Type Ia supernovae: Burning and detonation in the distributed regime

A simple, semianalytic 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 the 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).