On the acceleration of nuclear flame fronts in white dwarfs

The acceleration, due to Rayleigh-Taylor instability, of nuclear flame fronts in white dwarfs is examined. A simple model based on fractal geometry yields a general analytic formula for the dependence of the fractal dimension and effective flame speed with distance. This formula gives a physically based parameterization for the acceleration of the flame front and produces a smooth transition from a deflagration to a detonation. This result has relevance to Type Ia supernovae and accretion-induced collapse of white dwarf models.