Abstract
Abstract A large fraction of known exoplanets have short orbital periods where tidal excitation of gravity waves within the host star causes the planets’ orbits to decay. We study the effects of tidal resonance locking, in which the planet locks into resonance with a tidally excited stellar gravity mode. Because a star’s gravity mode frequencies typically increase as the star evolves, the planet’s orbital frequency increases in lockstep, potentially causing much faster orbital decay than predicted by other tidal theories. Due to nonlinear mode damping, resonance locking in Sun-like stars likely only operates for low-mass planets (M ≲ 0.1 M Jup), but in stars with convective cores it can likely operate for all planetary masses. The orbital decay timescale with resonance locking is typically comparable to the star’s main-sequence lifetime, corresponding to a wide range in effective stellar quality factor (103 ≲ Q′ ≲ 109), depending on the planet’s mass and orbital period. We make predictions for several individual systems and examine the orbital evolution resulting from both resonance locking and nonlinear wave dissipation. Our models demonstrate how short-period massive planets can be quickly destroyed by nonlinear mode damping, while short-period low-mass planets can survive, even though they undergo substantial inward tidal migration via resonance locking.
Highlights
Exoplanets have been easiest to detect at short orbital periods through transits or radial velocity measurements
Tidal dissipation within the star is parameterized by the effective tidal quality factor Q′ = Q/k2, where Q is the inverse of the phase lag between the tidal potential and the tidal bulge (Goldreich & Soter 1966) and k2 is the tidal Love number
Several additional factors may complicate this picture: if the hot Jupiters are born at some minimum period (e.g., 3 days), the slow tidal migration induced by resonance locking might prevent them from reaching short orbital periods before the massive star evolves off the main sequence
Summary
Exoplanets have been easiest to detect at short orbital periods through transits or radial velocity measurements. Tidal dissipation within the star is parameterized by the effective tidal quality factor Q′ = Q/k2, where Q is the inverse of the phase lag between the tidal potential and the tidal bulge (Goldreich & Soter 1966) and k2 is the tidal Love number In this model, the value of Q′ is related to the orbital decay rate by. They typically invoke a constant tidal quality factor Q′, or at best recompute a frequency-averaged Q′ at different time steps Such averaging is problematic because the effective Q′ for gravity waves or inertial waves is a sensitive function of forcing frequency, such that it has sharp minima over narrow frequency ranges surrounding resonances with stellar oscillations.
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