oklo

Last night, I received a mysterious e-mail from Gaspar Bakos of the Harvard-Smithsonian CfA. It consisted of a single line:

A phaeton tuned fun

Now I certainly wouldn’t want to detune anyone’s fun, so I’m turning the comments page off…

The “top ten” list provides a perennially easy vehicle for writing an end-of-the-year web log post. “Top three” lists, because they’re shorter, are even easier to write. In the interest of maintaining a near-weekly posting schedule, here’s my short-short list of the biggest exoplanet-related stories for 2008.

1. A raft of super-Earths and sub-Neptunes. The biggest news from 2008 was the announcement by the Geneva group that 30% of solar-type stars harbor Neptune or lower mass planets with orbital periods of 50 days or less. This discovery has far-reaching implications for ongoing planet detection efforts, and was completely unexpected by theorists. In short, a big deal.

2. HR 8799 b, c, and d. The discovery of massive planets via direct imaging was the marquee event of 2008 for the broader media. Stars more massive than the Sun seem to be uncannily effective at forming planets — it’s thus a good bet that more direct imaging detections will be coming on line shortly.

3. Radial Velocity holds its own. The S&P 500 may have been down almost 40% in 2008, but the detection rate for extrasolar planets held steady, with exoplanet.eu reporting 62 credible announcements. I had thought 2008 would be the year that the transit method pulled ahead, but the Doppler technique (turbo-charged by the populations of sub-Neptunes and giant planets orbiting giant stars) had a banner second half, logging 32 new worlds. Nonetheless, direct imaging and microlensing are really starting to produce, logging five planets and four planets respectively.

And looking forward? It’s always risky to make predictions, but here’s what I think we’ll have in hand by the end of 2009:

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.

It would be cool if 1 through 4 were all part of the same story, but we probably won’t be quite that lucky.

As anyone who’s used the systemic console knows, the numerical integration of planetary orbits is aggravatingly slow. For modern-day dynamicists, endless pages of algebra are often a thing of the past. Now it’s “hurry up and wait” while the computers grind through the integrations.

If you’re charting the courses of planets that have negligible planet-planet gravitational interactions, then life runs at interactive pace. Instead of integrating 6N coupled ordinary differential equations, you need only solve Kepler’s equation, M = E – e sin E, which parameterizes the position of the planet on its ellipse as a function of time.

In an era of environmental and economic collapse, solving M = E – e sin E for E doesn’t seem like a big problem. Simple iteration, for example, works quite well. Remarkably, however, as pointed out by Peter Colwell in his 1993 book Solving Kepler’s Equation Over Three Centuries, there have been scientific papers written about Kepler’s Equation and its solution in every decade since 1650. From the synopsis of Colwell’s book:

The sole subject of our work is Kepler’s Equation (KE) M = E – e sin E . In its narrowest form, the Kepler problem is to solve KE for E , given M in the interval and e in the interval [0,1]. In virtually every decade from 1650 to the present there have appeared papers devoted to the Kepler problem and its solution. We can see from a list of them that the problem has enticed a wide variety of scientists to comment on or involve themselves in its solution.

It is surely not unique in science for a specific problem to be given so much attention over so long a period–particularly if it resists solution, if its partial solutions are inadequate or unsatisfactory, or if it is recharged with new interpretations and new applications. Still, it is curious that the Kepler problem should have continued to be this interesting to so many for so long. Admittedly it is a problem central to celestial mechanics, but it is a technical little problem for which a number of satisfactory solutions are long known. With the advent of calculators and computers, there is no impediment to achieving quick solutions of great accuracy. The problem has neither the broad appeal of an Olbers Paradox, nor the depth and intractability of a many-body problem.

In common with almost any scientific problem which achieves a certain longevity and whose literature exceeds a certain critical mass, the Kepler problem has acquired an undeniable luster and allure for the modern practitioner. Any new technique for the treatment of transcendental equations should be applied to this illustrious test case; any new insight, however slight, lets its conceiver join an eminent list of contributors.

Perhaps the most influential article of the 1990s that touches directly Kepler’s equation is Wisdom and Holman’s 1991 paper that describes the N-body map. The basic idea is that the trajectories of interacting planets can be divided neatly into a part consisting of Keplerian motion, and a part consisting of the derangements brought on by the interplanetary gravitational tugs. A Wisdom-Holman integration avoids forcing the computer to continually rediscover Kepler’s ellipse, reducing much of the integration to repeated numerical evaluations of Kepler’s equation. For orbital integrations that don’t involve close encounters, this trick leads to an order-of-magnitude speed up. N-body maps have made it possible to (for example) readily integrate the motion of the solar system planets for the lifetime of the solar system.

