Carbon ignition in type Ia supernovae. II. A three-dimensional numerical model

The thermonuclear runaway that culminates in the explosion of a Chandrasekhar mass white dwarf as a Type Ia supernova begins centuries before the star actually explodes. Here, using a three-dimensional anelastic code, we examine numerically the convective flow during the last minute of that runaway, a time that is crucial in determining just where and how often the supernova ignites. We find that the overall convective flow is dipolar, with the higher temperature fluctuations in an outbound flow preferentially on one side of the star. Taken at face value, this suggests an asymmetric ignition that may well persist in the geometry of the final explosion. However, we also find that even a moderate amount of rotation tends to fracture this dipole flow, making ignition over a broader region more likely. Although our calculations lack the resolution to study the flow at astrophysically relevant Rayleigh numbers, we also speculate that the observed dipolar flow would become less organized as the viscosity becomes very small. Motion within the dipole flow shows evidence of turbulence, suggesting that only geometrically large fluctuations (similar to 1 km) would persist to ignite the runaway. We also examine the probability density function for the temperature fluctuations, finding evidence for a Gaussian rather than exponential distribution, which suggests that ignition sparks may be strongly spatially clustered.