The Magnetic Effect on Dynamical Tide in Rapidly Rotating Astronomical Objects

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 Alfvén 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.

Does magnetic field impact tidal dynamics inside the convective zone of low-mass stars along their evolution?

“…1. First, we note that Le 2 remains always smaller than unity, consistent with the previous works of Lin & Ogilvie (2018) and Wei (2018). Whether we look at the base or the top, Le 2 increases with decreasing initial rotation speed from the PMS until about 1Gyr.…”

“…From the results of this section, we conclude that the tidal forcing arising from the Lorentz force remains small in comparison to a pure hydrodynamical forcing. This conclusion is important, as it stresses that adopting a Coriolis-driven tidal forcing is justified to study the propagation and dissipation of tidally-forced magneto-inertial waves in the convective envelope of lowmass stars, despite the presence of a large-scale, dynamo generated magnetic field, as was done in Wei (2016Wei ( , 2018 and Lin & Ogilvie (2018).…”

“…This ratio results from the different length scales used in the magnetic scaling laws and in the definition of the Lehnert number (the length scales l c and R respectively). Specifically, we choose a definition of the Lehnert number that is consistent with the previous works of Lin & Ogilvie (2018) and Wei (2018).…”

“…The magnetic fields of solarlike stars originates from a powerful dynamo mechanism, sustained by turbulent convection and differential rotation in the convective envelope of the star (Brun & Browning 2017). Recent endeavours have been carried out to assess the effects of magnetism on tidally-excited inertial waves in stars (Wei 2016(Wei , 2018Lin & Ogilvie 2018). In the presence of a magnetic field, tidal waves excited in the CZ become magneto-inertial waves.…”

Ohmic dissipation in the Earth's outer core resulting from the free inner core nutation

“…Since the natural frequency of the FICN lies within the frequency range of inertial waves in a rotating fluid, the excitation of the FICN in turn generates inertial waves propagating in the fluid outer core, leading to conical shear layers around the characteristic surfaces of inertial waves (Hollerbach and Kerswell, 1995;Buffett, 2010b). However, the presence of a magnetic field would alter the propagation of inertial waves and therefore their typical length-scale and associated dissipation, provided that the magnetic field is sufficiently strong or the Ekman number is sufficiently small (Lin and Ogilvie, 2018;Wei, 2018). Given the extremely small Ekman number of the Earth's core, we expect non-negligible feedbacks of the magnetic fields on the nutation-induced inertial waves in the Earth's outer core.…”