As the first decade of the new millennium starts to draw to a close, I was pleased to see that the 350+ year tradition is continuing. In a recent astro-ph posting, Eric Ford shows how graphics cards can be commandeered to implement highly parallelized numerical evaluations of Kepler’s equation. Using mixed-precision arithmetic, he shows that graphics cards can offer a speed-up of a factor of ~600 over console-style evaluations of M = E – e sin E that use the regular ‘ol CPU. Having the clock hands move 600 times faster really brings Markov Chains to stochastically vibrant life.

And the 2010s? I think quantum computation might turn the order N^2 N-body problem into an order-N computation (see this post). That’ll free up the GPUs so that everyone can get back to playing Grand Theft Auto.

Image copyright 1951, 20th-Century Fox.

A search on “Alpha Centauri” in the news archives of the New York Times turns up an average of one or two hits per year, including a scattering of genuine astronomical news clippings about the stellar system itself.

For example, on August 31st, 1904, a bulletin datelined Lick Observatory reported that the distance to Alpha Centauri has been determined “spectroscopically”, although it’s fully uncommunicative of any further details. On December 27th 1925, there was an item (unfortunately tagged pay-to-play) that seems very much in the oklo.org vein:

NEAREST STAR FLIES TO US FROM SPACE; Its speed is Fourteen Miles a second. TWENTY-FIVE thousand years hence New York will be able to see Alpha Centauri our nearest stellar neighbor. Alpha Centauri travels toward the earth at the rate…

In many of the citations, Alpha Cen hits the stands in its role as a cultural touchpoint. For example, in the Dec. 28th, 1969 edition, one finds a post-Apollo, pre-Watergate prediction (presumably a joke):

Reading the Tea Leaves — What will happen in 1970… Vice President Agnew, cut in on a split screen, suggests that the U.S. launch a crash program to go to Alpha Centauri, the nearest star.

Similarly, upon reading Friday’s NYT edition, 20th Century Fox executives must have been elated to find that their publicity stunt for The Day the Earth Stood Still has been given a promotional write-up in the science section. Last Friday at Noon, it seems that the big-budget remake of the Cold-War classic was beamed in its entirety to Alpha Centauri. To one-sigma precision, the transmission will be illuminating Alpha Cen Bb sometime between Monday April 22nd, 2013 and Saturday April 29th, 2013, just a few months into Obama’s second term.

So what are the smart-money odds that the movie will actually get watched in the Alpha Cen system? Oklo.org recommends the following conditional probabilities:

fp = Chance of a habitable planet orbiting Alpha Cen B = 0.6

fl = Chance that live evolved on that planet = 0.01

fi = Chance that life developed intelligence = 0.1

fr = Chance that intelligence understood Maxwell’s Equations = 0.01

fn = Chance that Maxwell’s Equations are currently understood on Alpha Cen Bb = 64,000 / 3×10^9 = 0.0000213.

This gives (fp)x(fl)x(fi)x(fr)x(fn) = one in eight billion, with Alpha Cen Ab kicking in an additional one in a trillion chance.

The numerator in fn is a decision-market estimate corresponding to the long-term running mean (not median!) result of polling students in my classes as to how long they think we’ll remain capable of building radios. The denominator is an estimate of the span of past time during which Alpha Cen Bb could have conceivably harbored intelligence.

Signals beamed to other worlds are readily subject to misinterpretation. I’ve always enjoyed Michael Arbib’s take on the 1961 version of the Drake signal turned up side down:

Friday’s transmission does make one thing clear, though. If a genuine ETI signal is ever beamed to Earth, it’ll almost certainly be a commercial advertisement. The primary problem of interpretation will simply be to figure out how to wire back our cash.

UPDATE:

In the comments section, bruce01 makes the following astute observation:

Alpha Centauri, at declination -60 degrees, is barely above the horizon even from Florida. The web site:
http://www.deepspacecom.net/
says they are located near the Kennedy Space Center which is north of latitude 28 degrees. This makes the zenith angle of Alpha Centauri greater than 88 degrees as seen from the Space Center. You need to add to your equation the probability that the “beamed” signal made it through the Earth’s atmosphere without being totally scattered.

