them together into a 120-foot (37 m) long roll he then fed into the machine. This allowed him to type continuously without the interruption of reloading pages.

In the mid-1950’s, at the urging of Allen Ginsberg and William Burroughs, Keroac compiled a list of “essentials” for writing the spontaneous prose that comprises On the Road and his other work. Taken as a set of instructions, they seem almost perfectly designed to defy machine implementation in an NLG program. Take for example, the prescription for implementing proper structure:

STRUCTURE OF WORK
Modern bizarre structures (science fiction, etc.) arise from language being dead, “different” themes give illusion of “new” life. Follow roughly outlines in out fanning movement over subject, as river rock, so mind flowover jewel-center need (run your mind over it, once) arriving at pivot, where what was dim-formed “beginning” becomes sharp-necessitating “ending”and language shortens in race to wire of time-race of work, following laws of Deep Form, to conclusion, last words, last trickle-Night is The End.

One gets the feeling that the computers are still a decade or so away…

This coming July, the planet Neptune will have completed one full orbit since its discovery on September 23, 1846, an event which constituted the occasion, a week ago Sunday in Seattle, for a special session of the Historical Astronomy Division of the American Astronomical Society. From the conference program:

The year 2011 marks not only the 200th anniversary of the French mathematical astronomer Urbain Le Verrier’’s birth, but also the first return of Neptune to its optical-discovery position in 1846. Despite the passage of more than 164 years since that planet discovery, the circumstances surrounding the near-simultaneous mathematical predictions of a transuranian disturbing planet made by Le Verrier and John Couch Adams, a young Fellow in St. John’s College at the University of Cambridge, and the subsequent optical discovery of Neptune by German astronomer Johann Gottfried Galle at the Berlin Observatory continue to remain controversial. The double anniversary occurring in 2011 is an appropriate time to examine the Neptune discovery event from a number of new perspectives. In this session we shall explore how Cornwall shaped Adams’ early education and his method of locating the presence of a hypothetical disturbing planet. We shall examine the possibility that Adams (and perhaps Le Verrier as well) may have had Asperger’s Syndrome (high-functioning autism), a condition that may explain their difficulties in communicating and interacting with their contemporaries. The intense French press attack on British astronomers immediately after the discovery is examined in detail for the first time. The role that Benjamin Peirce’s analysis of Neptune’s actual orbit (which differed greatly from those hypothesized by Adams and Le Verrier) played in the development and European perception of American astronomy and mathematics will be discussed. We open and close the session with presentations placing the Neptune discovery event within the context of 19th-century science and relating it to modern-day searches for planets in the outskirts of the solar system and around other stars.

That Benjamin Peirce (pictured above), of the Harvard College Observatory, generally plays no role in the Astronomy 101 narrative of the discovery of Neptune is an interesting object lesson in itself: Nobody likes a playa hater. Peirce pointed out the inconvenient truth that the orbits calculated by Adams and LeVerrier, both of whom relied on Bodes’ law to inform their semi-major axes, are startlingly different from the actual orbit of Neptune:

In Peirce’s view, the discovery of Neptune constituted a “happy accident” because the event took place at the fortuitous time when the longitudes of the predicted and observed incarnations of Neptune lay near the same point on the ecliptic. Fast forward by one orbit, and the predictions don’t fare particularly well in a visual search with a 24.4 cm refractor:

Peirce did have a point. If you use a vague empirical law to inform a prediction, are you justified in reaping the accolades? Indeed, some of the praise that came to LeVerrier might justifiably have been seen as over-the-top:

I cannot attempt to convey… the impression that was made on me by the author’s undoubting confidence, but the firmness with which he proclaimed to the observing astronomers, `Look into the place which I have indicated and you will see the planet well.’

–George Bidell Airy, British Astronomer Royal

This scientist, this genius… had discovered a star with the tip of his pen, without other instrument that the strength of his calculations alone.

–Camille Flammarion

Now I’ll be the first to admit, I’m just about the last person who’s justified in taking the high road when it comes to planet “predictions”. For particularly egregious examples of my behavior in this particular regard, one need look no further than here, here or here. Nevertheless, here’s a set of obnoxiously rigorous criteria that I think would have satisfied even Benjamin Peirce’s exacting standards:

In order to be considered as having accurately “predicted” a planet, one must specify, prior to discovery, the planet’s

1. Mean anomaly to within +/- 19 degrees.
2. Argument of periastron to within +/- 19 degrees
3. Orbital eccentricity to within 0.1
4. Period to within 10%
5. Mass to within 10%
6. Inclination to within 10%
7. Longitude of the ascending node to within +/- 19 degrees.

Predictions are always popular around the New Year. When will exoplanet.eu list 1000 entries on its main catalog? When will that first million-dollar planet turn up? What will the spot price of molybdenum be on Dec. 31, 2011?

Rather than risk the scruffy inconveniences of being wrong on such near-term prognostications, “but last year, you said…”, I thought it’d be better to issue a comfortably long-term prediction: For how much longer will Earth-based observers be able to observe transits for HD 80606b?

HD 80606b has been a focus lately. We’re scrambling to get our (intriguing) new results written up and submitted before the proprietary period runs out on our Spitzer data from last year’s early January eclipse observations. As long-term readers know, HD 80606b is remarkable not only for its eccentricity and its transit, but also for the fortuitous orientation of its orbit. Several hours after the planet comes out of secondary eclipse, it passes through periastron, and shortly thereafter, its pseudo-synchronous rotation rapidly turns its unheated hemisphere toward Earth. Six days later, the planet passes through primary transit, and then it begins the long climb up to the cold-storage of apoastron.

At the 100,000 light-year scale of the galactic disk, HD 80606, at ~190 light-years distance, is right next door. Its proper motion is currently shifting it across the sky at a rate of 1/75,000th of a degree per year, and it is receding from Earth at a rate of 1 light year per hundred thousand years (about 1/3 the rate of the Pioneer probes). As it drifts through space, our vantage of the system gradually changes. Right now, HD 80606 and its binary companion HD 80607 are centered in the 0.8 deg x 0.8 deg view just below. During the last ice age, they were out of the frame.

Upon receiving the above image from Goddard Skyview, I was surprised to see that HD80606 and HD80707 are currently less than a full-Moon’s width away from an impressive 10th-magnitude flocculent spiral galaxy. Turns out to be NGC 2841, which lies 46 million light years distant, contains over a billion transiting planets, and looks fantastic in this close-up, taken from Johannes Schedler’s backyard observatory:

Image: Panther Observatory Styria, Austria

This galaxy has also been imaged with Spitzer at 3.5 (blue), 4.5 (green) and 8 (red) microns. Warm dust heated by star formation in the arms glows falsely in the red. Star formation has all but shut off in the inner spheroidal region, which shines in the shorter-wavelength infrared light of an older spheroid stellar population.

Where transiting planets are concerned, however, it’s quality, not quantity that matters, and proximity is everything. As our line of sight to the HD 80606 system slowly changes, the transit geometry will shift. While we know almost everything about HD 80606b’s orbit, the one thing that we don’t know is the orientation of the transit chord relative to the cardinal directions in the plane of the sky. As a result, the change in our viewpoint created by proper motion could be leading to a transit impact parameter that is either increasing, decreasing, or staying roughly the same.

In the event that the proper motion were leading to the maximum increase in the impact parameter, and if the orbital orientation was fixed in space, then the transits could end as soon as 27,000 years from now. The orbit, however, is not fixed. Both the node and the periastron line are precessing as a result of rotational and tidal deformation in the star and the planet, as a consequence of the torque exerted by HD 80607, and as a result of general relativity. It turns out that the relativistic precession dominates, and is forcing ‘606b’s periastron to circulate with a period of about 600,000 years. The precession is prograde, and so as a result, the star-planet distance at the transit midpoint is currently decreasing by about 300 km every transit.

As a result, even for the least optimistic geometry, transits of HD 80606b will persist for roughly the next million years due to the commensurability between the time-scale for relativistic precession and the time for the line-of-sight inclination change to fully sweep the transit chord across the star. In addition, with careful (JWST-caliber) timing of the changing interval between the secondary eclipse and the primary transit, as well as the duration of the primary transit, one should be able to get both a test of general relativity and a constraint on the plane-of-the-sky rotational orientation of the system. Cool!

There are a lot of good books in the public domain. In Oscar Wilde’s Picture of Dorian Gray, I’ve always been intrigued by the description of…

…the yellow book that Lord Henry had sent him. What was it, he wondered. He went towards the little pearl-coloured octagonal stand, that had always looked to him like the work of some strange Egyptian bees that wrought in silver, and taking up the volume, flung himself into an armchair, and began to turn over the leaves. After a few minutes he became absorbed. It was the strangest book that he had ever read.  […] The style in which it was written was that curious jewelled style, vivid and obscure at once, full of argot and of archaisms, of technical expressions and of elaborate paraphrases […] There were in it metaphors as monstrous as orchids, and as subtle in colour.

Google books, with its vast digitized sea, imbues the esoteric with the convenience of a TV dinner. While sitting at the gate in O’Hare waiting for the flights that would take me to the Torun Conference a few years ago, it occurred to me that it might be cool if my talk had a scan from an original edition of De revolutionibus orbium coelestium. A minute later, it had been pulled from the ether by my computer.

(A Rebours makes decidedly better reading. While Copernicus’ great work is at once, full of argot, archaisms, and technical expressions, it is wholly devoid of metaphors as monstrous as orchids, and as subtle in colour.)

