The impact of rotation on turbulent tidal friction in stellar and planetary convective regions

¹ 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
² LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France
³ IMCCE, Observatoire de Paris, UMR 8028 du CNRS, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France
⁴ Department of Astronomy, University of Geneva, Chemin des Maillettes 51, 1290 Versoix, Switzerland
⁵ SYRTE, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, LNE, 61 avenue de l’Observatoire, 75014 Paris, France

Received: 12 October 2015
Accepted: 27 April 2016

Abstract

Context. Turbulent friction in convective regions in stars and planets is one of the key physical mechanisms that drive the dissipation of the kinetic energy of tidal flows in their interiors and the evolution of their systems. This friction acts both on the equilibrium/non-wave-like tide and on tidal inertial waves in these layers.

Aims. It is thus necessary to obtain a robust prescription for this friction. In the current state-of-the-art, it is modelled by a turbulent eddy-viscosity coefficient, based on mixing-length theory, applied to tide velocities. However, none of the current prescriptions take into account the action of rotation that can strongly affect turbulent convection. Therefore, a new prescription that takes this into account must be derived.

Methods. We use theoretical scaling laws for convective velocities and characteristic lengthscales in rotating stars and planets that have been recently confirmed by 3D high-resolution non-linear Cartesian numerical simulations to derive the new prescription. A corresponding local model of tidal waves is used to understand the consequences for the linear tidal dissipation. Finally, new grids of rotating stellar models and published values of planetary convective Rossby numbers are used to discuss astrophysical consequences.

Results. The action of rotation on convection deeply modifies the turbulent friction applied on tides. In the regime of rapid rotation (with a convective Rossby number below 0.25), the eddy-viscosity may be decreased by several orders of magnitude. It may lead to a loss of efficiency of the viscous dissipation of the equilibrium tide and to a more efficient complex and resonant dissipation of tidal inertial waves in the bulk of convective regions.

Conclusions. To understand the complete evolution of planetary systems, tidal friction in rapid rotators such as young low-mass stars, giant and Earth-like planets must be evaluated. Therefore, we need a completely coupled treatment of the tidal evolution of star-planet systems and multiple stars, and of the rotational evolution of their components with a coherent treatment of the variations of tidal flows, and of their dissipation as a function of rotation.