Type Ia Supernova: Calculations of Turbulent Flames Using the Linear Eddy Model

TL;DR

This paper models turbulent carbon burning flames in Type Ia supernovae using the Linear Eddy Model, identifying regimes of flame behavior and conditions leading to detonation transition.

Contribution

It applies the Linear Eddy Model to explore turbulent flame regimes and transition conditions in Type Ia supernovae, providing new insights into detonation initiation.

Findings

Turbulent flames follow three regimes depending on density and turbulence.

Transition to detonation likely occurs near 10^7 g/cm^3 density with sufficient turbulence.

Numerical example demonstrates the development of a detonation.

Abstract

The nature of carbon burning flames in Type Ia supernovae is explored as they interact with Kolmogorov turbulence. One-dimensional calculations using the Linear Eddy Model of Kerstein (1991) elucidate three regimes of turbulent burning. In the simplest case, large scale turbulence folds and deforms thin laminar flamelets to produce a flame brush with a total burning rate given approximately by the speed of turbulent fluctuations on the integral scale, U_L. This is the regime where the supernova explosion begins and where most of its pre-detonation burning occurs. As the density declines, turbulence starts to tear the individual flamelets, making broader structures that move faster. For a brief time, these turbulent flamelets are still narrow compared to their spacing and the concept of a flame brush moving with an overall speed of U_L remains valid. However, the typical width of the individual flamelets, which is given by the condition that their turnover time equals their burning time, continues to increase as the density declines. Eventually, mixed regions almost as large as the integral scale itself are transiently formed. At that point, a transition to detonation can occur. The conditions for such a transition are explored numerically and it is estimated that the transition will occur for densities near 1 x 10**7 g/cm**3, provided the turbulent speed on the integral scale exceeds about 15% sonic. An example calculation shows the details of a detonation actually developing.