With millions of digitized books, one can step away from trying to find those individual bits of half-remembered ephemera, and instead treat all the words in all the books statistically. There was an article in Science last week (Michel et al. 2010) which received lots of press, and which contains a link to Google’s Ngram viewer.

An “Ngram” is a neologism for a specific string of N words. The idea is that you can trace cultural trends by charting the frequency with which words appear in books. For example, for 5 million books published between 1800 and 2000, the frequencies of appearance of 61 Cygni, Alpha Centauri, Proxima Centauri, Beta Pictoris, and 51 Pegasi are:

61 Cygni, which, in 1838 was the first star to have its distance correctly measured, was a marquee attraction during the Nineteenth Century. As a result of Thomas Henderson’s timidity in publishing his parallax, it took Alpha Centauri, which is closer, brighter, and more alluring, more than 80 years to surpass 61 Cygni’s fame. Proxima, which was discovered in 1915, has never managed to be as popular as Alpha, and, until recent decades, has struggled to keep up with 61 Cygni. Beta Pictoris makes its debut in 1983, and 51 Pegasi starts turning up after 1995.

As a visit to Borders will quickly confirm, books are fast losing their status as a cultural linchpin. For topics of current interest, Google trends is more the destination of choice. Here, one can follow the share of the total global search volume that a particular N-gram elicits. News reference volume is also charted. Among the stars of interest, there is a steady stream of searches on Alpha Centauri. Against this background, there are three rather notable spikes associated with Gliese 581, which, prior to 2007, languished in complete obscurity.

After the 2007 spike, Gliese 581’s mojo quickly faded to a small fraction of Alpha Centauri’s.

Interestingly, though, the 2010 pattern is behaving differently. In the months following the most recent spike, Gliese 581 has been running neck and neck with Alpha C in competition for the world’s notice.

Photo credit: Bill Lowenburg — From the Crash Burn Love Project

I sure enjoyed that article on Figure-Eight racing in last Sunday’s New York Times. The piece is a shameless sop, of course, to the smug ironic-hipster segment of the NYT readership — not unlike twelve-packs of Pabst Blue Ribbon stacked up in front of the checkout counter at Whole Foods — but it’s also a great story. The racers adhere to a pure recession-era hellenic ideal, risking life and limb for glory, complete with six-time world champion Bob Dossey channeling a latter-day wrath of Achilles.

And the exoplanet connection? Orbital mean-motion resonances with large libration widths bring to mind a smoothly-running Figure-Eight race. The planets roar around the parent star, continually missing each other at the intersections of their crossing orbits. Here’s an animation of the HD 128311 2:1 resonant pair, strobed over several hundred orbits.

(Animation was causing the site to slow down, so I took it down.)

To date, several such systems are known. In addition to HD 128311 b and c, a similar state of affairs also seems to hold in the HD 82943 and HD 73526 systems, both of which appear to harbor planets in 2:1 mean motion resonance with large libration widths. For all three of these systems, however, the degree of confidence that the correct dynamical configuration has been identified is somewhat less-than-satisfying. Rather than directly observing the resonant dynamics, one notes in each case that a whole bundle of model systems can be constructed which fit the radial velocity data. Within these large sets of allowed configurations, the ones that are dynamically stable over time scales of order the stellar lifetime tend to have large libration widths.

By contrast, Gliese 876 — the one system for which the radial velocity solution provides direct and unambiguous access to the resonant configuration — has its two largest planets lying very deeply in 2:1 resonance, and the libration width is just a few degrees. It bothers me that Gliese 876 seems to be so qualitatively different. It’s easy to wonder whether there might be an error of interpretation for the indirectly characterized systems.

Resonance libration widths are more than just a curiosity. They provide a record of the conditions that likely existed in the protostellar disks from which the planets formed. A turbulent disk produces transient density fluctuations that cause the libration width of a resonant pair of planets to undergo a random walk, much as a stochastically driven pendulum will, on average, tend to gradually increase the height of its swing. The plot below (which comes from a 2008 ApJ paper written with Fred Adams and Anthony Bloch) shows the results of five individual simulations in which gravitational perturbations mimicking those arising from disk turbulence are applied to integrations of the Gliese 876 A-b-c system. In each case, the libration width of the resonant argument tends to increase with time. Perhaps the Gliese 876 system was very lucky, and despite being buffeted managed to end up with a tiny swing. More likely, the gas flow in Gliese 876’s disk was relatively calm and laminar.

Until now, almost everything we know about extrasolar planets in resonance has come from the radial velocity surveys. This year, Kepler is also starting to contribute, with the announcement of  a new system — Kepler 9 — which exhibits detectable transit timing variations. The planets orbiting Kepler 9 were announced with media fanfare during the recent Haute Provence meeting, and a detailed article (Holman et al. 2010) will soon be published in Science. The Kepler 9 set-up is oddly reminiscent of Gliese 876. Two Saturn-sized (and somewhat less than Saturn-mass) planets orbit with periods currently in the vicinity of 19 and 39 days. Further in, an unfortunate super-Earth is stuck is a blistering 1.6-day orbit. Here are the orbits drawn to scale.

The planetary and stellar radii are not to scale, but rather, are sized to conform to the NASA press release artist’s impression of the system…

Kepler 9’s orbital geometry represents quite an extraordinary draw! All three planets can be observed in transit, and the strong gravitational interactions between the two outer planets lead to large deviations from strict periodicity. Indeed, the system is simultaneously tantalizing and maddening. The parent star is many times fainter than Gliese 876, meaning that it will be difficult to get a large collection of high-quality radial velocity measurements. In order to really characterize the dynamics of the system, it will be necessary to lean hard on transit timing measurements. The observations published in the Science article have a low per-point timing cadence; skilled amateur observers can obtain timing measurements that have higher precision and which significantly extend the time baseline, and so the system presents an excellent opportunity for small telescopes to obtain cutting-edge results. The parent star (in Lyra) is still up in the Northern Hemisphere’s evening sky, and there are transits coming up!

During the time that Kepler monitored the system last year, the orbit of the outer planet, “c” (P~38.9 d) was observed to be steadily decreasing by 39 minutes per orbit, and the orbital period of the inner planet, “b”  (P~19.2 d) was increasing by 4 minutes per orbit. Clearly, this state of affairs can’t continue indefinitely. If the system is in a 2:1 mean motion resonance, then over the long term, the periods of the two planets will oscillate around well-defined average values. The Kepler measurements strobed the system over a relatively small fraction of its overall cycle. An analysis of the planetary disturbing function (in which all but the most significant terms get thrown out) indicates that the libration time should be of order the orbital timescale (40 days) multiplied by the square root of the planets-to-star mass ratio (~100), or about ten years.

We don’t know exactly which part of the cycle Kepler dropped in on, and so the second derivative (rate of change of the rate of change) of the period could be either positive or negative. This means that there is a significant uncertainty on when the next transits will occur, but it also means that accurate measurements will immediately give a much better idea of what is going on.

The next opportunities will occur on October 5th (for 9c) and October 8th (for 9b). As always, observers should use the TRESCA website to double-check observing details and to submit light curves after the observations have been made. As the dates approach, I’ll post specific details for small-telescope observers — it will take a global effort to ensure that definitive observations are made. We’ll also soon be releasing an updated version of the systemic console that will allow for the modeling of TTVs in double-transit systems.

…are often risky, but can be illuminating nonetheless.

The astronomy decadal report, which was issued a few weeks ago, set forth three big-picture goals for the next decade: (1) searching for the first stars, galaxies, and black holes; (2) seeking nearby habitable planets; and (3) advancing understanding of the fundamental physics of the universe.

It’s looking quite likely that goal number two will be the first to get substantially met. For quite a while now, a plot of year of discovery vs. the known planetary Msin(i)’s has provided grist for speculation that the first announcement of an Earthlike Msin(i) will occur this year…

In all likelihood, the surface of the first Earth-mass object detected in orbit around a sun-like star will be better suited to oven-cleaning than life as we know it. An interesting question, then, is: when will the first potentially habitable planet be detected? As readers know, such a world will very likely be detected via either transit (MEarth, Warm Spitzer or Kepler) or by the radial velocity technique (HD 40307, Alpha Cen B, etc. etc.).

Earlier this year, I struck up an e-mail conversation with Sam Arbesman, a Research Fellow at Harvard who studies computational approaches to the social sciences. Sam has a rather eclectic spectrum of interests, and writes pieces for the Boston Globe and the New York Times on topics ranging from mesofacts to baseball statistics. He’s also in charge of collecting fares for the Milky Way Transit Authority.

We carried out a scientometric analysis to arrive at what we believe is likely to be a reasonably accurate prediction of the discovery date of the first potentially habitable extrasolar planet with a mass similar to Earth.

Our paper has been accepted by the journal PLoS One, and Sam just posted to arXiv, apparently with little time to spare. The best-guess date that emerged from the analysis is May 2011.

Audaciously, alarmingly close! Certainly soon enough, in any case, for us to look rather sheepish if we’re off by a significant amount…

Exciting times for the exoplanet field. The announcement of the first million-plus dollar world is only days to weeks to months or at most a year or two away, and in the interim, the planet census keeps expanding.

At the same time, however, all the new planets are accompanied by a certain creeping degree of frustration. I have a feeling that these worlds, and especially the super-Earths, will prove to be even more alien than is generally supposed. Artist impressions do a good job when it comes to gray and airless cratered surfaces, but are necessarily inaccurate or impoverished or both in the presence of masses more than a few tenths that of Earth. And because of the distances involved, we won’t be getting the really satisfying images any time soon.

