Tidal Response and Shape of Hot Jupiters

Published in Astrophysical Journal, 2021

Recommended citation: S M Wahl, D Thorngren, T Lu, B Militzer, ApJ, (in press).

Abstract

We study the response of hot Jupiters to a static tidal perturbation using the Concentric MacLaurin Spheroid (CMS) method. For strongly irradiated planets, we first performed radiative transfer calculations to relate the planet’s equilibrium temperature, Teq, to its interior entropy. We then determined the gravity harmonics, shape, moment of inertia, and the static Love numbers for a range of two-layer interior models that assume a rocky core plus a homogeneous and isentropic envelope composed of hydrogen, helium, and heavier elements. We identify general trends and then study HAT-P-13b, the WASP planets 4b, 12b, 18b, 103b, and 121b, as well as Kepler-75b and CoRot-3b. We compute the Love numbers, knm, and transit radius correction, Delta R, which we compare with predictions in the literature. We find that the Love number, k22, of tidally locked giant planets cannot exceed the value 0.6, and that the high Teq consistent with strongly irradiated hot Jupiters tend to further lower k22. While most tidally locked planets are well described by a linear-regime response of k_22 = 3 J2/q0 (where q0 is the rotation parameter of the gravitational potential, for extreme cases such as WASP-12b, WASP-103b and WASP-121b, nonlinear effects can account for over 10% of the predicted k22. k22 values larger than 0.6, as they have been reported for planets WASP-4b and HAT-P13B, cannot result from a static tidal response without extremely rapid rotation, and thus are inconsistent with their expected tidally-locked state.