Image Source.

Gl 436 b orbits its parent star in a short 2.64 days, and the discovery of transits indicates that its physical properties are quite similar to Neptune. The theoretical expectation is thus completely clear cut. “That orbit is circular, Son. Tidal dissipation has long since damped out that eccentricity.”

The data, however, stubbornly insist otherwise. When I do a one-planet fit to the radial velocities (incorporating the constraint on the mean anomaly imposed by Gillon et al.’s observation of the transit midpoint) then the distribution of bootstrap fits indicates e~0.13 +/- 0.03:

[Note: Stefano and Eugenio have been cranking away on the downloadable console code base, and the current beta-test version on the backend now contains a slew of new features, including a revved-up Hermite integrator and the ability to incorporate transit timing observations into the orbital fits. The user interface has been completely overhauled in order to maintain usability with the rapidly expanding feature set. We’ll be putting up some posts very soon that demo all this bling. In the interim, though, I definitely recommend downloading a copy and taking it for a test-drive.]

The latest console version.

In this post from last week, I looked at the possibility that gl 436 b’s eccentricity is being maintained by as-yet unpublished planets. There’s a hint of a long-term trend in the data that indicates a large and distant companion.

The lowest chi-square fit to th gj437_M07K data set (by user Schneidi) reduces the magnitude of the long-term trend by using a pair of planets on 53 and 399 day orbits.

In Schneidi’s fit, the bulk of the perturbation on planet b is provided by the 53-day plant “c” which also has close to a Neptune mass. In last week’s post, I looked at this model in gory detail. If the 53-day planet exists, and if its orbital plane is aligned for transits, then the transit will occur around June 7th.

For two planets like Gl 436 b and c, which aren’t in mean-motion resonance, and which aren’t on crossing orbits, the long-term evolution of the orbits is well-described by an approximation worked out by Laplace and Lagrange in the 1770s. In the Laplace-Lagrange theory, the gravitational interactions between a set of planets are assumed to be effective over a “secular” timescale that is much longer than the orbital periods of the planets themselves. The planets can thus be treated as flexible elliptical wires of varying mass density (highest near apoastron where the planets spend more time, and lowest near periastron where the least time is spent). The planets are able to trade eccentricity back and forth while keeping their semi-major axes fixed (orbital angular momentum is exchanged, but not orbital energy).

Last week, I was wondering whether the secular interchange of eccentricity could provide a mechanism for b to offload angular momentum as it tidally dissipates its orbital energy. If such a mechanism were effective, then it might explain why b’s orbit is still eccentric.

To look at this, I used a “double averaging” approximation to do a long-term numerical evolution of the 2-planet system in the presence of tidal damping. With this approach, one uses the Laplace-Lagrange theory to advance the system forward over a secular timestep of hundreds to thousands of years. After each secular timestep, one then applies tidal dissipation (modify semi-major axis and eccentricity so as to decrease the energy of planet b while conserving its angular momentum). Then one takes another secular timestep, etc. This approach should provide a reasonable picture of the orbital evolution so long as the secular time scale (thousands of years) is much shorter than the tidal evolution time scale (millions of years or more).

The answer is immediately clear. The presence of a 53-day planet “c” doesn’t stave off tidal circularization. In the graph above, I’ve assumed a Neptune-like tidal Q of 10,000 for b. The high-frequency secular exchange of angular momentum is of no use for maintaining b’s eccentricity. The orbit is circularized on an e-folding timescale of ~10 million years — much shorter than the current age of the star.

Guess I’m just not hip to where b’s scoring its e.

Image Source.

First, I squandered literally years of opportunity to coordinate a photometric follow-up transit search on Gl 436. Then I managed to incorrectly report the circumstances of the detection on the initial version of this (now corrected) oklo post! Naturally, I’m feeling sheepish, and my situation bears a distant echo to that of John Herschel (son of William), who was partly to blame for the inadequate coordination of an observational follow-up to John Couch Adams’ predictions of Neptune’s location.

Following the stunning news from the Continent of LeVerrier’s prediction and Galle’s successful detection of Neptune, Herschel likely realized at once that Neptune’s discovery would have gone to England had only he pressed Adams’ case more assiduously. In an October 1, 1846 letter to the London Athenaeum, Herschel hems and haws in a somewhat disingenuous effort to wriggle out of the uncomfortable situation that he had put himself in.