With my provincial day-to-day focus on Gl 876, Gl 581, HD 80606 et al., I tend to forget that we’ve got a full-blown planetary system right here in our back yard. It caught me by surprise, months after the fact, and via a thoroughly tangential channel, that a sober-minded case can be made for the presence of methane-based life on Titan. In fact, a detailed case has been made, complete with specific predictions, and, startlingly, those predictions now seem to have been confirmed.

In 2005, Chris McKay (whose office was just down the hall when I worked at NASA Ames’ Planetary System Branch) wrote an Icarus paper with Heather Smith proposing that methanogenic life might be widespread on Titan. McKay and Smith argue that one macroscopic consequence of such life would be a depletion of ethane, acetylene, and molecular hydrogen in Titan’s near-surface environment. Recent work seems to indicate that all three compounds are indeed depleted, which is very interesting indeed.

The details, and an assessment of the odds are a topic for another post. The simple fact that Titan is in the running at all is absolutely remarkable. Toto, I’ve a feeling we’re not on Mars anymore. Methane-based life in the Saturnian system would seemingly stand a far higher chance of stemming from a completely independent genesis. If Titan has managed to put together a biosphere, then there could very well be more life-bearing planets in the Galaxy than there are people.

The prospect of widespread life on Titan brings to mind the descent of the Huygens probe on January 14, 2005. I remember wondering, in the days running up to the landing, what the probe was going to see, and thinking that it was a once-in-a-lifetime moment of anticipation. Titan is the only world in our Solar System in which there was seemingly a chance, albeit very slim, of having a genuinely world-altering scene unfold upon touchdown. I knew that in all likelihood, the scene was likely going to look something like a cross between the Viking  and Venera panoramas, but I couldn’t quite squelch that lotto-player’s like expectation that pictures of a frigid silurian jungle would be radioed back across light hours of space…

As everyone knows, there was no golden ticket in the chocolate bar, but might we still have a chance to see something really exotic when the next probe touches down?

It’s always seemed to me that the relatively mundane ground-level view at the Huygen’s landing site was somewhat at odds with the electrifyling promise implicit in the probe’s descent sequence. From 150 kilometers up, the haze is just starting to part — the view is not unlike the one that Percival Lowell had through his telescope of Mars. Faint dusky markings that one can connect in the mind’s eye to just about anything:

From 20 kilometers up, a wealth of detail is visible. Alien rivers, shorelines, islands?

The Huygen’s signal was extremely weak. The images arrived in a jumble, with Earth’s largest radio telescopes straining to hear them. It’s interesting to imagine what the level of anticipation might have reached had we known of the atmospheric depletions, and had the images arrived in real time as the probe drifted down toward the surface. Here’s the view from six kilometers up. Think of the looking out the window of a Jetliner several minutes after the start of descent from cruising altitude:

From 2 kilometers up:

From .6 kilometers up:

From a mere 200 meters altitude:

What if we carry out the same exercise and land a probe at a random spot on Earth? To roughly 1-sigma confidence, we’d come in for a splashdown somewhere in the ocean. Out of sight of land, no macroscopic life visible, just water, clouds and blue sky, and just like Huygen’s landing on Titan, a disappointment with respect to what might have been…

So I decided to wrap up the post by forcing the hand of chance. Using true random numbers (generated, appropriately enough by random.org through the use of Earth’s own atmospheric noise) I drew a single random location on the surface of a sphere, and calculated the corresponding longitude and latitude. The result?

-26.478972 S, 132.022361 E.

Google Maps makes it possible to drift in like Huygens for a landing sequence at any spot on Earth. The big picture, of course, is completely familiar, so the suspense is heightened in this case by successively zooming out.

The next scene, which is roughly a mile on a side, is quite readily set into the mental context. The random spot is in the Australian outback. Red dust, scattered rocks, scrub brush, spindly trees, and most evocatively, a building, a cul-de-sac, and a lonely stretch of dirt road bisecting the lower right corner of the view. Of course, had the probe come in a few decades ago, the scene would be no less tantalizing than what we had from Huygens at similar altitude. Those could easily be boulders, not treetops.

Aside from the roads, at a scale similar to where Titan was first revealed, Titan holds out, if anything, more promise than -26.478972 S, 132.022361 E:

To set context, one can zoom all the way out. By coincidence, -26.478972 S, 132.022361 E is not far from the zone peppered by the reentry of Skylab on 11 July 1979, which ranged from 31° to 34°S and 122° to 126°E.

With a simulated Earth landing, we’re allowed to cheat, and get the full scoop on our landing spot. This is as simple as enabling geo-tagged photos and Wikipedia entries:

The wikipedia links are here and here. -26.478972 S, 132.022361 E is just over a rise from a solar power station on the Anangu Pitjantjatjara Yankunytjatjara local government area.

And imagine a probe touching down just in time to record this scene:

Image source.

The radii of the transiting extrasolar planets have been the source of a lot of consternation. It’s very hard to tell the mass of a planet simply by looking at how large it is.

In our own solar system, there’s a well-delineated correlation between planetary size and planetary mass, with the only modest exception being Uranus and Neptune. Uranus has the larger radius and Neptune has the larger mass. With the extrasolar planets, on the other hand, the situation is notoriously less clear-cut. Transiting planets, with HD 209458b providing the textbook example, are often considerably larger than expected, hinting at a cryptic energy source.

With the WASP and the HAT surveys firing on all cylinders, the catalog of well-categorized transiting planets has been growing quite rapidly. There are now close to 90 planets with reasonably well determined masses and radii, so I thought it’d be interesting to take stock of the catalog with an eye toward evaluating how bad the radius problem really is.

Back in 2003, Peter Bodenheimer and Doug Lin and I did a series of planet evolution calculations which solved for the equilibrium radii of giant planets made from hydrogen and helium (and both with and without solid cores). Our models spanned a range of planetary masses and surface temperatures, and they provide a baseline expectation for how large gas giant planets “should” be (radii are in Jovian units):

Clear trends can be seen by studying the table. For example, once planets get significantly more massive than Jupiter, they stop increasing their radii. This is a consequence of the interior equation of state growing progressively more electron degenerate. It’s also true that the hotter a planet gets, the larger it’s expected to be, and a core of heavy elements causes a planet to have a smaller overall radius.

With the baseline “no core” models in hand, it’s straightforward to see whether a newly discovered planet conforms to expectations. With some exceptions, the extrasolar planets have not tended to conform to expectations (a state of affairs that has held up quite robustly, in fact, across the entire exoplanet field, where theoretical predictions have rarely presented any real utility). A significant fraction of hot Jupiters are a lot larger than expected, and there are also some that have turned out to be considerably smaller than expected. For a given planet, we can define the “radius anomaly” as the fractional discrepancy between the predicted radius and the observed radius. A planet like HD 209458b has a large positive radius anomaly, whereas a planet like HD 149026b has a large negative radius anomaly.

One can garner clues to the source of the radius problem for extrasolar planets by regressing the radius anomalies against possible explanatory variables. The most dramatic effect comes when one plots radius anomaly as a function of effective planetary surface temperature:

As a general rule, the hotter the planet, the more severe the radius anomaly. This points to ohmic heating as the most likely culprit for pumping planets up. The hotter the planet gets, the larger the ionization fraction in the atmosphere, and the more effectively the weather is able to act as a toaster. Konstantin Batygin and Dave Stevenson’s recent paper on this topic is almost certainly barking up the right tree.

Another interesting correlation arises when one plots radius anomaly versus stellar metallicity after removing the planet temperature trend observed in the plot above. In this case, there’s a modest correlation with the opposite sign:

Planets with negative radius anomalies tend to orbit metal rich stars. This is a natural (and expected) consequence of the core accretion hypothesis for giant planet formation.

Simple linear dependencies on planetary temperature and stellar metallicity are able to account for more than half (but not all) of the observed variance in the radius anomalies. The missing factor could come from a number of sources — nonlinearity in the correct model description, observational biases, or perhaps something else altogether…

Finally, in the this-just-in Department, there’s a paper up on astro-ph this week detailing the discovery of HAT-P-18, and and HAT-P-19. These two planets certainly don’t enhance the suggestiveness of the above plots — their anomalies are anomalous. Both of the new Hats are relatively cool, relatively low mass planets orbiting relatively metal rich stars. And they’re both swelled up! Tidal heating? Could be.

It’s no exaggeration to assert that Galileo’s unveiling of Io, Europa, Ganymede and Callisto counts among the epic scientific discoveries of all time.

And certainly, it’s fair to say that the Galilean satellites of Jupiter constitute the original exoplanetary system. The Galilean satellites have been producing scientific insights for over four hundred years. Nearly all of the modern exoplanetary discoveries have antecedents — some quite recent, some centuries old — in Jupiter’s four moons.

The Galilean satellites can all be observed in transit across the face of Jupiter, and as early as 1656, the Sicilian astronomer Giovanni Hodierna, with his Medicaeorum Ephemerides, emphasized the importance of transit timing measurements for working out accurate predictive tables. In the late 1660’s, University of Bologna Professor Giovanni Cassini’s timing measurements and associated tables for the Jovian system were so impressive that he was tapped by Jean-Baptiste Colbert and Louis XIV to become director of the newly established Paris Observatory.

Giovanni Domenico Cassini (1625-1712). Prior to holding the directorship of the Paris Observatory, he was the highest paid astronomer at the University of Bologna, having been appointed to his professorship by the Pope.

