Distributed burning in Type Ia supernovae: A statistical approach

We present a statistical model which shows the influence of turbulence on a thermonuclear flame propagating in C+O white dwarf matter. Based on a Monte Carlo description of turbulence, it provides a method for investigating the physics in the so-called distributed burning regime. Using this method, we perform numerical simulations of turbulent flames and show that in this particular regime the flamelet model for the turbulent flame velocity loses its validity. In fact, at high turbulent intensities, burning in the distributed regime can lead to a deceleration of the turbulent flame and thus induce a competing process to turbulent effects that cause a higher flame speed. It is also shown that in dense C+O matter turbulent heat transport is described adequately by the Peclet number rather than by the Reynolds number, which means that flame propagation is decoupled from small-scale turbulence. Finally, at the onset of our results we argue that the available turbulent energy in an exploding C+O white dwarf is probably too low to make a deflagration-to-detonation transition possible.