Monthly Archives: October 2009

Q: What’s Jupiter’s Q?

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With the flood of detail from extrasolar planets, one can forget that our knowledge of the worlds in our own solar system is literally centuries ahead of what we know about planets orbiting other stars. For example, careful naked-eye observations can be used to derive better orbital models for Venus et al. than we currently possess for any exoplanet (assuming, of course, that one owns a good watch and eyesight sufficient to resolve the disk of Venus when it transits the Sun). One of the best ways to learn about what’s out there is to learn as much as we can about what’s right here.

In this vein, an important paper came out in Nature last summer, in which Lainey et al describe a direct and unprecedentedly accurate measurement of the present value of Jupiter’s tidal quality factor, Q. The tidal quality factor encapsulates the ability of an object to dissipate disturbances raised by tidal gravity. The lower the Q, the more capable is the body at damping out the perturbations generated by tidal forcing. Q can depend quite sensitively on the frequency at which perturbations occur, and with a few notable exceptions (for example, the Earth and the Moon), it is notoriously tricky to determine. Previous estimates for Jupiter’s Q ranged from Q~60,000 to over a million. By extension, Q values for Jupiter-mass extrasolar planets are often assumed to lie in this range.

In order to directly measure the Jovian Q, Lainey et al. adopted a procedure that’s conceptually very similar to what goes on inside the systemic console. They first collected measurements of the positions of the galilean satellites that were obtained from 1891 all the way through 2007. They then constructed an orbital N-body model that includes the full gravitational forces acting on Jupiter and the galilean satellites, and which incorporates the non-axisymmetric gravitational pulls exerted by the tidal bulges of Jupiter and Io. The fitted parameters — that is, the initial conditions and undetermined constants — for their model are the osculating orbital elements of the moons, and the values of Q/k2 for Jupiter and Io. (The Love number, k2, is a measure of the degree of central concentration of a body, and has a value of k2~0.37 for Jupiter. For more, see these posts, one, two, from last summer).
Lainey et al. varied the parameters and repeatedly carried out new integrations until the the agreement between where the integrated orbital model said the moons should be located and where they were actually observed was optimized. For this type of direct integrations, goodness-of-fit is highly sensitive to the amount of tidal dissipation in Io and in Jupiter — the larger the dissipation, the larger the effect on the orbit. As a consequence, when a best-fit orbital model is attained, one has direct estimates for the Q‘s of both Jupiter and Io.

And the result? The integrations suggest that the current value of Jupiter’s Q is of order 30,000. This suggests that Jupiter is much more dissipative than has been assumed, and is indeed quite comparable to Neptune or Uranus in terms of its ability to damp out tidal disturbances. The measured Q is low enough, in fact, to suggest that Jupiter currently lies in a state where the tidal forcing by Io is leading to a historically large rate of dissipation. Over the past several billion years, as the orbital frequencies of Io, Europa and Ganymede evolved through a range of values, Jupiter’s Q was on average likely quite a bit higher than it is now.

Jupiter’s low Q hints that the transiting Neptune-mass planet Gliese 436b is even more mysterious than previously though. Gliese 436b has a significantly eccentric orbit whose non-circular figure can only be understood if (1) there’s a suitably influential perturber in the system, or (2) there was a relatively recent disaster, or (3) if the planetary Q has somehow stayed anomalously high through billions of years of orbital evolution. No matter which one of these possibilities turns out to be correct, it’ll be a very interesting story.

the last first look

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As is usually the case, there’s been little or no shortage of interesting developments in the field of extrasolar planets. The biggest recent news has been the announcement at the Barcelona conference of a definitive mass for the ultra-short period transiting planet CoRoT-7b. It weighs in at a mere 4.8 Earth Masses (copy of the Queloz et al. preprint here).

Recall that CoRoT-7b caused quite a stir earlier this year with its weird properties. The planet’s year is a fleeting twenty hours and twenty nine minutes, and it induces a tiny transit depth of 0.03%. Unfortunately, the parent star presents a less-than-ideal target for high-precision radial velocity work. It has spots that come and go, and its stellar activity produces frustratingly noisy Doppler measurements. As a result, at the time of CoRoT-7b’s initial announcement, there was no definitive measurement of the planet’s mass.

That’s changed, however, with an unprecedentedly all-out deployment of the HARPS spectrograph. From the Queloz et al. preprint:

A total of 106 measurements between 30 and 60 minute exposure time each were obtained over 4 months, and with sometimes 3 measurements being taken on the same night.

Now in my notoriously biased opinion, such observational enthusiasm is perhaps best reserved for stars such as Alpha Cen B, but a fair argument can be made that the massive investment of time did pay off. Remarkably, the radial velocity data set shows that there are two short-period planets in the CoRoT-7 system. The outer companion, which doesn’t transit, has a period of 3.7 days and at least eight Earth masses. Most dramatically, by combining the mass and radius measurements of CoRoT-7b, one arrives at a density of 5.5 grams per cubic centimeter, essentially identical to that of the Earth, suggesting that the planet is largely composed of refractory materials. (I hesitate to apply the term “rocky” to the CoRoT-7c landscape for the same reason that I’d refrain from describing the Amazon Delta as “icy”.)

In a very real sense, the HARPS campaign on CoRoT-7b has given us our last first look at a fundamentally new category of planet — that is, a world lying in the factor-of-fourteen mass gap spanned by Earth and Uranus. And, from exo-political point of view, the stakes surrounding this discovery were very high. The first density measurement of a planet in this category could just as easily have been made by teams combining high-precision Doppler measurements with either (1) Warm Spitzer, (2) ground-based photometry, (3) Kepler, (4) MOST, (5) HST, or (6) CoRoT. So I can imagine that there was a certain impetus underlying the scheduling of that huge block of HARPS time.

The discovery could, however, still be waiting to be made. Despite all the effort with HARPs, there remains a hefty 70% error on the density determination. This means that there’s a ~16% chance that CoRoT-7b is actually less dense than Neptune.

I’ll go out on a limb: CoRoT-7b’s density will turn out to be anomalously high. More than 90% of “super Earths” will turn out to be “sub-Neptunes” as far as their density is concerned.