Determination of the Interior Structure of Transiting Planets in Multiple - Planet Systems

Tidal dissipation within a short-period transiting extrasolar planet perturbed by a companion object can drive orbital evolution of the system to a so-called tidal fixed point, in which the apsidal lines of the transiting planet and its perturber are aligned, and for which variations in the orbital eccentricities of both planet and perturber are damped out. Maintenance of the fixed-point apsidal alignment requires the orbits of both planet and perturber to precess at the same rate. Significant contributions to the apsidal precession rate are made by the secular planet-planet interaction, by general relativity, and by the gravitational quadropole fields created by the transiting planet’s tidal and rotational distortions. The precession arising from the planetary quadrupole can be the dominant term, and is strongly dependent on the planet’s internal density distribution, which is in turn controlled by the fractional mass of the planet incorporated into a heavy-element core. The fixed-point orbital eccentricity of the inner planet is therefore a strong function of the planet’s interior structure. We illustrate these ideas in the specific context of the recently discovered HAT-P-13 exo-planetary system, and show that one can already glean important insights into the physical properties of the inner P = 2.91 d, M = 0.85MJup, R = 1.28RJup transiting planet. We present structural models of the planet, which indicate that its observed radius can be maintained for a oneparameter sequence of models that properly vary core mass and tidal energy dissipation in the interior. We use an octopole-order secular theory of the orbital dynamics to derive the dependence of the inner planet’s eccentricity, eb, on its tidal Love number, k2b. We find that the currently measured eccentricity, eb = 0.021±0.009 implies 0.116 < k2b < 0.425, 0M⊕ < Mcore < 120M⊕, and Qb < 300, 000. Improved measurement of the eccentricity via transit and secondary eclipse timing, along with continued radial velocity monitoring, will soon allow for far tighter limits to be placed on all three of these quantities, and will provide an unprecedented probe into the interior structure of an extrasolar planet. ar X iv :0 90 7. 50 19 v1 [ as tr oph .E P] 2 8 Ju l 2 00 9