The Linear Instability of Astrophysical Flames in Magnetic Fields

Supernovae of Type Ia are used as standard candles for cosmological observations despite the as yet incomplete understanding of their explosion mechanism. In one model, these events are thought to result from subsonic burning in the core of an accreting Carbon/Oxygen white dwarf that is accelerated through flame wrinkling and flame instabilities. Many such white dwarfs have significant magnetic fields. Here we derive the linear effects of such magnetic fields on one flame instability, the well-known Landau-Darrieus instability. When the magnetic field is strong enough that the flame is everywhere sub-Alfvénic, the instability can be greatly suppressed. Super-Alfvénic flames are much less affected by the field, with flames propagating parallel to the field somewhat destabilized, and flames propagating perpendicular to the field somewhat stabilized. Trans-Alfvénic parallel flames, however, like trans-Alfvénic parallel shocks, are seen to be non-evolutionary; understanding the behavior of these flames will require careful numerical simulation. Subject headings: supernovae: general — white dwarfs – hydrodynamics — MHD — nuclear reactions, nucleosynthesis, abundances — conduction