  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.
