Type Ia Supernova: Burning and Detonation in the Distributed Regime

A simple, semi-analytic representation is developed for nuclear burning in Type Ia supernovae in the special case where turbulent eddies completely disrupt the flame. The speed and width of the ``distributed'' flame front are derived. For the conditions considered, the burning front can be considered as a turbulent flame brush composed of corrugated sheets of well-mixed flames. These flames are assumed to have a quasi-steady-state structure similar to the laminar flame structure, but controlled by turbulent diffusion. Detonations cannot appear in the system as long as distributed flames are still quasi-steady-state, but this condition is violated when the distributed flame width becomes comparable to the size of largest turbulent eddies. When this happens, a transition to detonation may occur. For current best estimates of the turbulent energy, the most likely density for the transition to detonation is in the range 0.5 - 1.5 x 10^7 g cm^{-3}.