Kelvin-Helmholtz Instability of the Magnetopause of Disc-Accreting Stars

TL;DR

This paper analyzes the Kelvin-Helmholtz instability at the magnetopause of accreting stars, revealing how shear flows and magnetic field orientation influence plasma stability and accretion processes.

Contribution

It provides a detailed magnetohydrodynamic analysis of KH instability at the star's magnetopause, including effects of magnetic field orientation and a quasi-linear saturation theory.

Findings

KH instability is most unstable for azimuthal waves perpendicular to the magnetic field.

The phase velocity of unstable waves matches disc matter velocity.

The density fluctuation spectrum follows a $k^{-1}$ power law.

Abstract

This work investigates the short wavelength stability of the magnetopause between a rapidly-rotating, supersonic, dense accretion disc and a slowly-rotating low-density magnetosphere of a magnetized star. The magnetopause is a strong shear layer with rapid changes in the azimuthal velocity, the density, and the magnetic field over a short radial distance and thus the Kelvin-Helmholtz (KH) instability may be important. The plasma dynamics is treated using non-relativistic, compressible (isentropic) magnetohydrodynamics. It is necessary to include the displacement current in order that plasma wave velocities remain less than the speed of light. We focus mainly on the case of a star with an aligned dipole magnetic field so that the magnetic field is axial in the disc midplane and perpendicular to the disc flow velocity. However, we also give results for cases where the magnetic field is at an arbitrary angle to the flow velocity. For the aligned dipole case the magnetopause is most unstable for KH waves propagating in the azimuthal direction perpendicular to the magnetic field which tends to stabilize waves propagating parallel to it. The wave phase velocity is that of the disc matter. A quasi-linear theory of the saturation of the instability leads to a wavenumber ($k$) power spectrum $\propto k^{-1}$ of the density and temperature fluctuations of the magnetopause, and it gives the mass accretion and angular momentum inflow rates across the magnetopause. For self-consistent conditions this mass accretion rate will be equal to the disc accretion rate at large distances from the magnetopause.