Tidal dissipation in magnetised, rotating stars and planets: linear calculations exploring various magnetic field configurations

Abstract

We study tidal flows in the convective envelopes of rotating, magnetised fluid bodies, such as low-mass stars and giant planets. In well-mixed convective regions, (magneto-)inertial waves are linearly excited by tidal forcing, and their dissipation can dominantly drive spin and orbital evolution in many close star-planet and binary star systems. We perform linear magnetohydrodynamic calculations of wavelike tides in spherical-shell geometry of a tidally-forced, rotating, incompressible, viscous and non-ideal magnetised fluid. Our calculations consider the widest range of magnetic field configurations to date (including both aligned and misaligned dipole fields, free-decay dipole and quadrupole fields, azimuthal "Malkus fields" and mixed poloidal-toroidal "Prendergast fields") to analyse the effects of magnetic fields on the wavelike response and dissipation. We find that the tidal response at a given frequency depends strongly on both magnetic field strength and geometry. Magnetic fields with strong poloidal components modify the flow more efficiently and introduce high-frequency Alfv\'enic resonances associated with weakly damped eigenmodes. When an enhanced (turbulent) viscosity is adopted, we find that viscous dissipation remains comparable to Ohmic dissipation for strong fields, in contrast to previous studies in which Ohmic dissipation was argued to dominate. We also explore the variation in magnetic effects as the shell thickness, magnetic Prandtl and Ekman numbers are varied. Finally, the frequency-averaged tidal power is found to be largely insensitive to the magnetic field in most cases, though significant deviations are found for free-decay fields. Our results have important implications for the tidal evolution of magnetised, rotating stars and planets.