Throughout the 1670s and 80s, Cassini wrestled with the fact that accurate transit timing measurements for the Jovian satellites create serious difficulties for models in which the moons travel on fixed orbits. Irregularities in the transit timings made from the Paris Observatory led to Ole Roemer’s determination of the finite speed of light in 1676, and by the early 1700s, observations of transit duration variations revealed that rapid nodal precession occurs in the Jovian system.

By middle of the Eighteenth Century, adequate data were in hand to demonstrate that a very curious relationship exists between the orbits of Io, Europa, and Ganymede. In 1743, the Swedish astronomer Pehr Wilhelm Wargentin (the first director of the Stockholm Observatory) published tables which made it clear that the 1:2:4 ratio in periods between Ganymede, Europa and Io is uncannily exact. Wargentin’s tables implied that a triple eclipse (in which all three satellites transit at once) would not occur until 1,319,643 CE at the earliest, and that the “argument”

between the mean longitudes of the satellite orbits is maintained to an extraordinary degree of accuracy. Geometrically, this means that the satellites engage in a cycle of six successive moon-moon conjunctions during the course of one Ganymedian orbit, and in so doing, manage to continually maintain ?_L=180°:

Laplace realized that a dynamical mechanism must be responsible for maintaining the cycle of conjunctions, and in 1784, was able to show that the angle ? is subject to a pendulum-like oscillation. If the satellites are perturbed slightly, then over the time, the satellite-satellite interactions conspire to cause ? to oscillate, or librate, back and forth about the equilibrium value of 180°. His theory for the satellites allowed him to derive the masses of the moons, and also predicted that the oscillation period for ? would be 2270d 18h.

In Laplace’s time, the observations were not accurate enough to sense any measurable amplitude for the libration — it appeared that the satellites were perfectly placed in the 1:2:4 resonant condition. We now know, however that ? librates with a tiny amplitude of 0.064°, and that the period of oscillation is 2071d, quite close to the value predicted by Laplace. Yoder and Peale (1981) have shown that the highly damped libration of ? can be understood as arising from a near-balance between tidal dissipation in Jupiter and tidal dissipation in Io. The presence of a dissipative mechanism has allowed the marble to have settled almost precisely into the bottom of the bowl.

On this evening’s astro-ph mailing, our team has posted a paper that describes our discovery of a second example of a Laplace three-body resonance. Continued radial velocity monitoring of the nearby red dwarf star Gliese 876 has shown that the well-known P~30d and P~61d giant planets in the system are accompanied by an additional planet with a mass close to that of Uranus and an orbital period P~124d. In contrast to the Jovian system, the best fit to the observations shows that the Laplace relation is librating around ?=0°, and that triple conjunctions do occur. The diagram above is easily modified to convey the schematic geometry of the new system:

The actual state of affairs, however, is more complicated than shown in the above diagram. The total mass of planets in the Gliese 876 system is about 1% the mass of the central body, whereas Jupiter is roughly 5000 times more massive than its satellite system. This means that the Gliese 876 planets experience proportionally larger mutual gravitational interactions than do the Galilean satellites. In addition, the orbits are much more eccentric, and the planet-planet secular interaction causes a rapid precession of 14° per orbit of the outer planet. We can, however, plot the orbits in a co-precessing frame in order to view the cycle at four equal time intervals:

The libration of the Laplace argument, ?, around zero has an amplitude of ~40°, indicating that the GJ 876 “pendulum” packs a swing that’s 625 times larger than that of the Galilean satellites. Indeed, when the system configuration is integrated forward in time for hundreds of years, it’s clear that a simple pendulum equation is not able to describe the evolution of the Laplace angle. The oscillations are chaotic, with a Lyapunov time measured in a mere hundreds to thousands of years, and the theory, especially if there is a non-coplanar component to the motion, will require Laplace-level expertise in the use of the disturbing function…

There’s more… stay tuned for the next post.

Some of the biggest exoplanet news so far this year has arrived in the form of Rossiter-McLaughlin measurements of the sky-projected misalignment angles, λ, between the orbital angular momentum vectors of transiting planets and their stellar spin vectors.

A significantly non-zero value for λ indicates that a system was subject to some rough action in the distant past. Both planet-planet scattering and Kozai migration, for example, can lead to systems with non-negligible λ’s. The recent paper by Triaud et al. (covered here) showed that such processes may be responsible for a startlingly significant fraction of the known transiting-planet systems.

The angle λ has the advantage of being measurable, but it has marked disadvantage of informing us only of the projected geometry of the system. To get a sense of the physically relevant quantity — the true degree of spin-orbit misalignment — one needs the direction of the stellar spin vector.

Kevin Schlaufman, one of the graduate students in our program here at UCSC, has worked out a very clever method of getting a proper statistically supportable guess of the complement misalignment angle between the orbit of the plant and the spin of its host star along the line of sight. I have to say that I’m quite enthusiastic about Kevin’s paper — it’s a big jump, not an incremental advance, and it’s well worth reading.

The method leverages the fact that a mature main-sequence star of given mass and age has a fairly predictable rotation period. Sun-like stars form with a wide range of rotation periods, but by the time they reach an age of ~0.5 billion years, there is a reasonably well-defined rotational period-stellar mass relation. During the remainder of their lives, main sequence stars then slow their rotation by shedding angular momentum via Alfven-like disturbances. Stellar spin-down rates are relatively large early on, and decrease with the passage of time.

A star’s projected rotational velocity can be measured by looking at the amount of rotational broadening in the spectral lines. This gives V_rot*sin(i_s), where i_s is the unknown angle between the star’s spin pole and the line of sight. The essence of the Schlaufman method is then immediately apparent. The mass and the age of the star allow you to infer V_rot. You measure V_rot*sin(i_s), and then bam! The inclination angle, i_s, is determined.

Reality, of course, is not so clear-cut. One has a host of errors and intrinsic variation to deal with, all of which blur out one’s ability to precisely determine i_s. Nevertheless, Kevin shows quite convincingly that the method has utility, and that it is possible to identify transit-bearing stars that are very likely strongly misaligned with the plane of the sky.

The results of the analysis confirm that massive and eccentric transiting planets (such as oklo.org fave HD 17156b) are substantially more likely to have significant spin-orbit misalignment than are garden variety Jupiter-mass hot Jupiters on circular orbits. Furthermore, to high confidence, it seems that systems with substantial spin-orbit misalignment tend to have host stars with masses greater than 1.2 solar masses. A reasonable conclusion is that there are two distinct and productive channels for generating short-period giant planets. The first is a disk migration process that leaves everything calm, orderly and aligned. The second, most likely involving Kozai cycling or a variant thereof, is telegenic, action packed, and leaves a system confused and misaligned, and perhaps stripped of several original fellow planets.

It’s not often that a near-doubling of the planetary census arrives in one chunk, and so the paper detailing the latest Kepler results is of quite extraordinary interest.

It’s definitely going to be tricky to use the results in the Kepler paper to draw secure new conclusions about the true underlying distribution of planets. Nevertheless, the results look quite intriguing from the standpoint of back-of-the-envelope speculations.

Details: the paper contains a list of 312 candidate planets originating from 306 separate stars. A further 400 stars with candidate planets have been held back (see yesterday’s post), largely because they are either bright enough for high-quality Doppler follow-up at less-than-exorbitant cost, or harbor candidates with radii less than 1.5 that of Earth, or both. The paper states that the 312 candidate planets were primarily culled from an aggregate of 88,196 target stars dimmer than magnitude 14. The analysis is based on two blocks of photometry, one lasting 9.7 days (starting on May 2 2009) and one lasting 33.5 days (starting on May 13 2009).

The candidates have a slightly eclectic selection of associated data. The main table lists a radius, a transit epoch, and an orbital period for each candidate. There’s information about the parent stars as well, including apparent magnitude, effective temperate, surface gravity, and stellar radius. This is enough to make some intriguing plots. For example, the splash image for this post is a Hertzsprung-Russell diagram charting the locations of the candidates’ parent stars. The sizes of the points are directly proportional to the planet radii, and the color code is keyed to estimated planetary effective temperature. Most of the planets have surface temperatures of order 1000K or more, but there’s one rather singular object in the list, a 1.34 Rjup candidate on a 10389.109(!)-day orbit about a 9.058 solar radius G-type giant that (if it’s a planet) would have a photospheric temperature of order 180K. Certainly, a 1.34 Rjup radius is intriguing for such an object, as any non-pathological cold giant planet should be the size of Jupiter or smaller. Presumably, if the light curve showed evidence of a Saturn-style ring system, or better yet, an Earth-sized satellite, then KIC11465813 would chillin’ in the V.I.P. room.

A question of great interest is whether the list of candidates can add support to the recent radial velocity-based result that a large fraction of ordinary stars in the solar neighborhood are accompanied by a Neptune-or-lower mass planet with an orbital period of 50 days or less.

To get a first idea, I did the following quick (and extremely rough) Monte-Carlo calculation. I took 88,196 stars, and assumed that half of them have a planet with an orbital period drawn uniformly from the 1-d to 50-d orbital range. I then drew the planet masses uniformly from the 1-Earth-mass to 17-Earth-mass range, assumed Neptune-like densities of 1.6 gm/cc, circular orbits, and random orientations. For simplicity, the parent stars’ masses and radii are distributed uniformly from 0.7 to 1.3 times the solar value. I assumed that the 88,196 stars were observed continuously for 33.5 days, and require two transits to appear within the observation interval for a candidate to count. In keeping with the redaction policy, candidates are rejected if their radii were less than 1.5 that of Earth.

