systemic

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The discovery of new planets is rarely clear cut. No sooner does a new world (Vesta, Neptune, Pluto) emerge, than the wrangling for the credit or the naming rights starts. And it’s usually possible to find a reason why the prediction (or even the planet itself) wasn’t really valid in the first place.

The trans-Uranian planet predicted by Urbain J. J. Le Verrier and John Couch Adams happened to coincide quite closely with Neptune’s actual sky position in September 1846, but the orbital periods of their models were too long by more than 50 years. Le Verrier’s predicted planetary mass, furthermore, was too large by nearly a factor of three, and Adams’ mass prediction was off by close to a factor of two.

In England, following the announcement of Neptune’s discovery, and with the glory flowing to Le Verrier in particular and France in general, the Rev. James Challis and the Astronomer Royal George Airy were denounced for not doing enough to follow up Adams’ predictions, “Oh! curse their narcotic Souls!” wrote Adam Sedgwick, professor of geology at Trinity College.

Nowadays, with the planet count up over 200, the prediction and discovery of a new world doesn’t quite carry the same freight as it did in 1846. No editorial cartoons, no Orders of Empire, and no extravagant public praise to the discoverer, such as that heaped by Camille Flammarion on Le Verrrier, who wrote, “This scientist, this genius, has discovered a star with the tip of his pen, without other instrument than the strength of his calculations alone!”

Nevertheless, I don’t want to be shoehorned into the ranks of the “narcotic souls” as a result of not properly encouraging the bringing to light of any potential planetary discoveries in the systemic catalog of real stellar radial velocity data sets. As of Dec. 30th, 2006, over 3,680 orbital fits have been uploaded to the systemic backend. It’s definitely time to start sifting carefully through the results that the 518 registered systemic users have produced. Over the next few weeks we’ll be introducing a variety of analysis and cataloging tools that will make this job easier, but there are some interesting questions that can be answered right away. Foremost among these is: what are the most credible (previously unannounced) planets in the database?

The backend uses the so-called reduced chi-square statistic as a convenient metric for rank-ordering fits:

In the above expression, N is the number of radial velocity data points, and M is the number of activated fitting parameters. As a rule of thumb, a reduced chi-square value near unity is indicative of a “good” fit to the data, but this rule is not exact, and should hence be applied with caution. The observational errors likely depart from a normal distribution, and more importantly, the tabulated errors don’t incorporate the astrophysical radial velocity noise produced by activity on the parent star. Furthermore, it’s almost always possible to lower the reduced chi-square statistic by introducing an extra low-mass planet.

Eugenio recently implemented the downloadable console‘s F-test, which can provide help in evaluating whether an additional planet is warranted. The F-test is applied to two saved fits and returns a probability that the two fits are statistically identical. As an example, pull up the HD 69830 data set and obtain the best two planet fit that includes the 8.666-planets and 31-day planets. Save this fit to disk. Next, add the 200-day outer planet and save the resulting 3-planet fit to disk (using a separate name). Clicking on the console’s F-test button allows the F-test to be computed using the two saved fits:

In the case of HD 69830, there’s a 1.7% probability that the 2-planet fit and the 3-planet fit are statistically identical. This low probability indicates that the third planet is providing a significant improvement to the characterization of the data. It’s likely really out there orbiting the star.

So here’s the plan: Let’s comb through the systemic “Real Star” catalog, and find the systems that (1) contain an unannounced planet(s) in addition to the previously announced members of the system (see the exoplanet.eu catalog for the up-to-date list). (2) have a F-test probability of less than 2% of being statistically identical, and (3) are dynamically stable for at least 10,000 years. If you find a system that meets these requirements, post your findings to the comments section of this post.

Disclaimer: this exercise is for the satisfaction of obtaining a better understanding of the planetary census, and also for fun. When the planets do turn up, I’m going to sit back with a bottle full of bub and enjoy any scrambles for priority from a safe distance.

Happy New Year, y’all!

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I now have a topographic Mars globe on my desk, and I’ve been staring at it. It’s common knowledge that the northern Martian hemisphere is low-lying and nearly uncratered, but this was never hammered home to me until I spent time staring at an actual globe, tracing the shorelines of the vanished ocean.

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When J. Edgar Hoover was getting on in years, his aides would often tell scheduled visitors to his office that he was unable to meet with them because he was “in conference”. In reality, this meant that Hoover was napping at his desk.

It might seem that the refrain of, “we’re busy working on the systemic back-end” is an equally convenient euphemism for long lapses between posts on the front end. Nevertheless, we have been busy getting the new oklo xserve quad xeon up and running. The whole site has now been replicated and tested, the server is live and on air, and very shortly, we’ll be flipping the switch. Can’t wait, man!

With the vast increase in processing power afforded by the xserve, we’ll be able to provide a much more extensive suite of research tools to oklo visitors. In particular, it’ll be possible to dynamically generate the kinds of correlation diagrams that are currently only available from our estimable continental competition: exoplanet.eu.

It’s always interesting to look through the latest versions of the correlation diagrams to see whether the various trends and hints of trends are holding up. The a-e plot is worth examining, as is the plot that charts the number of planetary discoveries per year over the past decade. As of today, exoplanet.eu lists 192 planets that have been detected with the radial velocity method. Plotting the masses of these planets against their periods on a log-log plot (and running the resulting screenshot through Illustrator) yields the following:

For Keplerian orbits, the relationship between the radial velocity half-amplitude of the parent star and the orbital period of the planet is given by:

If we assume that the mass of the planet is negligible in comparison to the mass of the star and if we further assume edge-on, circular orbits around solar mass stars, then we get the dashed lines in the figure that show detection thresholds for K=3 m/s and K=1 m/s. The three planets orbiting HD 69830 stand out in this diagram as the most striking discoveries of 2006.