“The remarkable calculations of M. Le Verrier – which have pointed out, as now appears, nearly the true situation of the new planet, by resolving the inverse problem of the perturbations – if uncorroborated by repetition of the numerical calculations by another hand, or by independent investigation from another quarter, would hardly justify so strong an assurance as that conveyed by my expression above alluded to. But it was known to me, at that time, (I will take the liberty to cite the Astronomer Royal as my authority) that a similar investigation had been independently entered into, and a conclusion as to the situation of the new planet very nearly coincident with M. Le Verrier’s arrived at (in entire ignorance of his conclusions), by a young Cambridge mathematician, Mr. Adams; – who will, I hope, pardon this mention of his name.”

Herschel also wrote urgently to his friend William Lassell, a wealthy beer brewer from Liverpool, and a skilled observer who owned a fine 24-inch reflector. Herschel exhorted him to partially salvage the situation for himself and for Britain through a search for “satellites with all possible expedition!!”

Lassell began observing Neptune immediately, and within a week had spotted what was later confirmed to be Neptune’s satellite Triton. This, however, did little to assuage the court of British public opinion, and Challis, Airy, and Herschel were savaged for their inaction. “Oh, curse their narcotic Souls!” wrote Adam Sedgwick, professor of Geology at Trinity College.

[I culled these anecdotes from my favorite book on the topic of Neptune, Vulcan, LeVerrier and 19th-century dynamical astronomy; “In Search of Planet Vulcan — The Ghost in Newton’s Clockwork Universe” by Richard Baum and William Sheehan.]

Unfortunately, even with the exertion of all possible expedition, the detection of satellites orbiting Gl 436 b is a long shot. Large moons orbiting a planet only 0.02 AU from the parent star are almost certainly dynamically unstable (as shown here), and would, in any case, require exquisite photometry to detect. But one can, however, investigate the possibility that Gl 436 b might point the way toward other detectable planets in the system.

The first clue that Gl 436 might harbor more than one planet comes from planet b’s considerable, e~0.16, eccentricity. It’s surprising to find a P=2.644 day planet on a non-circular orbit. Given that its tidal quality factor, Q, is likely similar to Neptune’s, it should have circularized a long time ago — unless there’s a source of ongoing gravitational perturbation.

Gl 436 b’s high eccentricity means that, like Jupiter’s moon Io, it’s experiencing a lot of tidal heating. It’s internal luminosity is likely of order 10^20 Watts, which is in the rough ballpark of the amount of energy that the planet intercepts from the red dwarf parent star. Another interesting consequence of the non-zero eccentricity is that b will have a pseudo-synchronous spin period. That is, tidal forces will have forced the planet into a rotational period of 2.29 days, which allows it to optimally show one face to the star during periastron passage when the tidal forces are strongest. Jonathan Langton has done a simulation of the surface flow pattern (assuming a water-vapor atmosphere). The following 1.1MB animations (“eastern” view, and “western” view) trace two full orbits in the planet’s frame, and show the slow synodic drift of the baking daylit hemisphere.

If there’s a perturbing companion to Gl 436 b, then it’s a reasonable guess that it lies in roughly the same orbital plane, meaning that there’s a non-negligible chance of transit. It would certainly be nice if such a transit could be predicted in advance…

The first task is to look at whether the published radial velocity data set for Gl 436 gives any hint of additional planets. Going to the “Real Star” catalog on the systemic backend, and calling up the “gj436_M07K” dataset shows a wide variety of fits that have been submitted by systemic users over the past nine months:

Unlike the case of Gl 581c, there’s no particularly compelling evidence for a second planet. In sifting through the various fits that have been submitted, one finds that a second planet with a mass similar to Uranus and a period of 53 days is probably the most likely candidate perturber, and using the console, I find an unpublishably high false-alarm probability of 49% for a planet “c” with these properties. (The discussion boards on the systemic backend indicate that the systemic users have also arrived at this conclusion.)

On the other hand, however, a coin-flip isn’t half-bad odds, and what better low-stakes venue than a blog for an analysis? Let’s go ahead and assume that the 53-day candidate is really there.