The simulation suggests that ~1100 candidate planets should be present in a 88,196 star sample. Encouragingly, this is at least order-of-magnitude agreement, although there’s a hint that the Kepler yield might be lower than what the RV results are implying. It will be very interesting to see what a more careful comparison has to say…

It’s always exciting when the exoplanets rise to the fore of the national discourse.

This morning’s New York Times has a very interesting article about the Kepler Mission’s proprietary data policy. In April, NASA granted the Kepler team an additional window, through February 2011, in which photometry for 400 particularly interesting stars is to be kept out of the public domain.

The article contains all the elements of exoplanetary intrigue that foreshadow traffic spikes for oklo.org in the months ahead. From the P.I., Bill Borucki:

“If I sent you 0’s and 1’s it would be useless… If we say ‘Yes, they are small planets — you can be sure they are.'”

From Ohio State’s Scott Gaudi:

“They need help,” he said, “If they were more open they would be able to get more science out…”

Delicious mention of formal non-disclosure agreements. Big-picture discussions of the meaning of data ownership in the context of federally funded research. 12,000 “suspicious dips” painstakingly distilled to 750 planetary candidates — a near-doubling, in one fell swoop, of the galactic planetary census.

And the oklo.org take? The astronomical enterprise is sometimes an excellent sandbox, a model, for understanding real-world problems. As an interested outsider, I definitely relish the challenges posed by a high-profile data set released under partial duress — a collection of both the ones and the zeroes, where the redactions can speak volumes.

Transit timing variations have a certain allure. Most extrasolar planets are found by patiently visiting and revisiting a star, and the glamour has begun to drain from this enterprise. Inferring, on the other hand, the presence of an unknown body — a “Planet X” — from its subtle deranging influences on the orbit of another, already known, planet is a more cooly cerebral endeavor. Yet to date, the TTV technique has not achieved its promise. The planet census accumulates exclusively via tried and true methods. 455 ± 21 at last count.

Backing a planet out of the perturbations that it induces is an example of an inverse problem. The detection of Neptune in 1846 remains the classic example. In that now increasingly distant age where new planets were headline news, the successful solution of an inverse problem was a secure route to scientific (and material) fame. The first TTV-detected planet won’t generate a chaired position for its discoverer, but it will most certainly be a feather in a cap.

Where inverse problems are concerned, being lucky can be of equal or greater importance than being right. Both Adams’ and Le Verrier’s masses and semi-major axes for Neptune were badly off (Grant 1852). What counted, however, was the fact that they had Neptune’s September 1846 sky position almost exactly right. LeVerrier pinpointed Neptune to an angular distance of only 55 arc-minutes from its true position, that is, to the correct 1/15,600th patch of the entire sky

In the past five years, a literature has been growing in anticipation of the detection of transit timing variations. The first two important papers — this one by Eric Agol and collaborators, and this one by Matt Holman and Norm Murray — came out nearly simultaneously in 2005, and showed that the detection of TTVs will be eminently feasible when the right systems turn up. More recently, a series of articles led by David Nesvorny (here, here, and here) take a direct stab at outlining solution methods for the TTV inverse problem, and illustrate that the degeneracy of solutions, the fly in the ointment for pinpointing Neptune’s orbit, will also be a severe problem when it comes to pinning down the perturbers of transiting planets from transit timing variations alone.

In general, transit timing variations are much stronger and much easier to detect if the unseen perturbing body is in mean-motion resonance with the known transiting planet. In a paper recently submitted to the Astrophysical Journal, Dimitri Veras, Eric Ford and Matthew Payne have carried out a thorough survey of exactly what one can expect for different transiter-perturber configurations, with a focus on systems where the transiting planet is a standard-issue hot Jupiter and the exterior perturber has the mass of the Earth. They show that for systems lying near integer period ratios, tiny changes in the system initial conditions can have huge effects on the amplitude of the resulting TTVs. Here’s one of the key figures from their paper — a map of median TTVs arising from perturbing Earths with various orbital periods and eccentricities:

The crazy-colored detail — which Veras et al. describe as the “flames of resonance” — gives the quite accurate impression that definitive solutions to the TTV inverse problem will not be easy to achieve. One of the conclusions drawn by the Veras et al. paper is that even in favorable cases, one needs to have at least fifty well-measured transits if the perturber is to tracked down via timing measurements alone.

The Kepler Mission holds out the promise of systems in which TTVs will be simultaneously present, well measured, and abundant. In anticipation of real TTV data, Stefano Meschiari has worked hard to update the Systemic Console so that it can be used to get practical solutions to the inverse problem defined by a joint TTV-RV data set. An improved console that can solve the problem is available for download, and a paper describing the method is now on astro-ph. In short, the technique of simulated annealing seems to provide the best route to finding solutions.

A data set with TTVs alone makes for a purer inverse problem, but it looks like it’s going to be generally impractical to characterize a perturber on the basis of photometric data alone. Consider an example from our paper. We generated a fiducial TTV system by migrating a relatively hefty 10 Earth-mass planet deep into 2:1 resonance with a planet assumed to be a twin to HAT-P-7. We then created data sets spanning a full year, and consisting of 166 consecutive measurements, each having 17-second precision, and a relatively modest set of radial velocity measurements. We launched a number of simulated annealing experiments and allowed the parameters of the perturbing planet to float freely.

The resulting solutions to the synthetic data set cluster around configurations where the perturber is in 2:1 resonance (red symbols), and solutions where it is in 3:1 resonance (blue symbols). Furthermore, increasing the precision of the transit timing measurements to 4.3 seconds per transit (solid symbols) does little to break the degeneracy:

The upshot of our paper is that high-quality RV measurements will integral to full characterizations of the planets that generate TTVs. At risk of sounding like a broken record, this means that to extract genuine value, one needs the brightest available stars for transits…

It’d be rather unsettling to sit down with a cup of coffee one morning, and learn from astro-ph that the orbital period of Mars is not 1.88 years as is widely believed, but is rather a mere 7.83 months.

Last week, Rebekah Dawson and Dan Fabrycky posted a paper that gave me an equivalent jolt, and which has likely touched off a certain uproar within the planet-hunting community. Their claim is that the periods of a number of A-list planets, including 55 Cnc e and HD 156668 b are in fact aliases, and that the true periods of these worlds are startlingly different. Dawson and Fabrycky argue that the true period of 55 Cnc e is a fleet 0.7365 days (revised from 2.817d), and that HD 156668b orbits with a period of 1.2699 days rather than the published value of 4.6455d. Other well-known worlds may well be in line for a similar treatment.

Sometimes, things seem very clear in retrospect. In the graph just below, I’ve plotted the reflex velocity curves for two planets. One has a period of 1.61803 days, the other has a a period of 2.61803 days. If one happens to observe only at the times when the curves intersect, then it’s clear that there’s no way to tell them apart.

In the particular case above, the intersections of the sinusoids are separated by exactly one day. If the true period of the system is 1.61803 days, then we would say that the 2.61803 day period is an alias produced by the 1-day observing frequency. In general, for an observing frequency, f_o, and a true period, f_t, aliases exist at frequencies f=f_t+m*f_o, where m is an integer.

Aliases are a problem in Doppler surveys because observations are most efficiently done when the star is crossing the meridian, leading to a natural spacing of one sidereal day (23h 56m) between data points. Further periodicities in data-taking arise because RV survey time is usually granted during “bright” time when the Moon is up, and as a consequence of the yearly observing season for non-circumpolar stars. Aliases are minimized when observations are taken randomly, but the nuts and bolts of the celestial cycles impose regularity on the timestamps.

In reducing the period of 55 Cnc e to a sizzling 17.7 hours, the probability that the planet transits is raised to a very respectable 25%. Seems to me like rolling the dice with a few hours of Warm Spitzer time might be in order.

Controversy generates revenue for exoplanet weblogs and supermarket tabloids alike, so I’m always happy when planet-related press releases roll out dramatic, far-reaching claims. Last week’s ESO press release — “Turning Planetary Theory Upside Down” — was quite satisfactory in this regard…

Upon digging into the back story, one finds that the observations underlying the press release are fully uncontroversial — it’s the big-picture interpretation that’s turning heads. Using Doppler velocity measurements taken during transit, Triaud et al. (preprint here) have measured the sky-projected misalignment angles, λ, for six of the transiting planets discovered by the SuperWASP consortium.

After an initial run of nine transiting planets were found to have sky-projected misalignment angles close to zero, the current count now has 8 out of 26 planets sporting significant misalignment. In the standard paradigm where hot Jupiters form beyond the ice line and migrate inward to reach weekend-length orbits, one would expect that essentially all transiting planets should be more or less aligned with the equators of their parent stars.

The standard migration paradigm, however, leaves at least two questions rather vaguely answered. First, why do the hot Jupiters tend to halt their inward migration just at the brink of disaster? The distribution of orbital periods — slew of selection biases aside — shows a durable peak near ~3 days. Second, why are transiting planets with well-characterized companions so scarce? In general, if one finds a giant planet with a period of ~10 days or more, the odds are excellent that there are further planets to be found in the system. For the known aggregate of transiting planets, and for hot Jupiters in general, additional planets with periods of a few hundred days or less are only infrequently found.

