Magnetic effect on dynamical tide in rapidly rotating astronomical objects

TL;DR

This study uses numerical MHD simulations to show that magnetic fields significantly influence dynamical tides in rapidly rotating astronomical objects, affecting flow structures, wave dispersion, and dissipation mechanisms.

Contribution

It demonstrates how magnetic fields alter tidal dynamics, including flow destruction, resonance broadening, and dissipation scaling, providing a way to estimate internal magnetic field strength.

Findings

Magnetic fields destroy internal shear layers in rotating flows.

Magnetic fields broaden the tidal resonance range.

Tidal dissipation scales with the square of magnetic field strength.

Abstract

By numerically solving the equations of rotating magnetohydrodynamics (MHD), the magnetic effect on dynamical tide is studied. It is found that magnetic field has a significant impact not only on the flow structure, i.e. the internal shear layers in rotating flow can be destroyed in the presence of a moderate or stronger magnetic field (in the sense that the Alfv\'en velocity is at least of the order of 0.1 of the surface rotational velocity), but also on the dispersion relation of waves excited by tidal force such that the range of tidal resonance is broadened by magnetic field. A major result is that the total tidal dissipation scales as square of the field strength, which can be used to estimate the strength of internal magnetic field in the astronomical object of a binary system. Moreover, with a moderate or stronger field the ratio of the magnetic dissipation to the viscous dissipation is almost inversely proportional to magnetic Prandtl number (i.e. the ratio of viscosity to magnetic diffusivity), and therefore in the astrophysical situation at small magnetic Prandtl number magnetic dissipation dominates over viscous dissipation with a moderate or stronger field.