DEFLAGRATION-TO-DETONATION TRANSITION IN THERMONUCLEAR SUPERNOVAE

We derive the criteria for deflagration to detonation transition (DDT) in a Type Ia supernova. The theory is based on two major assumptions: (1) detonation is triggered via the Zeldovich gradient mechanism insi de a region of mixed fuel and products, and (2) the mixed region is pr oduced by a turbulent mixing of fuel and products either inside an act ive deflagration front or during the global expansion and subsequent c ontraction of an exploding white dwarf. We determine the critical size of the mixed region required to initiate a detonation in a degenerate carbon-oxygen mixture. This critical length is much larger than the w idth of the reaction front of a Chapman-Jouguet detonation. However, a t densities greater than similar or equal to 5 x 10(6) g cm(-3), it is much smaller than the size of a white dwarf. We derive the critical t urbulent intensity required to create the mixed region inside an activ e deflagration front in which a detonation can form. We conclude that the density rho(tr) at which a detonation can form in a carbon-oxygen white dwarf is low, less than 2-5 x 10(7) g cm(-3) but greater than 5 x 10(6) g cm(-3).