Constraints on the Delayed Transition to Detonation in Type Ia Supernovae

Abstract

We investigate the possibility of a delayed detonation in a type Ia supernova under the assumption that the transition to detonation is triggered by turbulence only. Our discussion is based on the Zeldovich mechanism and suggests that typical turbulent velocities present during the explosion are not strong enough to allow this transition to occur. Although we are able to show that in carbon-rich matter (e.g., $X(^{12}$C$) = 0.75$) the possibility of a deflagration to detonation transition (DDT) is enhanced, even in this case the turbulent velocities needed are larger than the expected value of $u'(L) \approx 10^7 {cm s}^{-1}$ on a length-scale of $L \approx 10^6$ cm. Thus we conclude that a DDT may not be a common event during a thermonuclear explosion of a Chandrasekhar-mass white dwarf.