Indeed. Furthermore, for the entire duration of the broadcast, Alpha Cen (RA 14h:39m, DEC -60deg:50min) was below the horizon as viewed from 28 35 06N, 80 39 04W. One can’t help but wonder whether bruce01 may have made a vital contribution to the solution of the long-running Fermi Paradox.

I’m absolutely confident, though, that any organization with the reach and technical expertise advertised by the Deep Space Communications Network would maintain a fully staffed southern hemisphere station for their broadcasts to the southern skies.

I like it when remarkable exoplanet results are disguised within more-or-less innocuously titled papers. A nice example occurred this summer, with “The HARPS search for southern extra-solar planets. XIII. A planetary system with 3 Super-Earths (4.2, 6.9, & 9.2 Earth masses)”. While it’s true that the three planets orbiting HD 40307 are indeed cool, the Geneva team announced much bigger news in the discussion section of the article. They reported, almost offhandedly, that 1/3 of solar-type stars have sub-Neptune mass planets with periods of 50 days or less. That’s the most important planet news since the discovery of hot Jupiters.

Another instance can be found in last weekend’s astro-ph mailing under the file-to-read-later title, “A Smaller Radius for the Transiting Exoplanet WASP-10b“. In this article, John Johnson and collaborators demonstrate 0.47 millimagnitude per-sample photometry with a cadence of 1.3 minutes from the ground. At first glance, their light curve of a WASP-10b transit looks like it came from outer space:

For comparison, here’s the classic 2001 HST composite light curve of the HD 209458b transit that really did come from outer space:

The HST light curve has an 80 second (1.33 min) cadence, and a per-point precision of 0.11 millimagnitudes. Because of HST’s low-Earth orbit, however, it took four separate transits to assemble the composite light curve:

On a per-transit basis, then, Johnson et al.’s ground-based photometry is 22% the value of the HST photometry. That is extraordinary value for the dollar.

The WASP-10 curve was obtained with a type of CCD called an orthogonal transfer array, which controls how the starlight is spilled onto the individual pixels. By distributing the incoming photons in a highly disciplined manner over a larger area of the detector, saturation is staved off, and the duty cycle is improved.

WASP-10-b is a 12.7 magnitude star, and so its transit light curve certainly benefits from having control stars of similar magnitude in the field of view of the 2.2m telescope. The most interesting transiting planets occur around brighter stars (accessible to Spitzer). Nevertheless, it seems quite probable that an observational set-up using a neutral density spot filter for the primary star would allow similar precision on brighter stars. (Back in the day, Tim Castellano used the spot filter technique to check HD 187123 for transits by its hot Jupiter.)

It’s interesting to look at a few of the possibilities that open up if one can do 80sec–0.47mmag photometry from a facility that’s not dauntingly oversubscribed.

Transit timing is high on the list. TTV precision scales in direct proportion to photometric precision, and it scales with cadence to the -1/2 power. For the Wasp-10b transit, the moment of the central transit was measured to a precision of 7 seconds. At this level, it’s possible to sense the presence of very small perturbing planets, especially if one also has precise radial velocities. Stefano has been burning the midnight oil to improve the systemic console for research-grade use. One of the primary capabilities of the new console is an enhanced transit timing analysis suite that is capable of fully exploiting timing measurements at the 5-10 second level. We’ll be officially rolling out the new console quite soon. (In the interim, you can get the current build here.)

Should transit timing indicate the presence of an Earth-mass perturbing companion, then there’s a reasonable chance that the perturber also transits the parent star. If the timing model can give good predictions for when the transit might occur, then 80sec–0.47mmag is fully sufficient to detect Earths from the ground.

In the figure just below, I’ve zoomed in on an out-of-transit portion of Johnson et al’s Wasp-10b light curve. At this scale the 10^-4 depth of a transiting Earth is just resolved at weblog resolution. By binning the photometry into half-hour chunks, one reaches this resolution. A transit by an Earth-sized planet could thus be a multi-sigma detection in a single night. Hot Damn!

