Toward a magnetohydrodynamic theory of the stationary accretion shock: toy model of the advective-acoustic cycle in a magnetized flow

TL;DR

This paper develops a magnetohydrodynamic theory for the stationary accretion shock instability, analyzing how magnetic fields influence the advective-acoustic cycle and growth rates in a simplified model relevant to stellar core collapse.

Contribution

It introduces a MHD framework for the advective-acoustic cycle, considering different magnetic field orientations and their impact on instability growth rates in a toy model.

Findings

Horizontal magnetic fields significantly increase cycle efficiencies and growth rates.

Vertical magnetic fields have minimal effect in super-Alfvenic regimes.

Magnetic field orientation critically influences the stability of accretion shocks.

Abstract

The effect of a magnetic field on the linear phase of the advective-acoustic instability is investigated, as a first step toward a magnetohydrodynamic (MHD) theory of the stationary accretion shock instability taking place during stellar core collapse. We study a toy model where the flow behind a planar stationary accretion shock is adiabatically decelerated by an external potential. Two magnetic field geometries are considered: parallel or perpendicular to the shock. The entropy-vorticity wave, which is simply advected in the unmagnetized limit, separates into five different waves: the entropy perturbations are advected, while the vorticity can propagate along the field lines through two Alfven waves and two slow magnetosonic waves. The two cycles existing in the unmagnetized limit, advective-acoustic and purely acoustic, are replaced by up to six distinct MHD cycles. The phase differences among the cycles play an important role in determining the total cycle efficiency and hence the growth rate. Oscillations in the growth rate as a function of the magnetic field strength are due to this varying phase shift. A vertical magnetic field hardly affects the cycle efficiency in the regime of super-Alfvenic accretion that is considered. In contrast, we find that a horizontal magnetic field strongly increases the efficiencies of the vorticity cycles that bend the field lines, resulting in a significant increase of the growth rate if the different cycles are in phase. These magnetic effects are significant for large-scale modes if the Alfven velocity is a sizable fraction of the flow velocity.