Tidal Migration of Exoplanets around M Dwarfs: Frequency-dependent Tidal Dissipation

Abstract

The orbital architectures of short-period exoplanet systems are shaped by tidal dissipation in their host stars. For low-mass M dwarfs whose dynamical tidal response comprises a dense spectrum of inertial modes at low frequencies, resolving the frequency dependence of tidal dissipation is crucial to capturing the effect of tides on planetary orbits throughout the evolutionary stages of the host star. We use nonperturbative spectral methods to calculate the normal mode oscillations of a fully convective M dwarf modeled using realistic stellar profiles from MESA. We compute the dissipative tidal response composed of contributions from each mode, as well as nonadiabatic coupling between the modes, which we find to be an essential component of the dissipative calculations. Using our results for dissipation, we then compute the evolution of circular, coplanar planetary orbits under the influence of tides in the host star. We find that orbital migration driven by resonance locking affects the orbits of Earth-mass planets at orbital periods P orb ≲ 1.5 days and of Jupiter-mass planets at P orb ≲ 2.5 days. Due to resonantly driven orbital decay and outward migration, we predict a dearth of small planets closer than P orb ∼ 1 day and similarly sparse numbers of more massive planets out to P orb ∼ 3 days.