And then there’s the Transitsearch angle. There are a number of Neptune-mass planets that (to my knowledge) have not been adequately checked for transits because their predicted photometric depths were just too small. At the 80sec-0.47mmag level, these planets come right into play. A short list would include (1) 55 Cancri e (11 Earth masses, 10.1% transit probability, 0.065% transit depth), (2) HD 219828b (19 Earth masses, 15.6% transit probability, 0.027% transit depth), 3) HD 40307b (4.3 Earth masses, 6.8% transit probability, 0.052% transit depth), (4) HD 69830b (10.2 Earth masses, 4.9% probability, 0.072% transit depth), and (5) HD 160691d (14.38 Earth masses, 5.6% probability, 0.056% transit depth). Assuming that your RV fits are up to date and that you’re first on the sky with one of these bad boys, your expectation value can run into hundreds of thousands of Swiss Francs per hour.

Academics across the United States know the feeling at the end of the long Thanksgiving weekend. Four days were to be given over (at least partially) to catching up with a long list of slipped deadlines and overdue tasks. Like the last line of a haiku, Sunday afternoon arrives.

The red dwarf stars, on the other hand, have mastered the art of having enough time. A trillion years from now, the science of extragalactic astronomy will have long since ended, but Proxima Centauri, our nearest stellar neighbor, will be shining more or less unaltered from its current recessionista persona.

Proxima will never turn into a red giant. Like the other low-mass red dwarfs, it will grow steadily brighter and bluer as it ages, eventually turning itself into a helium white dwarf that gradually cools and fades to black.

The galaxy is filled with red dwarfs, and so as a result, the total luminosity of the Milky Way will stay surprisingly constant for a long time to come. A few years ago, Fred Adams, Genevieve Graves and I wrote a conference proceedings that looks in detail at the future luminosity evolution of the galaxy.

As the Milky Way’s stellar population ages, the more massive stars (The Sun, Sirius, Alpha Cen A and B, Tau Ceti et al.) die off. For hundreds of billions of years, their flagging contributions to the galactic luminosity are very nearly compensated by the increase in luminosity of smaller stars. This state of affairs will persist until about 800 billion years from now, at which time the remaining main sequence stars will all have less than ~30% of the solar mass. These stars never experience the large luminosity increase associated with the red giant phase, and the galactic light curve declines gently for about 7 trillion years as the lowest mass stars slowly die. During this long autumn, the galaxy as a whole should look quite blue, because the light is dominated by stars that have aborted their journey up the red giant branch and grown bluer. Eventually, after about 8 trillion years, even the smallest stars have run out of hydrogen and the night sky finally goes black for the duration.

Just trying to put the arrival of Monday morning in perspective.

When I got home last Saturday, Sirius had just risen above the neighbors’ roof. The air was dramatically clear. In spite of the Santa Cruz city lights, I could make out stars down to fourth magnitude. The seeing, however, must have been incredibly bad, with a large amount of turbulence at high altitude. Sirius was twittering stochastically from white and blue to brief moments of intense, unmistakable fire-engine orange. Scintillation has got to be at the root of the red Sirius anomaly.

The back of every introductory astronomy textbook contains separate one-page lists of the nearest stars to the Sun and the brightest stars in the sky. I’ve never paid much attention to the lists of brightest stars. Rigel, Deneb, and Hadar are hundreds of parsecs away, hot-tempered, short-lived and ultimately rather tiresome. It’s more interesting to pore over the lists of nearest stars. Alpha Centauri, Eta Cassiopeiae, Tau Ceti, 61 Cygni, Barnard’s star…

It’s always seemed odd to me that Sirius and Alpha Cen are at or near the top of both lists. Sirius, the brightest star in the sky, is in the fifth-nearest system, and Alpha Cen A, the fourth-brightest star is in the nearest system. It’s as if Henry Winkler lived three houses down your street in one direction and Barry Manilow lived five houses up the street in the other direction.

Over a lifetime, the constellations seem fixed, but on geologic timescales, the Sun rapidly drifts through completely new lists of nearest stellar neighbors. A kilometer per second is a parsec in a million years, and stars in the solar neighborhood have a velocity dispersion of ~30 km/sec. This means that the list of nearest 100 stellar systems undergoes a complete turnover roughly every 300,000 years, and over Earth’s 4.5 billion year lifetime, the tables in the back of the Astronomy 101 textbooks have gone through thousands of completely different editions.