HD 80606b provides a clue that processes other than disk migration might be generating the observed population of hot Jupiters. The planet HD 80606b, its parent star HD 80606, and the binary companion HD 80607 form a “hierarchical triple” system, in which the two large stars provide an unchanging Keplerian orbit that drives the orbital and spin evolution of HD 80606b. If we imagine that HD 80606b and HD 80606 are both subject to small amounts of tidal dissipation, then to plausible approximation, this paper by Eggleton & Kiseleva-Eggleton argues that (i) the orbital evolution of “b”, (ii) the spin vector of “b”, and (iii) the spin vector of HD 80606 itself  can be described by a set of coupled first-order ordinary differential equations:

where e and h are vectors describing the planetary orbit, and where Ω_1 and Ω_2 are the spin vectors for HD 80606 and HD 80606b. The equations are somewhat more complicated than they appear at first glance, with expressions such as:

making up the various terms on the right hand sides.

Numerical integrations of the ODEs indicate that solutions exist in which the e and h vectors for `606b are bouncing like a ’64 Impala. Check out, for example, this solution vector animation by Dan Fabrycky (using initial conditions published by Wu and Murray 2003) which shows the leading scenario for how HD 80606b came to occupy its present state.

HD 80606b is imagined to have originally formed in a relatively circular orbit that was roughly 5 AU from its parent star, and which happened to be at nearly a right angle to the plane of the HD 80606-HD80607 binary orbit:

The large mutual inclination led to Kozai oscillations in which ‘606b was cyclically driven to very high eccentricity. During the high-eccentricity phases, tidal dissipation within the planet gradually drained energy from the orbit and decreased the semi-major axis:

Eventually, the orbital period became short enough so that general relativistic precession was fast enough to destroy the Kozai oscillations, and the planet was marooned on a high-eccentricity, gradually circularizing orbit that is severely misaligned with the stellar equator — exactly what is observed:

With HD 80606b, the case for Kozai-migration is pretty clear cut. The guilty party — the perturbing binary companion — is sitting right there in the field of view, and the scenario provides an easy explanation for anomalously high orbital orbital eccentricity. The only “just-so” provision is the requirement that the planet-forming protoplanetary disk of HD 80606 started out essentially perpendicular to the orbital plane of its wide binary companion.

The Triaud et al paper and the press release draw the much more dramatic conclusion that Kozai cycles with tidal friction could be the dominant channel for producing of the known hot Jupiters. From the abstract of their paper:

Conclusions. Most hot Jupiters are misaligned, with a large variety of spin-orbit angles. We observe that the histogram of projected obliquities matches closely the theoretical distributions of using Kozai cycles and tidal friction. If these observational facts are confirmed in the future, we may then conclude that most hot Jupiters are formed by this very mechanism without the need to use type I or II migration. At present, type I or II migration alone cannot explain the observations.

Can this really be the case? Might it be time to start reigning in the funding for studies of Type II migration in protostellar disks?

A key point to keep in mind is that Rossiter-McLaughlin measurements yield the sky-projected misalignment angle, λ, between the stellar spin and planetary orbital angular momentum vectors, and not the true misalignment angle, ψ, in three-dimensional space. That is, with transit spectroscopy alone, you can’t discern the difference between the following configurations:

In a paper published in 2007, Dan Fabrycky carried out integrations of the Eggleton-Kiseleva-Eggleton equations for an ensemble of a thousand star-planet-star systems that experience HD80606-style Kozai migration coupled with tidal friction. From the results of the integrations, he constructed a histogram showing the distribution of final misalignment angles, ψ:

The first nine Rossiter-McLaughlin observations of transiting planets all produced values for λ that were close to zero, in seeming conflict with Fabrycky’s distribution for ψ. The jump-the-gun conclusion, then, was that Kozai-migration is not an important formation channel for hot Jupiters.

With the spin-orbit determinations that appear in the Triaud et al. paper, there are now a total of 26 λ determinations. A fair fraction of the recent results indicate severely misaligned systems, and Triaud et al. show a histogram over λ (or in their notation, β):

In order to compare the observed distribution of λ measurements with Fabrycky’s predicted distribtion of Kozai-migration misalignments, ψ, Triaud et al. assume that the distribution of spin axes for the transit-bearing stars is isotropic. With this assumption, one can statistically deproject the λ distribution and recast it as a &#968 distribution, giving a startlingly good match between Fabrycky’s theory (blue dashed line) and observation:

When I first saw the above plot, I had a hard time believing it. The assumption that the spin axes of transit-bearing stars are isotropically distributed seems somewhat akin to baking a result into the data. Nevertheless, it is true that if Kozai migration produces the hot Jupiters, then the current ψ distribution is right in line with expectations.

In early 2009, Fabrycky and Winn did a very careful analysis of the 11 Rossiter measurements that were known at that time. Among those first 11 measurements, only XO-3 displayed a significant sky-projected spin-orbit misalignment. From the sparse data set, Fabrycky and Winn concluded that there were likely 2 separate populations of transit-bearing stars. One population, in which the spins and orbits are all aligned, constitutes (1-f)>64% of systems, whereas a second population, sporting random alignments, is responsible for f<36% of systems (to 95% confidence).

Bottom line conclusion? More Rossiter-McLaughlin measurements are needed, but I think its safe to say that Kozai-migration plays a larger role in sculpting the planet distribution than previously believed. If I had to put down money, I’d bet f=50%.

Competition keeps everyone on their toes, and the exoplanet Doppler detection game is no exception.

The California Planet Search has recently done a major overhaul of their exoplanets.org website, and the results are impressive. The redesigned site is now fully interactive, and it must be seeing a lot of traffic. Certainly, I can count myself as a frequent visitor!

Perhaps the most exciting feature of the site is a plotting applet that seamlessly connects to an up-to-date and curated database of the known extrasolar planets. In the “advanced” mode, one can get very finely tuned plots that can tell interesting stories. As an example, here is a plot of RV half-amplitudes of the known planets plotted against the RMS of the residuals to the fits. The color of the points corresponds to discovery year (cool = back in the day) and the size of each point corresponds to the number of published RV data points for the planet (those five big points correspond to 55 Cancri b-f which has a very extensive data set).

The plot shows that progress comes in part from competition. As the competing Doppler surveys push to lower Ks, there has a been a trend toward decreased signal-to-noise for the detections. It looks like oklo.org posts a few years from now will likely be discussing systems with K~60 cm/sec. At that amplitude, one is plausibly talking habitable worlds.

Another interesting plot comes from plotting parent star metallicity against planet mass. As with most of the interesting diagrams, a logarithmic scaling is required. The parent star masses are keyed to the sizes of the individual points, and color is assigned to eccentricity. The software has the nice feature that a cursor placed on a dot informs you of the planet name. This plot shows the benefit of looking at lower mass stars, and it shows how the metallicity correlation is diminished as one pushes below roughly a Saturn mass (evidence, of course, for core accretion):

The exoplanets.org site also contains a very useful planet table, which is giving the competition (in this case, exoplanet.eu) a run for its money.

The question of how the world’s top Doppler teams match up in league play is something that I imagine comes up quite a bit in exoplanet-related water-cooler discussions. A suitable scoring system is therefore in order, and the tables on exoplanets.org make this a very doable proposition.

After some thought, I’ve decided to adopt the system used for cross-country running, with the K‘s of the team’s planets replacing the times of the team’s runners. (The image for this post is from a 1983 dual meet between two high school teams from Central Illinois. If you look carefully, you can see that the coach is hurling an acorn at yours truly, presumably because of the much wider-than-expected gap between runners #2 and #3.) In the exoplanet context, the cross-country scoring system encourages fluid changes of lead — one or two high-grade multiple super-Earth systems can catapult a team to the top of the board. From the wikipedia article:

When two or more teams of cross country runners compete, a score may be compiled to determine which team is the better. Points are awarded to the individual runners of eligible teams, equal to the position in which they cross the finish line (first place gets 1 point, second place gets 2 points, etc). Teams are considered ineligible to score if they have fewer than the meet’s required number of scorers, which is typically five. Only the first five runners in for a team are counted towards that team’s score; the points for these runners are summed, and the teams are ranked based on the total, with lowest being best. In the event of a tie, the rules vary depending on the competition; often the team that closes scoring first wins, though in the US NCAA ties are possible. In high school competition, if two teams tie, then the victor is decided by whose sixth runner, the first one whose score does not count, finished first.

The lowest possible score in a five-to-score match is 15 (1+2+3+4+5), achieved by a team’s runners finishing in each of the top five positions. If there is a single opposing team then they would have a score of 40 (6+7+8+9+10), which can be considered a “sweep” for the winning team. In some competitions a team’s sixth and seventh runner are scored in the overall field and are known as “pushers” or “displacers” as their place can count ahead of other runners. In the above match, if there are two non-scoring runners and they came 6th and 7th overall, the opponent’s score would be 50 (8+9+10+11+12). Accordingly, the official score of a forfeited dual meet is 15-50.

According to the above rules, there are currently three RV teams in the running. The Geneva Extrasolar Planet Search (whose planets I’ve listed with SWISS on the table), the California Planet Search (planets listed with CPS), and the Earthbound Planet Search (who I’ve marked as EPS):

The score as of this morning? SWISS 25, EPS 47, CPS 62…

So when presented with that particular formulation, I generally prefer to get the bad news first:

Stefano Meschiari and I have investigated how the new radial velocity data for the HAT-P-13 system affect the possibility of measuring transit timing variations for the short-period planet “b” as the heavy, long-period planet “c” rumbles through its periastron passage later this spring.