To the eye, there are two curious clusters of planets in the diagram. At short periods (P~3d) we have the hot Jupiters. Most of these have masses (times the sine of the unknown inclination) somewhat less than Jupiter. At longer periods (P>100d) we have a second prominent clump of planets. These are the Eccentric Giants, and their masses average out at a significantly higher value (between 2 and 3 times the mass of Jupiter). Part of the difference in mass is due to selection bias, but nevertheless there is a real effect. Like the planet-metallicity connection, this effect is telling us something about either planet formation or planet migration (probably the latter).

Anyone got an idea regarding what’s going on? Let’s get a discussion going in the comment section. Over the past week, I’ve been flooded by depressingly clumsy attempts at comment spam from single-minded robots with mechanical enthusiasms for satellite TV service and online poker, e.g. “Great blog, keep it comming.” It’d be nice to see some signal in the noise…

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Despite posts here, here, here, here, here, and here, I’m not obsessed with HD 80606b. Really! It’s just that it’s such a bizarre and unique world that I’m convinced that it has the potential to give us a lot of insight into how extrasolar Jovian planets behave.

Consider planetary spin periods. As a consequence of angular momentum conservation, both Jupiter and Saturn spin quite quickly. Their days last 9.92425 hours and 10.65622 hours, respectively. The subnebulae from which they formed were large and slowly rotating, and as the planets contracted, they were compelled to spin up to their current rapid rotation rates.

The hot Jupiters that have been observed so far in the infrared using the Spitzer space telescope are all close enough to their parent stars to have been brought into synchronous rotation. That is, their spin periods are the same as their orbital periods and (assuming that they’re in Cassini state #1) they always present the same hemisphere to the star. The weather on these planets will be strongly influenced by the presence of a permanent day side and a permanent night side.

HD 80606b is different. Tidal forces arising during the periastron passages of its 111.4297 day orbit will have brought it into a state of pseudo-synchronization, in which the spin frequency is ~82% of the instantaneous orbital angular frequency that the planet has as it whips through periastron. More precisely, Piet Hut, in this paper from 1981 shows that,

Plugging in 111.4297 days for HD 80606b’s orbital period and e=0.937 for its eccentricity, we get a spin period of 1.535 days, or 36.8 hours. We’re thus in position to understand how the surface of the planet is exposed to intense stellar irradiation during the periastron passage. From this, as we’ll show in upcoming posts, we can make predictions about what Spitzer will see if it observes the star during the time surounding periastron. The geometry looks like this:

In the above diagram, the sense of the orbit is counterclockwise, and the position of the planet is shown at successive 24-hour intervals. If we were to observe from a fixed longitude on the planetary sphere (shown as the red bar at Noon on the leftmost planetary position) then we spin through 235 degrees worth of rotation every 24 hours. At the end of the first 24-hour period, we’re still on the night-side of the planet. During the second 24-hour period, our spot receives it’s strongest heating, and, because of the orbital motion, the day on the equator lasts considerably longer than the usual 18.4 hours. Our spot then receives more than 24 hours worth of darkness to cool off. It’s on the night-side as the planet makes its closest approach to the star. Shortly before dawn during this 24-hour interval, our own Sun crosses the local meridian, an totally inconspicuous 9th magnitude star shining down onto the turbulent steam-choked atmosphere.

Tis the season! If you’re like me, you’re probably looking for ways to minimize your exposure to malls, crowds, and overloaded sleighs. If so, we here at oklo have devised a one-stop solution for all of your holiday gifts. On Dec. 11th, Taylor and Francis publishers is releasing Numerical Methods in Astrophysics, by Peter Bodenheimer, Michal Rozyczka, Hal Yorke, and myself.

From the publishers description:

This guide develops many numerical techniques for solving major astrophysics problems. After an introduction to the basic equations and derivations, the book focuses on practical applications of the numerical methods. It explores hydrodynamic problems in one dimension, N-body particle dynamics, smoothed particle hydrodynamics, and stellar structure and evolution. The authors also examine advanced techniques in grid-based hydrodynamics, evaluate the methods for calculating the gravitational forces in an astrophysical system, and discuss specific problems in grid-based methods for radiation transfer. The book incorporates user manuals and a CD-ROM of the numerical codes.

It should start shipping Dec. 11th, order yours today!

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Sorry about this long lapse in new posts. The end of the academic quarter has left me awash in deadlines and scrambling to get everything done.

Nevertheless, we’ve been making progress behind the scenes. The new oklo server has been delivered, configured, and slotted into a rackspace in a dedicated server room. To use the vernacular, it’s hecka fast. Over the next several days, we’ll be transferring the site over to the new machine, and then it’ll be bye-bye bluehost.

HD 80606 is looking more interesting all the time. I’m working on a writeup of what we’ve been learning. It really has the potential to give us an unambiguous value for the radiative time constant appropriate to the atmospheres of hot Jupiters. The next ’606 day is December 26th, and I’ll be sending out a circular to the transitsearch.org observers to get a definitive confirmation that it doesn’t transit. Here’s the promotional poster (inspired by the SAO Moonwatch program, while simultaneously attempting to achieve a retro cold-war-flying-saucers feel):

Finally, keep fitting the last batch of Systemic Jr. systems. We need to get a full range of good fits for all of the data sets in order to carry out some very interesting analyses…