The Hipparcos catalog multi-parameter search tool lists 1549 stars with distances less than 25 parsecs. For stars like Alpha Cen B and Sirius, this list is complete. That is, if we go out to 25 parsecs, we know about all the K0V stars, whereas the census of the lowest-mass (and hence extremely dim) red dwarfs is significantly incomplete beyond five parsecs or so. The 1549 nearest stars in the Hipparcos catalog all have their apparent V magnitudes listed and these are easily converted to absolute magnitudes since the distances are known to high accuracy. With the absolute magnitudes in hand, I wrote a short program that repeatedly draws new random 3D distributions of the 1549 stars within our 25-parsec sphere. By doing this, it’s possible to get a sense of how unusual it is to have stars like Sirius and Alpha Cen B essentially right next door. Given that this is just a blog post, I ignored any modifying effects arising from individual stars adhering into binary and multiple systems.

First, Sirius. I ran 1,000 trials, and filtered for instances in which a star that is instrinsically as bright or brighter than Sirius lies as close or closer than Sirius’ current 2.64-parsec distance. This condition was satisfied in 31 of the trials, and in one trial, two stars fit the bill. In a rough sense, then, the presence of Sirius is “unusual” at the 3% level.

As Oklo readers are no doubt aware, I’m rooting for a high-cadence Doppler velocity campaign on Alpha Cen B. The relevant question in this case is: What are the odds that we have a stellar neighbor that is as visibly bright or brighter than Alpha Cen B (V<1.34) with an absolute magnitude equal to or fainter than B (Mv>5.71)? We want a bright star so that a smaller telescope can be used, and so that a maximum number of observations can be made. We want an intrinsically dimmer cooler star because the radial velocity method works at the peak of its ability with K-type dwarfs, and because the radial velocity half-amplitude at given mass is larger and because the habitable zone is closer to the star.

Interestingly, adopting this criterion, Alpha Cen B is also unusual at the 3% level. In 1000 trials, a star that’s intrinsically dimmer than Alpha Cen B that (as a result of proximity) is visibly brighter on the sky occurred 28 times, and in one instance, two such stars made the grade.

Alpha Cen B is special for a number of other reasons: (1) metallicity, (2) binary plane orientation, (3) presence of Alpha Cen A as a control star, (4) sky position, (5) age. It’s sort of like having it turn out that Bono lives right next door.

I was reading a newspaper article last weekend, and ran across one of the more satisfying aphorisms. Chance favors the prepared mind. I just like the ring of that.

Along roughly similar lines, it’s curiously inspiring when someone gets a great, lucky opportunity, and then really steps up to the plate and knocks the ball out of the park. I’ve been trying to identify the best examples of this phenomenon. Consider, for example, when Brian Johnson was offered the lead vocal for AC DC. It’s hard to argue with worldwide sales of 42 million for Back in Black.

What about instances drawn from Astronomy? Johannes Kepler jumps to mind, but everyone already knows the the raft of Copernicus-Brahe-Galileo-Kepler anecdotes. I like the story of Joseph Fraunhofer (lifted from Wikipedia):

Fraunhofer was born in Straubing, Bavaria. He became an orphan at the age of 11, and he started working as an apprentice to a harsh glassmaker named Philipp Anton Weichelsberger. In 1801 the workshop in which he was working collapsed and he was buried in the rubble. The rescue operation was led by Maximilian IV Joseph, Prince Elector of Bavaria (the future Maximilian I Joseph). The prince entered Fraunhofer’s life, providing him with books and forcing his employer to allow the young Joseph Fraunhofer time to study.

After eight months of study, Fraunhofer went to work at the Optical Institute at Benediktbeuern, a secularised Benedictine monastery devoted to glass making. There he discovered how to make the world’s finest optical glass and invented incredibly precise methods for measuring dispersion. In 1818 he became the director of the Optical Institute. Due to the fine optical instruments he had developed, Bavaria overtook England as the centre of the optics industry. Even the likes of Michael Faraday were unable to produce glass that could rival Fraunhofer’s.

The quality of Fraunhofer’s optics played a large role in providing Bessel with the precision that he needed to measure the parallax of 61 Cygni. In explicitly demonstrating the staggering distances to the stars, Bessel was able to bring to a 200+ year scientific quest to a dramatic finish. Hard to argue with that.

Anybody who knows anything about candy knows that “fun size” isn’t any fun at all. The same is true for terrestrial planets. Fun size objects like Mercury, the Moon, Ceres, Vesta and Pallas are airless cratered and dead.

