Interplay between tidal flows and magnetic fields in non-linear simulations of stellar and planetary convective envelopes

ABSTRACT Stars and planets in close systems are magnetized, but the influence of magnetic fields on their tidal responses (and vice versa) and dissipation rates has not been well explored. We present exploratory non-linear magnetohydrodynamical (MHD) simulations of tidally excited inertial waves in convective envelopes. These waves probably provide the dominant contribution to tidal dissipation in several astrophysical settings, including tidal circularization of solar-type binary stars and hot Jupiters, and orbital migration of the moons of Jupiter and Saturn. We model convective envelopes as incompressible magnetized fluids in spherical shells harbouring an initially (rotationally aligned) dipolar magnetic field. We find that depending on its strength (quantified by its Lehnert number $\rm{Le}$) and the magnetic Prandtl number $\rm{Pm}$, the magnetic field can either deeply modify the tidal response or be substantially altered by tidal flows. Simulations with small $\mathrm{Le}$ exhibit strong tidally generated differential rotation (zonal flows) for sufficiently large tidal amplitudes, such that both the amplitude and topology of the initial magnetic field are tidally impacted. In contrast, strong magnetic fields can inhibit these zonal flows through large-scale magnetic torques, and by Maxwell stresses arising from magnetorotational instability, which we identify and characterize in our simulations, along with the role of torsional Alfvén waves. Without tidally driven zonal flows, the resulting tidal dissipation is close to the linear predictions. We quantify the transition $\mathrm{Le}$ as a function of $\mathrm{Pm}$, finding it to be comparable to realistic values found in solar-like stars, such that we predict complex interactions between tidal flows and magnetic fields.