Type Ia Supernova: Burning and Detonation in the Distributed Regime

TL;DR

This paper develops a semi-analytic model for turbulent nuclear burning in Type Ia supernovae, describing how distributed flames evolve and under what conditions they transition to detonation, with implications for supernova explosion mechanisms.

Contribution

It introduces a simplified model for turbulent flame behavior in supernovae and predicts the density range where detonation may occur.

Findings

Distributed flame width becomes comparable to turbulent eddy size at critical conditions.

Detonation transition likely occurs at densities 0.5-1.5 x 10^7 g/cm^3.

Distributed flames are stable until a critical width is reached.

Abstract

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}.