For the past several years, I’ve been agitating for a dedicated radial velocity search for potentially habitable King-size terrestrial planets in the Alpha Centauri system. A number of factors (brightness, age, spectral type, metallicity, orientation, and sky position) make Alpha Cen B overwhelmingly best star in the sky for detecting habitable planets from the ground and on the cheap.

Planets are dynamically stable in the habitable zone of Alpha Cen B. It’s also true that if one starts with hundreds of lunar-sized embryos in the Alpha Cen system, then the formation of King-size terrestrial planets is effectively a given.

But there’s a snag. Those embryos may never have formed. Recent work by Philippe Thebault and his collaborators makes a case that the Alpha Centauri system provided an unfavorable environment for the accretion of planetary embryos, and as a result, the prospects for finding a habitable planet right next door may be depressingly slim. Thebault et al’s first paper (here) clears out the planets around A, and their second paper, which came out at the beginning of this month (here), deals effectively with B.

The basic idea works like this. During the epoch when kilometer-sized bodies are trying to accrete and grow, the presence of a binary stellar perturber forces planetesimal orbits in the circumprimary disks to be eccentric. This eccentricity forcing occurs in the presence of gas drag on the planetesimals. For a population of equal-mass bodies, gas drag and gravitational forcing cause the periastra of the planetesimal orbits to line up. When such phasing occurs, neighboring particles have small relative velocities, collisions are gentle, and the planetesimals are able to grow via collisional agglomeration.

Unfortunately, both the forced eccentricity and the phase angle relative to the binary periastron depend on planetesimal mass. If the disk contains bodies of different sizes, then one gets crossing orbits and larger collision velocities. Planetesimals don’t stick together when they’re bashed together.

Thebault and his collaborators sum up their bottom line results in the following table (which I’ve clipped directly out of their Alpha Cen B paper):

The column on the left lists the initial conditions. The column on the right gives the radius beyond which construction of embryos is thwarted. Conditions that are consistent with the disk that gave rise to our Solar System are encapsulated in the “minimum-mass solar nebula” (MMSN) nominal case. When the MMSN is used as an initial condition for Alpha Cen B, the region exterior to 0.5 AU is unfriendly to accretion. In order for embryos to form in the habitable zone, one’s best bet is to crank up the disk gas density by a factor of at least several. (The table indicates that a 10xMMSN initial conditions allows embryos to form all the way out to 0.8 AU).

Even when confronted with these results, I’m still cautiously long Alpha Cen Bb. It’s not that I think the simulations are wrong or that there is any problem with the outcomes that they produce. Rather, I don’t think a high gas density in the inner AU of the Alpha Cen B disk is cause for alarm. In a nutshell, I don’t see evidence that the MMSN is of any particular utility for explaining the extrasolar planetary systems that we’ve found so far, and hence I’m not depressed that high gas densities were required for Alpha Cen B to have fostered an accretion-friendly environment. Reconstitute, for example, the HD 69830 protoplanetary disk or the 55 Cnc protoplanetary disk. I’m plain skeptical of the validity of a fiducial MMSN scaling for the disks that orbited the Alpha Cen stars. The Alpha Cen binary has twice the total mass of the Solar System, and more than two thousand times the total angular momentum.

We need to do the experiment and find out what’s really there.

As more and more extrasolar planets are characterized, the correlation diagrams steadily increase in their intrinsic appeal. Each planet is attached to a number of interesting quantities (planetary Msin(i), period, and eccentricity, and parent star metallicity, apparent brightness and mass, to name just a few).

The two most important correlation diagrams are probably the mass-period diagram and the eccentricity-period diagram. Ideally, one would like to plot logM, logP, and e in three dimensions, but I’ve always felt that static 3D diagrams don’t work very well. I think one is best off scaling the size of the symbol to Msin(i) and going with a 2D diagram of eccentricity vs log Period. I fooled around with various scalings, and decided that a point radius proportional to Msin(i)**0.4 looks the best.

That leaves color to impart additional information. As the number of planets increases, one is increasingly better off allowing the points in correlation diagrams to be partially transparent. An opacity of 0.7 give an immediate depth of field for overlapping points, and will continue to work well on Keynote slides until there are more than a thousand planets.

The planet-metallicity correlation can be made evident by mapping the metallicity of the parent star onto the hue of the point. With a rainbow scale where red is Fe/H=-0.5 (low metallicity) and violet is Fe/H=0.5 (high metallicity) it’s immediately clear that the planets found to date are skewed toward metal rich stars.