First, recall the overall set-up. HAT-P-13 was discovered in transit by Gaspar Bakos and his HAT Net collaborators last summer. HAT-P-13 “b” is a standard-issue hot Jupiter with 0.85 Jupiter masses and a fleeting 2.916-day orbital period. The radial velocity follow-up indicated that the system also contains an Msin(i)~14.5 Jupiter mass object on an eccentric orbit with a P~430 day period. If the two planets are close to coplanar, then the system should have tidally evolved to an eccentricity fixed point — a configuration that allows one to extract Juno-mission style interior information from the inner planet for free.

System Version 1.0 for HAT-P-13 generates significant transit timing variations for the inner planet during the weeks surrounding the periastron passage of the outer planet. In a post two weeks ago, I showed some invigorating calculations by Matthew Payne and Eric Ford, which charted the details of the timing variations. Here’s a figure inspired by the Payne-Ford analysis that uses the systemic console’s TTV routines to zoom in on the imminent HAT-P-13 periastron:

The above picture is quite rosy, at least as far as the outlook for TTVs is concerned. With orbital models that are based on the Bakos et al. discovery data for the system, the transit-to-transit time intervals for planet b veer from ~17 seconds shorter than average to ~17 seconds longer than average (relative to the long-term mean) as planet c runs through its periastron and exerts its maximum perturbing influence. This shift from a compressed period to an expanded period occurs rather abruptly over a span of about 2 weeks. Most provocatively, there are significant and feasibly observable differences between the TTV profiles produced by the coplanar configuration and by the configurations with 45-degree mutual inclinations. And finally, all the action was predicted to occur just before the end of HAT-P-13’s yearly observing season (see Bruce Gary’s revived AXA page for wealth of additional detail). It’s not hard to revel in the thought of all the ground-based observers pooling their results (in the spirit of 1761 and 1769) and emerging with a big-picture result!

The new Winn et al. data, however, definitely rain on the TTV parade. The augmented (out-of-transit) data set now shows that the period of planet c is about 20 days longer than previously believed, and c’s eccentricity also drops slightly, from e_c=0.69 to e_c=0.666. With the new orbital model, the differences in the TTVs generated by the co-planar and mutually inclined configurations are considerably smaller. The overall amplitude of the variations is cut nearly in half, and the excitement is pushed far more precariously against the end of the observing season:

And the good news? As described in the last post, the Winn et al. data show that the orbital plane of planet b is probably aligned with the equator of the parent star, which, in turn, means that it’s quite likely that the b-c system is indeed coplanar.

If we assume coplanarity, then the system should be at an eccentricity fixed point in which the apsides of the two planets are aligned. A measurement of the eccentricity of planet b then allows the interior structure and the tidal dissipation of planet b to be measured.

The augmented radial velocity data set permits a better measurement of planet b’s orbital eccentricity. Figure 5 of the Winn et al. paper has the relevant plot, which shows the distribution of Markov-Chain models for the eccentricity and apsidal angle of planet b. If the orbits are aligned, then the true model needs to fall within the red dotted lines, which mark the position of the (much better determined) apsidal line for planet c. From looking at the figure, the apsidally aligned configurations seem to have e_b ~ 0.01±0.005.

I asked Josh if he could send a histogram that shows the distribution of eccentricities for planet b for the subset of models that satisfy the alignment criterion. He got back to me very quickly with the following plot:

The result is: e_b = 0.0106 ± 0.0040, which implies a best-guess planetary structure that has (1) a small core, (2) a Love number k_2~0.34, and (3) a tidal dissipation quality factor Q~10,000 (see our paper, Batygin, Bodenheimer & Laughlin 2009 for details).

HAT-P-13c could easily wind up being 2010’s version of HD 80606b — a long-shot transit candidate that pans out to enable extraordinary follow-up characterization, while simultaneously allowing small-telescope ground-based observers to stunt on the transit-hunting space missions.

The HAT-P-13 system has already gotten quite a bit of oklo.org press (see articles [1], [2], and [3]). It generates intense interest because it’s the only known configuration where a transiting short-period planet is accompanied by a long-period companion planet on an orbit that’s reasonably well characterized by radial velocity measurements. Right after the system was discovered, we showed that if the orbits of the two planets are coplanar, then one can probe the interior structure of the transiting inner planet by getting a precise measurement of its orbital eccentricity. The idea is that the system has tidally evolved to an eccentricity fixed point, in which the apsidal lines of the two planets precess at the same rate. Both the precession rate and the inner planet’s eccentricity are single-valued functions of the degree of mass concentration within the transiting planet.

Early this year, Rosemary Mardling expanded the analysis to the situation where the two planets are not orbiting in the same plane (her paper here). If there is significant non-coplanarity, the system will have settled into a limit cycle, in which the eccentricity of the inner planet and the alignment angle of the apsidal lines cycle through a smoothly varying sequence of values. The existence of a limit cycle screws up the possibility of making a precise statement about planet’s b’s interior, even if one has an accurate measurement of the eccentricity.

When one ties all the lines of argument together, it turns out that there are two different system configurations that satisfy all the current constraints. In one, the planetary trajectories are nearly co-planar, with the inclination angle between the two orbits being less than 10 degrees. If the system has this set-up, then we’ll be in good position to x-ray the inner planet. In the alternative configuration, the orbital planes have a relative inclination of ~45 degrees, and the limit cycle will hold.

Matthew Payne, a postdoc at Florida, along with Eric Ford, have done a detailed examination of the transit timing variations that the two configurations will produce. (Transit timing variations — or TTV as all the hipsters were referring to them last week at SXSW — have been all the rage during the last few years, but have so far generated more buzz than results. That should change when HAT-P-13 takes the stage.) Payne and Ford found that timing variations should amount to tens of seconds near the periastron of planet c, which should in turn allow a resolution of whether the system is co-planar or not:

HAT-P-13 is a tough system for small-telescope observers to reach milli-magnitude precision at a cadence high enough to accurately measure the transit timing variations. Nevertheless, the top backyard aces will be giving it a go. Bruce Gary has reactivated the AXA especially for the event, and University of Florida grad student Ben Nelson has written a campaign page for Lubos Brat’s Tresca database. The best transits for detecting TTV will be occurring during April and May. This is an opportunity to really push the envelope.

If the system turns out to be close to coplanar, then there’s a non-negligible probability (of order 5-10%) that planet c will be observable in transit. The transit window is centered on April 12th, and is uncertain by a few days to either side. Small telescope observers will definitely be competitive in checking for the transit. In an upcoming post, we’ll take a look at the details and the peculiarities of this remarkable opportunity.

It’s been rather arduous past few days as the HST Cycle-18 proposal deadline — 5 PM PST, Friday Feb. 26th, to be exact — bore down like a freight train.

During the past year, I’ve become quite intrigued by the remarkable (and well known) HST observation by Vidal Madjar et al. (2003), who discovered that the Lyman-alpha transit depth of HD 209458b is a whopping 15% (as opposed to the mere 1.5% of the star’s light that gets blocked during the optical transit). The implication of this result is that the planet is surrounded by an outflowing, escaping wind of hydrogen, and the discovery has sparked a lot of theoretical work.

A good test for planetary outflow hypotheses is to see what they predict for eccentric planets that undergo drastic changes in stellar heating during the course of the orbit. Fred Adams and I have been working on hydrodynamical models for these situations, and it soon became clear that oklo.org fave HD 17156b, the P=21.2d, e=0.67 transiting planet provides an intriguing observational opportunity for HST/STIS. HD 17156 is currently the fourth-brightest known parent star of a transiting extrasolar planet (after HD 209458, HD 189733 and HD 149026) and it lies in HST’s so-called continuous viewing zone for part of the year. This means that a full transit can be observed without having to take those leisurely once-per-96-minute pit stops every time Earth blocks the view.

The geometry of the transit, furthermore, is such that the planet is getting its maximum sunburn just a few hours after transit egress. Our calculations indicate that it should take the upper atmosphere only a matter of hours to react to the increased heating, so we’re optimistic about the possibility that not only will HST detect a deep transit in the UV, but that it might even be able to detect the Lyman-alpha transit depth increasing during the course of the transit. Here’s the basic idea:

As of a few minutes ago, the proposal was received safe and sound at STScI, so now it’s time to kick back, wait, and see if it passes muster with the TAC…

I’ve got an upcoming event planned in New York City that should be pretty interesting. From the UCSC Newsletter:

UCSC astronomer joins composer Philip Glass to explore music of the universe

UC Santa Cruz Astronomer Gregory Laughlin joins acclaimed composer Philip Glass February 21 in a “Brainwave” discussion at the Rubin Art Museum in New York.

For its third year and in conjunction with the exhibition Visions of the Cosmos, Brainwave is a series of 20 sessions this winter and spring that bring together eminent thinkers from multiple disciplines with neuroscientists and astrophysicists to ponder big thoughts about “things that matter.”

Laughlin and Glass appear in the third Brainwave event titled “How Do We Listen to the Music of the Spheres?”

Laughlin is a professor of astronomy and astrophysics whose research delves into orbital dynamics and the evolution of planetary systems. Glass is one of the most influential composers of the past half-century. Though sometimes called a “minimalist,” Glass describes his compositions as “music with repetitive structures.”

Laughlin said he and Glass will explore commonalities between music and orbital dynamics. The museum’s initiative to pair the two was sparked in part by Laughlin’s articles on his blog oklo.org that delve into ways to “sonify” planetary movements.

He developed software to map planetary systems as audible waveforms. He said he became intrigued by the realization that planetary systems can be used as a type of nonlinear digital synthesizer and can provide an enormous palette of sound — sounds never before heard.

The Laughlin/Glass Brainwave session begins at 6 p.m. Sunday, February 21 at the Rubin Museum of Art at 150 West 17 St., New York City. Admission is $25.

