Carbon Ignition in Type Ia Supernovae: An Analytic Model

The observable properties of a Type Ia supernova are sensitive to how the nuclear runaway ignites in a Chandrasekhar mass white dwarf at a single point at its center, off-center, or at multiple points and times. We present a simple analytic model for the runaway based upon a combination of stellar mixing-length theory and recent advances in understanding RayleighBenard convection. The convective flow just prior to runaway is likely to have a strong dipolar component, though higher multipoles may contribute appreciably at the very high Rayleigh number (10) appropriate to the white dwarf core. A likely outcome is multi-point ignition with an exponentially increasing number of ignition points during the few tenths of a second that it takes the runaway to develop. The first sparks ignite approximately 150 200 km off center, followed by ignition at smaller radii. Rotation may be important to break the dipole asymmetry of the ignition and give a healthy explosion. Subject headings: Supernovae, hydrodynamics