systemic

With HAT-P-13c rapidly coming ’round the mountain, there was a very timely update on astro-ph last night. Josh Winn and his collaborators have obtained an additional slew of radial velocities which (1) demonstrate using the Rossiter-McLaughlin effect that the inner planet b’s orbit is likely well aligned with the stellar equator, (2) modify the orbital parameters, including the period of the outer massive planet, and (3) hint at a third body further out in the system.

How do these updates affect the unfolding story?

The Rossiter-McLaughlin measurement gives an estimate of the angle λ = -0.9°±8.5°, which is the angular difference between the sky-projected orbital angular momentum vector and sky-projected stellar spin vector. A non-intuitive mouthful. If we’re viewing the star edge-on, then λ = -0.9° amounts to a determination that the planet’s orbital plane is well-aligned with the star’s equator. (See this post for a discussion of what can happen if the star’s rotation axis is tipped toward the Earth). The good news from the measurement is that it’s a-priori more likely that planets b and c are coplanar — that happy state of affairs which will permit direct measurements of planet b’s interior structure and tidal quality factor. If, on the other hand, the planets b and c have a large mutual inclination, then b’s node will precess, and measurement of a small value for λ will occur only at special, relatively infrequent, times during the secular cycle. A close to co-planar configuration also increases the likelihood that the outer planet can be observed in transit.

With their beefed-up data set of out-of-transit Doppler velocities, Winn and his collaborators are able to get a better characterization of the planetary orbits. The best-fit orbital period and eccentricity of the outer planet are slightly modified when the new data are included. The best-guess center of the transit window for c has “slipped” to April 28, 2010, with a current 1-σ uncertainty of 2 days.

The later date, however, is not an excuse for procrastination! Measuring the TTV for this system is a giant opportunity for the whole ground-based photometric community, and a definitive result will require lots of good measurements of lots of transits starting now (or better yet, last month.) I’ll weigh in in detail on this point, along with the challenge posed by Mr. D very shortly…

Image Source.

Cranking out a paper invariably takes longer than one expects. Last week, I was confident that Konstantin and Peter and I would have our HAT-P-13 paper out in “a day or so”, and then it ended up taking the whole week. As of ten minutes ago, however, it’s been shipped off to the Astrophysical Journal Letters. It’s also been submitted to astro-ph, hopefully in time to make tomorrow’s mailing.

In the meantime, here’s a link to (1) the .pdf of our text, and (2) the two figures (one, two) both in .gif format. The two figures are 800 pixels across, all the better for dropping in to presentations.

Put briefly, HAT-P-13 is an absolutely remarkable set-up. The presence of the outer perturbing body in its well-defined orbit allowed us to show that the system has undergone long-term evolution to a “tidal fixed point”. In this state of affairs, secular variations in the orbital elements of the two planets have been damped out by tidal dissipation, the apsidal lines of the orbits have been brought into alignment, and most importantly, the two orbits precess at the same rate. The paper shows how the eccentricity of the inner planet is a sensitive function of the planet’s interior structure, and in particular, the degree of central concentration (parameterized by the “Tidal Love Number”, k_2).

Here’s a schematic that shows what’s going on:

Right now, the eccentricity of the inner planet is determined to rather modest precision e=0.021 +/- 0.009. The system is transiting, however, and so when Warm Spitzer measures the secondary eclipse time, the error on the eccentricity measurement will drop dramatically. The situation will also benefit from an improved measurement of the planet’s radius. When improved measurements come in, it’ll be possible to literally read off the planet’s core mass and, in addition, the value of the much-discussed tidal quality factor Q.

In reviewing grant proposals and observing proposals that seek to study extrasolar planets, one notices that two cliches turn up with alarm-clock regularity. Number one is Rosetta Stone, as in this or that planetary system is a Rosetta Stone that will enable astronomers to obtain a better understanding of the formation and evolution of planetary systems. Number two is ideal laboratory, as in this or that system is an ideal laboratory for studying the processes that guide the formation and evolution of planetary systems.

A terse unsolicited e-mail from Gaspar Bakos always means that a big discovery is in the offing, and today was no exception:

Hello Greg,

You may like this.
http://xxx.lanl.gov/abs/0907.3525

Best wishes
Gaspar

Indeed! HAT-P-13b and c constitute a really exciting discovery. For a number of reasons, this system is a Rosetta Stone among extrasolar planets, and in large part, this is because the system is an ideal laboratory for studying processes such as tidal dissipation and orbital evolution.

HAT-P-13 harbors the first transiting planet that has a well-characterized companion planet. In this case, the outer companion has a P=428 day orbit, an Msin(i) of 15 Jupiter masses, and an eccentricity, e=0.7. In the following diagram, the orbits and the star are shown to scale; the small filled circles that delineate the outer orbit show the position of the outer planet at 4.28 day intervals.

Illustrator-editable PDF of the above

Of obvious interest is the question of whether planet c can be observed in transit. The a-priori probability is seemingly enhanced by the transit of the inner planet. (Give that one to the good Reverend Bayes). The next opporunity rolls around in April 2010, with the opportunity to observe secondary transit following a bit more than two months later.

It’ll be quite something if planet “c” does transit. A sense of the wide open spaces in the system can be obtained by plotting the star and the two planets to scale with their respective separations at the moment of inferior conjunction. Given the width restriction of the blog post format, one needs to present this plot vertically:

There’s a lot more to say about the HAT-P-13 system — so much in fact, that Peter Bodenheimer, Konstantin Batygin and I are furiously writing an ApJ letter. Should have it out the door in a day or so, with a roundup to follow here on oklo.org immediately thereafter…