A subgrid-scale model for deflagration-to-detonation transitions in Type Ia supernova explosion simulations

Numerical implementation

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany
² Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Campus Hubland Nord, Emil-Fischer-Str. 31, 97074 Würzburg, Germany
e-mail: friedrich.roepke@astro.uni-wuerzburg.de

Received: 15 March 2013
Accepted: 27 July 2013

Abstract

Context. Delayed detonations of Chandrasekhar-mass white dwarfs are a promising model for normal Type Ia supernova explosions. In these white dwarfs, the burning starts out as a subsonic deflagration and turns at a later phase of the explosion into a supersonic detonation. The mechanism of the underlying deflagration-to-detonation transition (DDT) is unknown in detail, but necessary conditions have been recently determined. The region of detonation initiation cannot be spatially resolved in multidimensional full-star simulations of the explosion.

Aims. We develop a subgrid-scale model for DDTs in thermonuclear supernova simulations that is consistent with the currently known constraints.

Methods. The probability of a DDT occurring is calculated from the distribution of turbulent velocities measured on the grid scale in the vicinity of the flame and the fractal flame surface area that satisfies further physical constraints, such as fuel fraction and fuel density.

Results. The implementation of our DDT criterion provides a solid basis for simulations of thermonuclear supernova explosions in the delayed detonation scenario. It accounts for the currently known necessary conditions for the transition and avoids the inclusion of resolution-dependent quantities in the model. The functionality of our DDT criterion is demonstrated by the example of one three-dimensional thermonuclear supernova explosion simulation.