Over the next week, as I’m preparing for the event, I’ll be working extensively with the sonification capability of the systemic console. Just below, is a reprinted post that touches on this very cool, and still relatively unexplored feature. If you’ve worked with the Console’s N-body sonification, and if you’ve found interesting results, feel free to send me .fit files — an extraordinarily effective form of compression(!) — and I may be able to use them in the discussion.

Potentially the most interesting feature on the downloadable systemic console is the “sonify button”, which integrates the model planetary system specified by the state of the console sliders and produces a .wav format CD-quality audio file of the resulting radial velocity waveform. Not interested in planets? The console is a stand-alone non-linear digital synthesizer. It’s capable of producing strange, remarkable, musically useful sounds. They merely need to be located within the uncountable infinity of solutions to the gravitational N-body problem.

First, use the console to build an interesting multi-planet system (for this purpose, there’s no need to try to fit whatever data is in the window.) Then click the sonify button. This brings up a dialogue window which enables the user to make several specifications for the sound file that is produced.

The most important user-specified parameter is the frequency onto which the orbital period of the shortest-period planet on the console is mapped. If, for example, the innermost planet has a period of 365.25 days, then a 440 Hz map will play 440 years worth of evolution in one second. (440 Hz corresponds to the A below middle C.) Mapping the radial velocity curve onto a high-frequency note extends the total number of orbits that go into the sample, and thus increases the integration time required to produce the sample. You can also specify the length of the sample, and you can exert simple control over the attack and decay rate of the envelope for the overall waveform.

Once you’ve produced the sound file, it appears in the “soundClips” subdirectory within the systemic parent directory. Both of these directories are automatically created when you download and expand the console — see the instruction set for the downloadable console for more details. With a Macintosh, you get the best results if you play the sample right from the folder. i-Tunes seems to want to convert the samples to .mp3 format in a manner that introduces audible noise, and we’re not yet sure how to resolve this issue.

To the extent that planets orbit independently of one another, the console behaves like a simple additive synthesizer, in which the individual Kepler waveforms add to form a composite sound. Much more interesting, is the situation when planets experience significant gravitational interaction, leading, for example, to resonance and to nonlinear instability (here are examples, 1, 2, from the resources page of both types of waveforms). Close encounters provide discontinuities between individual blocks of sound that resemble the results of granular synthesis.

The strongest 2-planet mean-motion resonances occur when the pair of planets share a common period and engage in a one-to-one resonant motion. There are a variety of different one-to-one resonances, including binary planet orbits (e.g. Earth and Moon), trojan configurations, and generalizations of retrograde satellite orbits. In this last category, one can have two planets with the same semi-major axis, but with different eccentricities. If one starts the planets in the following configuration, then the motion is dynamically stable, and evolves in a complicated way over time.

The motion leads to an interesting audio wave-form, in which you can hear the system cycling between configurations in which both planets are modestly eccentric and configurations in which one orbit is nearly circular while the other one is highly eccentric. As a specific example, set the console to the following configuration: P1=P2=10 days, M1=M2=0.3 Mjup, MA1=180., MA2=190., e1=0.9, e2=0.1, long1=0.0, long2=0.0. If you increase MA2 to about 225 degrees while keeping the other parameters fixed, you’ll hear the system go unstable.

Evolving, high-eccentricity orbits tend to have an insect-like quality, which brings to mind the 1986 album, The Insect Musicians, by Greame Revell (formerly of SPK). From the album jacket:

For the two years 1984-85, Graeme Revell traveled from Australia to Europe, to Africa, Indonesia and North America recording and negotiating copyrights of insect sound recordings. It took another full year sampling and metamorphosing some forty sounds thus gathered using the Fairlight Computer Musical Instrument, to produce this record. The only sounds used are those of insects, altered digitally and combined into a unique orchestra of instruments, an orchestra of strange and delicate timbres, music of natural rhythm and texture.

The minimum threshold level for amazement will rise quickly once Kepler’s discoveries start to accumulate, and already, it’s getting very hard to remember which transiting planet is unusual for which reason. Let’s see, was it TrES-4 or WASP-17 that had that styrofoam-like density? Or was it both of them?

Even in a crowded field, though, HAT-P-13 is likely to endure as a touchstone. In the next five years, it’s likely that there will emerge only a select handful of systems in which a well-characterized transiting planet orbiting a relatively bright star is being substantially perturbed by a companion on a well-characterized orbit:

After the HAT-13 system was announced, we showed that the planets “b” and “c” should have evolved to an eccentricity fixed point configuration, in which the orbits’ apsidal lines co-rotate, and in which the orbital eccentricity of planet “b” has a very sensitive dependence on its internal structure. Further modeling, using reasonable assumptions, gives strong limits on the tidal Q of planet “b”. In essence, one can potentially accomplish with an exoplanet a big chunk of what the Juno Mission expects to accomplish at Jupiter at of order a thousandth of the cost.

Our analysis assumed that HAT-P-13 b and c are on co-planar orbits. There’s an interesting new paper by Rosemary Mardling that explores the significantly more complex situation that arises if the orbital planes of the planets are significantly misaligned. In this case, tidal dissipation in the inner planet causes the system to settle into a limit cycle, where the eccentricity and the angle between the apsides circulate on a secular timescale, and the easy insight into the structure of planet b is no longer possible.

Interestingly, however, Mardling’s analysis suggests that if the orbits are misaligned, then the mutual inclination is likely to be in the neighborhood of 45 or 50 degrees. A mutual inclination of, say, 30 degrees is inconsistent with the currently observed parameters of planet b. The following two diagrams (figure 8 a and b) from her paper show how this works:

Within the next few months, we should get improved values for the eccentricity and radius of planet b, which will significantly shrink the size of the peach-colored boxes in the two figures above. HAT-P-13c is also currently headed in for periastron, with the next transit opportunity scheduled for April 12, 2010. A transit by planet c would provide strong evidence that the system is reasonably close to co-planar (and would be quite remarkable in its own right!) Furthermore, during the periastron passage of c, there should be readily detectable transit timing variations for b, which should give us a shot at distinguishing between the co-planar case and the case with a mutual eccentricity of 45-50 degrees. In the next post, I’ll look in detail at the numbers…

Image by JUNe (source)

At the beginning of the year, I made five exoplanet-related predictions:

1. A 1.75 Earth Mass planet orbiting a Main Sequence star.

2. A confirmed case of transit timing variations.

3. A transiting planet in a well-characterized multiple-planet system.

4. A transiting super-Earth (or more precisely, on the basis of observed composition, a transiting sup-Neptune).

5. 417 planets listed on exoplanet.eu.

So how did I do?

Prediction 1 was just a bit on the optimistic side. At present, the extrasolar planet with the lowest Msin(i) orbiting a Main Sequence star is Gliese 581e, with Msin(i)=1.94±0.22 Earth masses. So the forecast panned out to within the 1-sigma error. (Mayor et al.’s discovery paper is here, oklo.org coverage of the discovery is here, here, and here).

Prediction 2 falls just short of unambiguous fulfillment. HAT-P-13b is clearly going to exhibit transit timing variations, and soon, but as discussed in Bakos et al.’s discovery paper, it’s not clear whether they’ve already been observed.

Prediction 3 is satisfied by HAT-P-13b and c. The characterization is so good, in fact, that we’re able to effectively look inside HAT-P-13b.

Prediction 4 was doubly satisfied. First, by CoRoT-7b (a transiting super-Earth), and second, by GJ 1214b (a transiting sub-Neptune).

Prediction 5: 415 planets are listed (as of 12/31/2009) on exoplanet.eu…

I was catching up on astro-ph.EP this morning, and came across Paper #20 from the HARPS Search for Southern Extrasolar Planets. The authors report the detection of two new planets orbiting BD 08-2823, a nearby, moderately active K-dwarf. The inner planet in this new system has a mass comparable to Uranus (Msin(i)=14.4 Earth Masses) and an orbital period of 5.60 days — yet another example from the huge population of super-Earths and sub-Neptunes lying in short-period orbits around the Sun’s closest neighbors. As described in the paper, the two new planets emerged serendipitously from a thwarted attempt to identify transiting planets using the Hipparcos database.

What caught my eye about BD 08-2823b, is the fact that the parent star has not yet been monitored for transits. The a-priori probability that BD 08-2823b can be observed in transit is >7%. The star is observable from both hemispheres, at V=9.86 it’s a natural for small-telescope ground-based observers, and it’s up right now!

A successful detection is no walk in the park: The expected transit depth is of order 1.2 millimag, right at the limit of what’s been demonstrated by skilled small-telescope observers. The possible short-term activity of the parent star will demand multiple confirmations in the event that transits are indeed occurring. The current transit ephemeris is uncertain by more than a day to either side of the predicted transit midpoints (just added to the Transitsearch.org candidates table).

The transit valuation metric (described here) assigns a real-world value to the detection of a given transiting planet. It’s a way of cutting through hype, and it keeps a necessary spotlight on the fact that the cost of detecting a given transiting planet is not necessarily proportional to the scientific value of the planet detected.

If BD 08-2823b transits, its value using the metric works out to ~3 Million dollars. In other words, a detection would amount to a major discovery (something that’s getting increasingly harder to pull off, given this past year’s flood of results). In expectation, factoring in the 7% transit probability, the value is 210K. On a per-night basis, this is well over twice the value of Keck time, and yet it can be had by a good observer with a good backyard telescope. The next opportunities are centered on Jan 1st, and Jan 7th.