Variation of tidal dissipation in the convective envelope of low-mass stars along their evolution^⋆

Laboratoire AIM Paris-Saclay, CEA/DSM – CNRS – Université Paris Diderot, IRFU/SAp Centre de Saclay, 91191 Gif-sur-Yvette Cedex, France
e-mail: stephane.mathis@cea.fr

Received: 5 May 2015
Accepted: 29 June 2015

Abstract

Context. Since 1995, more than 1500 exoplanets have been discovered around a wide variety of host stars (from M- to A-type stars). Tidal dissipation in stellar convective envelopes is an important factor that shapes the orbital architecture of short-period systems.

Aims. Our objective is to understand and evaluate how tidal dissipation in the convective envelope of low-mass stars (from M to F types) depends on their mass, evolutionary stage, and rotation.

Methods. Using a simplified two-layer assumption, we analytically compute the frequency-averaged tidal dissipation in the convective envelope. This dissipation is due to the conversion into heat of the kinetic energy of tidal non-wavelike/equilibrium flow and inertial waves because of the viscous friction applied by turbulent convection. Using grids of stellar models allows us to study the variation of the dissipation as a function of stellar mass and age on the pre-main sequence and on the main sequence for stars with masses ranging from 0.4 to 1.4 M_⊙.

Results. During their pre-main sequence, all low-mass stars have an increase in the frequency-averaged tidal dissipation for a fixed angular velocity in their convective envelope until they reach a critical aspect and mass ratios (respectively α = R_c/R_s and β = M_c/M_s, where R_s,M_s,R_c, and M_c are the star’s radius and mass and its radiative core’s radius and mass). Next, the dissipation evolves on the main sequence to an asymptotic value that is highest for 0.6 M_⊙ K-type stars and that then decreases by several orders of magnitude with increasing stellar mass. Finally, the rotational evolution of low-mass stars strengthens the importance of tidal dissipation during the pre-main sequence for star-planet and multiple star systems.

Conclusions. As shown by observations, tidal dissipation in stars’ convection zones varies over several orders of magnitude as a function of stellar mass, age, and rotation. We demonstrate that i) it reaches a maximum value on the pre-main sequence for all stellar masses and ii) on the main sequence and at fixed angular velocity, it is at a maximum for 0.6 M_⊙ K-type stars and decreases with increasing mass.