Tidal Response and Shape of Hot Jupiters

We study the response of hot Jupiters to a static tidal perturbation using the concentric MacLaurin spheroid 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 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, and Kepler-75b and CoRot-3b. We compute the Love numbers, k_(nm), and transit radius correction, ΔR, which we compare with predictions in the literature. We find that the Love number, k₂₂, of tidally locked giant planets cannot exceed a value of 0.6, and that the high T_(eq) consistent with strongly irradiated hot Jupiters tends to further lower k₂₂. While most tidally locked planets are well described by a linear regime response of k₂₂ = 3J₂/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. The 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.