The effect of turbulent intermittency on the deflagration to detonation transition in SN Ia explosions

Abstract

We examine the effects of turbulent intermittency on the deflagration to detonation transition (DDT) in Type Ia supernovae. The Zel'dovich mechanism for DDT requires the formation of a nearly isothermal region of mixed ash and fuel that is larger than a critical size. We primarily consider the hypothesis by Khokhlov et al. and Niemeyer and Woosley that the nearly isothermal, mixed region is produced when the flame makes the transition to the distributed regime. We use two models for the distribution of the turbulent velocity fluctuations to estimate the probability as a function of the density in the exploding white dwarf that a given region of critical size is in the distributed regime due to strong local turbulent stretching of the flame structure. We also estimate lower limits on the number of such regions as a function of density. We find that the distributed regime, and hence perhaps DDT, occurs in a local region of critical size at a density at least a factor of 2-3 larger than predicted for mean conditions that neglect intermittency. This factor brings the transition density to be much larger than the empirical value from observations in most situations. We also consider the intermittency effect on the more stringent conditions for DDT by Lisewski et al. and Woosley. We find that a turbulent velocity of $10^8$ cm/s in a region of size $10^6$ cm, required by Lisewski et al., is rare. We expect that intermittency gives a weaker effect on the Woosley model with stronger criterion. The predicted transition density from this criterion remains below $10^7$ g/cm$^3$ after accounting for intermittency using our intermittency models.