systemic

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There’s a provocative paper up on the astro-ph today. Ignasi Ribas and two collaborators are reporting the “possible discovery” of a 4.8 Earth mass planet in an exterior 2:1 mean motion resonance with the transiting hot Neptune Gliese 436b. Planet four three six b is the well-known subject of great consternation, great scientific value, and many an oklo.org post. (For the chronological storyline, see: 1 (for background), 2, 3, 4, 5, 6, 7, 8, 9, and 10.)

Here’s the basic idea. Ribas et al. note that a single-planet fit to the Maness et al. (2007) radial velocity data set (which is listed as gj_436_M07K on the systemic console) has a peak in the residuals periodogram at P~5.1866 days:

Using this periodogram peak as a starting point, they get a keplerian 2-planet fit that lowers the reduced chi-square from ~4.7 to ~3.7. They then point out that this detection can potentially be confirmed by measuring variations in transit timing. In their picture, the presently-grazing transit has come into visibility only within the last 2.5 years or so, as a result of orbital precession. The transit light curve should thus be showing significant variations in duration as well as deviations from a strictly periodic sequence of central transit times.

This will be a huge big deal if the claim holds up. For starters, it’ll provide a natural explanation for Gl 436b’s outsize eccentricity. And everyone’s been on the lookout for a strongly resonant transiting system with a short orbital period. For the time being, though, I’m withholding judgment. As a first point of concern, Ribas et al. are presenting a keplerian fit to the radial velocities. Yet for the orbital configuration they are proposing, it’s absolutely vital to take planet-planet interactions into account. One can see this by entering their fit into the console. (Use a mean anomaly at the first RV epoch 2451552.077 for planet b=40.441 deg, corresponding to their reported time of periastron of Tp_b=HJD 2451551.78, and a mean anomaly for planet c=268.14 deg, corresponding to their reported value of Tp_c=HJD 2451553.4.) One can also dial in a long-term trend if one wants, but this isn’t necessary. Once the fit is entered, the reduced chi-square is 3.7. Activate integration. (Hermite 4th-order is the faster method.) When the planets are integrated, their mutual interactions utterly devastate the fit, driving the reduced chi-square up to 85.018. Using the zoomer and the scroller, you’ll see that the integrated radial velocity curve and the keplerian curve start off as a good match, but then rapidly get completely out of phase.

In order to examine the plausibility of a two-planet fit in 2:1 mean motion resonance, one needs to fit the radial velocity data with integration turned on. It is also important to include the existing transit timing data in the fit (and to do this, it’s best to use the most recent, so-called unstable version of the console). Over at Bruce Gary’s amateur exoplanet archive (AXA), there are now three transit timing measurements listed, with the latest obtained by Bruce himself this past New Years Eve. The HJD measurements of central transit should be added to the gj436.tds file, along with the HJD 2454280.78149 +/- 0.00016 central transit time measured by Spitzer.

Ideally, the Spitzer secondary transit timing data should also be included, but at the moment, the distribution version of the console does not have the capability to incorporate secondary transit measurements. One approach would be to get a self-consistent fit, and then see whether the epoch of secondary transit matches that observed by Spitzer.

Have fun…

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Messenger flew by Mercury last week, and photographed vast swaths of terrain that, until now, had never been seen. The new landscapes, as expected, are cratered, barren, and utterly moonlike. The galaxy could contain a hundred billion planets that would be hard, at first glance, to distinguish from Mercury, and within our cosmic horizon, there are probably of order as many Mercury-like worlds as there are sucrose molecules in a cube of sugar.

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Nevertheless, we do gain something extraordinary whenever a new vista onto a terrestrial world is opened up. Galileo was the first to achieve this, when he turned his telescope to the Moon and saw its three-dimensional relief for the first time. Mariner 4 and Mariner 9 accomplished a similar feat for Mars. The Magellan spacecraft revealed the Venusian topography. And once Messenger has photographed the full surface of Mercury, there will be a profoundly significant interval before we get our next up-close view of an unmapped terrestrial planet. My guess is that it’ll be Alpha Centauri B b.

The Messenger website is well worth a visit. I was particularly struck by the movie that the spacecraft made of the Earth during the close fly by of March 2005. During the course of 24 hours, the spinning Earth recedes into the black velvet distance and space travel seems like the real thing.

Mercury’s orbit, with its 88 day period and its eccentricity of 0.2 could slip unnoticed into the distribution of known exoplanets. It’s vaguely comparable, for example, with the orbit of HD 37605 b. This Msini=2.3 Mjup gas giant has an apoastron distance similar to Mercury’s, but dives much closer to its star during periastron.

We’ve been interested in HD 37605 b lately because its orbit dips in and out of the insolation zone where water clouds are expected to exist. At the far point of the 55 day orbit, it should be possible for white clouds to form out of a clear steamy atmosphere. At close approach, the clouds are turning to steam.

Jonathan Langton’s models for this planet show persistent polar vortices, which sequester cooler air, and which may remain cloudy even during the hot days surrounding periastron. The vortices are tenaciously long-lived, and tracer particles seeded into the vortices leak out only slowly. It would be interesting to know what sort of chemistry is brewing in the steamy hothouse environment of trapped and noxious air.

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On the UCSC Science Library shelves, we have an 1828 edition of Pierre Simon de Laplace’s Oeuvres that includes the five-volume Mecanique Celeste. At moments like this, it’s great to have a camera on one’s cellphone:

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Laplace’s identification of the 5:2 near-resonance between Jupiter and Saturn allowed him to augment the exisiting second-order Laplace-Lagrange secular analysis to produce a theory of planetary motion that was in extraordinary agreement with the observations of the late eighteenth century. His success in explaining the so-called Great Inequality was likely a contributing factor in the development the concept of Laplacian determinism, of a clockwork universe.

In 1802, during William Herschel’s visit to Paris, Herschel and Laplace had a meeting with Napoleon, who, like Thomas Jefferson, appears to have been not much taken with a system of the world created and dictated by natural law:

The first Consul then asked a few questions relating to Astronomy and the construction of the heavens to which I made such answers as seemed to give him great satisfaction. He also addressed himself to Mr. Laplace on the same subject, and held a considerable argument with him in which he differed from that eminent mathematician. The difference was occasioned by an exclamation of the first Consul, who asked in a tone of exclamation or admiration (when we were speaking of the extent of the sidereal heavens): “And who is the author of all this!” Monsieur De la Place wished to shew that a chain of natural causes would account for the construction and preservation of the wonderful system. This the first Consul rather opposed.

[Source: Herschel's diary of his visit to Paris in 1802, as found in C. Lubbock's _The Herschel Chronicle_, p. 310, see here for a nice background.]

I like the extrasolar planet game because it’s simultaneously up-to-the-minute and steeped in tradition. With systems like Gliese 876, we’re approaching roughly the same effective degree of refinement in our detection of planet-planet orbital perturbations that was possible in the late eighteenth century for Jupiter and Saturn. As a result, someone like Laplace, were he to materialize (see today’s NYT) in the Interdisciplinary Sciences Building here at UCSC, could roll up his french cuffs and immediately begin contributing publishable work. The same would certainly not be true if one of his equally luminous scientific contemporaries, say Antoine Lavoisier, were to suddenly walk in to a modern-day chemistry lab.

Will be making an effort to post more frequently. Thanks for your continued readership and participation as oklo.org heads into its third year.