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It’s Ohmic

January 30th, 2011 4 comments


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…

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NLG

January 23rd, 2011 Comments off

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…

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Neptune after one orbit

January 17th, 2011 5 comments

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.

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A safe prediction

January 1st, 2011 1 comment


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!

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