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

Abstract

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 apses of the transiting planet and its perturber are aligned, and variations in orbital eccentricities vanish. Significant contribution to the apsidal precession rate is made by gravitational quadrupole fields, created by the transiting planets tidal and rotational distortions. The fixed-point orbital eccentricity of the inner planet is therefore a strong function of its interior structure. We illustrate these ideas in the specific context of the recently discovered HAT-P-13 exoplanetary system, and show that one can already glean important insights into the physical properties of the inner transiting planet. We present structural models of the planet, which indicate that its observed radius can be maintained for a one-parameter sequence of models that properly vary core mass and tidal energy dissipation in the interior. We use an octupole-order secular theory of the orbital dynamics to derive the dependence of the inner planet's eccentricity, e_b, on its tidal Love number, k_(2b). We find that the currently measured eccentricity, e_b = 0.021 ± 0.009, implies 0.116 < k_(2b) < 0.425, 0 M_⊕ < M_(core) < 120 M_⊕, and 10,000 < Q_b < 300,000. Improved measurement of the eccentricity will soon allow for far tighter limits to be placed on all of these quantities, and will provide an unprecedented probe into the interior structure of an extrasolar planet.

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