Tidal Response and Shape of Hot Jupiters

TL;DR

This study models the tidal response and shape of hot Jupiters using the CMS method, revealing that their Love number k_22 cannot exceed 0.6 and that some observed high values are inconsistent with static tidal theory.

Contribution

It provides the first detailed calculations of tidal Love numbers and shape parameters for hot Jupiters using a two-layer interior model and compares results with observational data.

Findings

Love number k_22 of hot Jupiters is capped at 0.6.

High T_eq leads to lower k_22 values.

Some observed high k_22 values are inconsistent with static tidal response.

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, T_eq, 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, k_nm, and transit radius correction, Delta R, which we compare with predictions in the literature. We find that the Love number, k_22, of tidally locked giant planets cannot exceed the value 0.6, and that the high T_eq consistent with strongly irradiated hot Jupiters tend %lead to further lower k_22. While most tidally locked planets are well described by a linear-regime response of k_22 = 3 J_2/q_0 (where q_0 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 k_22. k_22 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.