At the current time, the console software isn’t configured to incorporate transit information into radial velocity fits. In particular, when one has a transit, one gets (1) an excellent determination of the period, and (2) an accurate ephemeris of the moment when the transiting planet and the parent star both lie on the line of sight to the Earth. Condition (2) provides a constraint on the fit that replaces the transiting planet’s Mean Anomaly as a free parameter. I have a Fortran code (that I wrote for an analysis of the orbit of HD 209458b) that handles this situation, and so I can carry out a self-consistent two-planet fit that takes advantage of the transit ephemeris for b reported in the Gillon et al. paper. This 2-planet fit (based on the 53-day Uranus suggested by the fits submitted to the systemic backend) has a chi-square statistic of 3.09, and an RMS scatter of 3.91 m/s. The orbital parameters of the planets are: P_b=2.64385d, P_c=53.57724d, e_b=0.1375, e_c=0.2281, omega_b= 347.999 deg, omega_c=185.146 deg, M_b=0.0697 M_jup, and M_c=0.0417 M_jup. The Mean Anomaly of the putative planet “c” at JD 2451552.077 is 100.69 degrees.

One would certainly prefer to see a beefier perturber for Gl 436 b. When I compute the Laplace-Lagrange 2nd-order secular theory for the above system (including the effects of general relativistic precession) I find that b’s eccentricity cycles between e_min=0.135 and e_max=0.160 with a period of 13,000 years. This is much shorter than the time scale for orbital circularization, but it’s not immediately clear to me whether the secular perturbations from c would be able to maintain such a large eccentricity for b over billions of years. Does anyone know the answer offhand? That is, if b and c both formed with sizable eccentricities, would the secular interaction prevent circularization by providing c with a mechanism to offload angular momentum?

In any case, if c is for real, and if its orbital plane is properly aligned for central transits, then they will occur on (all times UT):

ingress JD: 2454152.02 2007, Feb 20, 12:34
egress JD: 2454152.19 2007, Feb 20, 16:29

ingress JD: 2454205.60 2007, April 15, 2:24
egress JD: 2454205.77 2007, April 15, 6:24

ingress JD: 2454259.18 2007, June 7, 16:14
egress JD: 2454259.34 2007, June 7, 20:14

ingress JD: 2454312.75 2007, July 31 06:04
egress JD: 2454312.92 2007, July 31 10:04

I’m now doing a more detailed analysis to see if c can maintain the observed eccentricity of b over the long term. If it’s a go, then I’ll run a bootstrap calculation to determine the probable error on the above predictions. It might be useful, however, to mark down June 6th-8th on the calendar.

Image Source.

I’m still astounded by the dramatic detection of the transit of Gl 436b, and I’m working on some posts that sort through the scientific results and implications that this discovery is generating.

GJ 436b was found using the same basic strategy that led to the detection of the transits of HD 209458b, HD 149026b, and HD 189733b. First, the planet is located with the radial velocity technique. Doppler velocities, of course, do not give the inclination of the planetary orbit, but they do give a prediction of when transits would occur if the line of sight to the system lies within a small enough angle of the planet’s orbital plane.

Short-period planets have higher a-priori chances of being observed in transit (a 12% probability is typical for a hot Jupiter on a short-period orbit) and so in general, most of the RV-detected planets with orbits of less than a week are checked photometrically for transits by members of the discovery team before the planet is publicly announced. The discovery teams found the transits of HD 209458b, HD 1409026b, and HD 189733b. Dramatically not so, however, with Gl 436b.

Note: In the initial version of this post, I jumped to some incorrect conclusions about how the Gl 436 discovery was made. This article on swissinfo caused me to infer that the initial April 2nd detection of the transit was a postcard-perfect story of an independent small-observatory follow-up of the variety encouraged by transitsearch.org. It turns out, however, that the OFXB telescope is tightly linked to the Geneva program. The Gl 436 detection was made in the course of an ongoing systematic survey of the known planet-bearing M-stars and K-stars, and of as-yet unannounced new candidates discovered by HARPS and SOPHIE. Michael Gillon, lead author on the Gl 436 paper, and the lead scientist for the photometric follow-up effort was kind enough to correct my facts.

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Literally seconds after I pressed the submit button on this afternoon’s TrES-3 post, the telephone rang. Eugenio.

“Did you see astro-ph? the Swiss have a transiting Neptune around Gl 436!”

I stayed up almost all night last night finishing my NASA PGG proposal, and so the cogs in my brain were turning rather slowly.

“Gl 436?” I asked, confused, “That doesn’t sound right. You’re sure it’s not Gl 674?”