Looks cool.

The Mathematica Hue command allows control of hue, saturation, brightness and opacity. The HSB color scheme potentially allows for quantities to be displayed simultaneously, meaning that 6D correlation diagrams are possible. Can the saturation and brightness indices be put meaningfully to work?

I think the answer is probably yes, but my sense is that it will be tough to get a full return from all three color dimensions. In the diagram below, metallicity maps to hue (as before) and the V magnitude of the parent star maps to brightness. Only hues from 0.00 to 0.70 are used, to avoid the wrap-around. Saturation is left at 1.00 for all points:

Barfy colors are now in the lead, and some extra information is imparted. The hot Jupiters (in the lower left hand corner of the diagram) are noticeably darker than the eccentric giants. This is because increasingly, the hot Jupiters are being located by transit surveys, which look at much dimmer stars than does the RV method which surveys stars that are typically in the V=5-8 range. The extra color dimension is thus giving a sense of one of the biases in the diagram — Hot Jupiters are overrepresented because they’re easier to find.

What happens when one uses all three color dimensions? In the following diagram, the degree of color saturation is mapped to the mass of the parent star. With the first scaling that I tried, there’s not a whole lot of change from the previous plot. I think, though, that with more experimentation, the color saturation can be put to use. Note, too, that the dynamic range is reduced by the up-front demand for 70% transparency.

The diagrams really benefit from higher resolution. For example, looking at the hot Jupiters, there’s an interesting zone of avoidance at the lower left hand corner. The lower-mass planets are not populating the region that contains the hottest and most circular hot Jupiters. This might stem from a fundamental composition difference, although it’s also true that Neptune-mass planets don’t turn up yet in transit surveys.

Last night, I noticed Venus and Jupiter hanging low and bright about ten degrees apart in the deep blue twilight. Noctilucent cirrus clouds hinted that the full Moon had just risen on the other side of the sky. No matter how intricate the detail in a radial velocity curve, no matter how fine-grained the transit ingress, there’s something undeniably tantalizing and mysterious about the direct image. There’s a certain solidity to seeing with your own eyes.

The embargo just lifted, and by now, the news of the images of the planets orbiting HR 8799 and Fomalhaut are all over the media. NYTimes, check. Washington Post, check. Fox News, check.

I was very happy to see that the media coverage of these two amazing, largely independent discoveries ended up quite fair and balanced. I had been wondering whether perhaps HR8799 would get shouldered out of the limelight. There’s definitely something to be said for steppin’ into the ring with the HST Press Machine at your back, and a cool-looking picture of a planet orbiting (of all stars!) Fomalhaut. A star with a name like a rocket.

Fomalhaut, furthermore is Magnitude 1. HR8799 checks in with B=6.198 and V=5.964. “It’s up now, in the Great Square of Pegasus, slightly too dim to see with the naked eye. But your cat’s eyes are actually sensitive enough to see it! If you’re so inclined, you can make your cat go outside tonight and share in this historic discovery.”

I think it’s quite significant that these planets have been detected around stars that are more massive than the Sun. We already know from the radial velocity surveys (and specifically the targeted surveys of John Johnson and Bunei Sato) that higher-mass Jovian planet formation was more efficient around higher-mass stars than around stars of solar mass and below. Johnson and Sato surveyed “retired” A-type stars that are now turning into red giants, and which are cool enough to have the deep lines in their spectra that the RV-detection method requires. Johnson and Sato both independently found that these stars are frequently producing planets that are more massive than Jupiter in orbital periods of several hundred days.

Sato’s detection in early 2007 of a 7.6 Jupiter-mass planet orbiting Epsilon Tauri (2.7 solar masses) in the Hyades is probably a good example of the type of planet that’s showing up in these new images, and Eps Tau b provides good support for the case that this category of objects arose from gravitational instability. The Hyades were a tough environment for planet formation via core accretion, due to the intense UV radiation that caused the disks to lose gas quickly (see this oklo post).

Remnant debris disks would be expected around young stars that had massive enough disks to trigger gravitational instability. Also, in general, the more massive the star, the more massive the disk. And finally, if the planets formed via gravitational instability, one wouldn’t expect a bias toward high metallicity. If this idea is correct, as more of these planets are imaged, there shouldn’t be a metallicity correlation with the parent star.

