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The effect of a magnetic field on the linear phase of the advective-acousticinstability is investigated, as a first step toward a magnetohydrodynamic (MHD)theory of the stationary accretion shock instability taking place duringstellar core collapse. We study a toy model where the flow behind a planarstationary accretion shock is adiabatically decelerated by an externalpotential. Two magnetic field geometries are considered: parallel orperpendicular to the shock. The entropy-vorticity wave, which is simplyadvected in the unmagnetized limit, separates into five different waves: theentropy perturbations are advected, while the vorticity can propagate along thefield lines through two Alfven waves and two slow magnetosonic waves. The twocycles existing in the unmagnetized limit, advective-acoustic and purelyacoustic, are replaced by up to six distinct MHD cycles. The phase differencesamong the cycles play an important role in determining the total cycleefficiency and hence the growth rate. Oscillations in the growth rate as afunction of the magnetic field strength are due to this varying phase shift. Avertical magnetic field hardly affects the cycle efficiency in the regime ofsuper-Alfvenic accretion that is considered. In contrast, we find that ahorizontal magnetic field strongly increases the efficiencies of the vorticitycycles that bend the field lines, resulting in a significant increase of thegrowth rate if the different cycles are in phase. These magnetic effects aresignificant for large-scale modes if the Alfven velocity is a sizable fractionof the flow velocity.

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