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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 guided by a combination of stellar mixing-length theory and analogy to Rayleigh-Benard convection. The convective flow just prior to runaway is likely to have a strong dipolar component, although this dipole may be unstable at the very high Rayleigh number (1025) appropriate to the white dwarf core. A likely outcome is multipoint 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.