Bruce Macintosh was kind enough to point me to some links that his team has set up. The images and movies are well worth a visit:

Travis and Christian put together a temporary holding pen at
http://www.photospheres.us/barman/HR8799/

My personal favorites are the “real” orbital motion one
http://www.photospheres.us/barman/HR8799/Movie00-HR8799-real-orbitalmotion.mov

and the movie showing the rotational imaging technique:
http://www.photospheres.us/barman/HR8799/Movie04-HR8799-adi.mov
(left panel is raw Keck images with the image derotator off, so artifacts
are fixed while stuff on the sky rotates; middle panel is image with a
weighted-moving-average PSF subtracted; rightmost is the cumulative derotated
image.)

Also a finding chart showing HR8799 and 51 Peg.

The HR8799 family portrait, with three planets zipping around on Keplerian orbits immediately brings to mind our own outer solar system. Ironically, however, if the GI formation hypothesis is correct, we’re actually observing planetary systems that have even less kinship to our own than do systems like HD 209458b and 51 Peg that harbor hot Jupiters (which oddball as they seem, probably formed via core accretion, just like Jupiter).

The HST photo of the photoevaporating molecular clouds of M16 is the iconic go-to image, but it’s always struck me as veering toward flash over substance. The “pillars of creation” name combines with the visual cues to create the illusion that you’re looking at something in an up-down gravitational field.

I think my favorite astronomical image is the not-quite-so-famous photo of Barnard 68. Here, one gets a far more immediate and accurate sense of what one is actually seeing. A cold, black self-gravitating cloud, looming in the foreground, blotting out the stars. It’s easy to imagine a sped-up film which depicts the cloud boiling and writhing with its internal turbulence.

There’s a certain undeniable menace to the dark cloud, and not without reason. If we rewind the tape by 4.54 billion years, all the material in our own solar system would have looked not unlike Barnard 68. If viewed in time-lapse, the pre-solar dark cloud would have collapsed from inside out upon itself, leading to the formation of the Sun, the planets, and eventually, a vanguard of five delicately engineered probes heading tentatively out into the galaxy. There would have indeed been cause for long-term concern…

Creepy undertones aside, Barnard 68 is a great slide to show during talks about star and planet formation. If the Sun is a 0.2mm grain of sand in San Francisco, Barnard 68 is half a mile across and located roughly at the distance of Los Angeles. The dark cloud itself is the equivalent of grinding up one percent of three small grains of sand, and dispersing the resulting powder through a half-mile wide volume.

The last time I gave a talk, it occurred to me that I’d never had enough faith in common sense to actually question whether that last analogy is appropriate, and indeed nobody in an audience has ever called me on it. Is it really possible to grind up 3% of a sand grain so that it creates an opaque half-mile wide cloud? That sounds totally nuts!

Asteroid 99942 Apophis (Image Source).

The absolute finest that one could envision grinding up a sand grain, while still retaining it in some sense as powdered “sand”, would be to the level of individual silica (SiO2) molecules. A 0.2 mm grain contains roughly 6×10^17 silica molecules. There’d thus be ~2×10^16 molecules available to disperse through the half-mile-wide volume of our model for Barnard 68. Scaling up to the solar mass, this would imply a Barnard 68 chock full of kilometer-wide asteroids, whereas in reality, the dust in Barnard 68 is micron-sized, roughly the consistency of cigarette smoke.

If the metals in Barnard 68 were in the form of km-wide asteroids, the cloud would indeed be transparent — fewer than one in a billion of the photons from the background stars would be absorbed on their way through the cloud.

Image Source.

The month of October slipped by. No new oklo posts. Like seemingly everyone else, I’ve been in a state of continual distraction regarding the election. Instead of writing posts about planets, spare moments are spent scanning the news.

Sometimes, if you’re waking up in the middle of the night, there’s perspective in the knowledge that one can build a fully to-scale model of the Earth-Sun system by taking a grain of sand and holding it two arms lengths away from a dime. A real time simulation can then be put into effect by moving the sand grain through 6.92 degrees per week.

I do have a post nearly done in draft form, but my colleague, Prof. Jonathan Fortney, eliminated any chance that I’ll get it finished and posted before Nov. 5th, by introducing me to fivethirtyeight.com. Over there, you can get the latest polling data with a 10,000-trial Monte-Carlo sheen: