Interplay between tidal flows and magnetic fields in nonlinear simulations of stellar and planetary convective envelopes

TL;DR

This paper explores how magnetic fields influence tidal responses and dissipation in stellar and planetary convective envelopes through nonlinear MHD simulations, revealing complex interactions dependent on magnetic field strength and properties.

Contribution

It provides the first detailed nonlinear simulations showing how magnetic fields modify tidal flows and dissipation in convective stellar and planetary envelopes, highlighting the role of magnetic parameters.

Findings

Magnetic fields can either modify or be altered by tidal flows depending on their strength.

Strong magnetic fields inhibit zonal flows through magnetic torques and Maxwell stresses.

Tidal dissipation remains close to linear predictions when zonal flows are absent.

Abstract

Stars and planets in close systems are magnetised but the influence of magnetic fields on their tidal responses (and vice versa) and dissipation rates has not been well explored. We present exploratory nonlinear 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 circularisation of solar-type binary stars and hot Jupiters, and orbital migration of the moons of Jupiter and Saturn. We model convective envelopes as incompressible magnetised fluids in spherical shells harbouring an initially (rotationally-aligned) dipolar magnetic field. We find that depending on its strength (quantified by its Lehnert number Le) and the magnetic Prandtl number Pm, the magnetic field can either deeply modify the tidal response or be substantially altered by tidal flows. Simulations with small 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 magneto-rotational instability, which we identify and characterise in our simulations, along with the role of torsional Alfv\'en waves. Without tidally-driven zonal flows, the resulting tidal dissipation is close to the linear predictions. We quantify the transition Le as a function of 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.