But he was right. It is Gl 436 b that’s transiting, and this is easily the biggest planet-related discovery so far this year. New results from the Swiss team have been coming so thick and fast that it’s hard to even keep them all straight. Let me be the first to offer my heartfelt — and let’s admit it, envious — congratulations.

First, the hard facts that we’ve all been waiting for. The planet has a mass of 23 Earth-masses and an orbital period of 2.64385 days. It orbits a red dwarf star 33 light years away. The temperature on the planet is somewhere in the oven-cleaning neighborhood of 600K (327K, 620F). No habitability news stories on CNN for this fine fellow. The transit depth is a healthy 0.6%, which implies that the the planet’s radius is ~25,000 km. That’s four times that of the Earth, and essentially identical to the 24,764 km radius of Neptune.

The Neptune-like radius indicates that the planet is largely composed of water. This means that it formed beyond the snow-line in Gl 436’s protoplanetary disk and then migrated inward to its present location.

Remarkably, Gl 436b has been known for over two years. In the original discovery paper (on which yours truly was a co-author) there are a number of photometric observations of the star taken over a long period. When the data are folded at the orbital period of the planet, no transit was visible. It looks like systematic effects associated with the analysis of long-baseline photometry may have resulted in the baby being thrown out with the bathwater. In retrospect, that clump of points just to the right of the predicted transit interval may actually be the transit.

Lesson learned. Even if folded photometry shows no sign of a transit, it’s important to follow up with a time-series that covers an entire predicted transit window. This object is within reach of dozens of amateur observers, and it has been sitting in the transitsearch.org candidates table since 2004. Had I pushed for observations of this planet in the same way that we pushed for Gl 581 b and Gl 876 b and c, then we would have gotten it. But to the Victor belongs the prize, and I’m thrilled that this long-awaited Neptune-mass transiting planet has turned up.

The opportunities for follow-up on this discovery are enormous. First, the eccentricity of Gl 436 b appears to be alarmingly high. Single planet fits to the radial velocity data indicate e=0.16. The orbit, however, should have been tidally circularized quite a while ago. It’s likely that there’s additional perturbing bodies in the system. To get a discussion going, look at this fit by user flanker on the systemic backend. There’s an urgent need to start fitting this system to get multiple-planet fits that have (1) low chi-squares and (2) low F-test statistics for planets beyond the known transiting planet “b”. If you find a good fit, upload it to the backend.

Gl 436 should be placed under constant photometric surveillance. If you’re capable of doing sub-1% photometry, please get out there on the sky whenever the night is clear and Gl 436 is at low air mass. If there are additional planets in the system, then it’s completely possible that they are transiting as well.

In addition, it’s very important to collect the best possible time-series data for future Gl 436 transits. By timing when the transits occur, it will be possible to derive the orbital elements of significant additional perturbing bodies. This endeavor is within the reach of careful amateur and small-telescope observers.

And then there’s the Rossiter effect:

Folding the downloadable systemic console‘s gj436_M07K dataset at 2.64385 days shows two points that have (possibly) had their velocities altered as a result of being taken during transit:

And finally, no more major discoveries this week, please! I’ve got to finish my Kepler Participating Scientist proposal to NASA, which is due on Friday.

Image Source.

Looks like this week is good for at least one new transiting planet. Francis O’Donovan (Caltech) and his collaborators have just announced the discovery of TrES-3 and it’s a hot property. The planet is nearly twice Jupiter’s mass, and has a radius about 30% larger than Jupiter. The most remarkable characteristic of the planet is its extremely short orbital period. Thirty one hours, twenty minutes and fifty five seconds. I’ve learned that shady Glenngary Glen Ross-type operators have begun promoting real estate on this planet. Don’t get suckered in! TrES-3 is undergoing orbital decay as a result of tidal evolution, and sooner or later it’s going to merge with its parent star.

TrES-3 exhibits a nice symmetry. The radius of the central star is 16.5% of the planet’s orbital radius, and the planet’s radius is 16.5% the radius of the star. The transit itself is practically a grazing transit, which leads to a bell-shaped light curve. As soon as this post goes up, I’ll add the ephemerides to the transitsearch.org candidates page. With a whopping 2.5% transit depth and a transit just about every day, this is a great starter world for Northern Hemisphere observers who want to bag their first extrasolar planet.