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

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.

Neutrino and gravitational wave signal of a delayed-detonation model of type Ia supernovae

“…[53]), even a small additional energy loss could, in principle, lead to very different final explosion. This is, however, not the case here as the time at which the first DDT occurs is only slightly delayed (t = 0.958 s).…”

“…5,52]. For details about our implementation of the DDT model see Ciaraldi-Schoolmann et al [53]. We distinguish between weak neutrinos produced in nuclear reactions and thermal neutrinos produced by thermal plasma processes.…”

Two transitional type Ia supernovae located in the Fornax cluster member NGC 1404: SN 2007on and SN 2011iv

“…Other mechanisms suggested invoke crossing shock waves produced in the highly turbulent medium (Livne 1999) and mixing by shear flows in rapidly, differentially rotating WDs (Höflich 2006;Uenishi et al 2003;. The mechanism(s) for small scale mixing is still under debate and in all simulations the transition from the deflagration to detonation phase is initiated by microscopic mixing within the adopted parameterisation (see, e.g., Livne & Arnett 1995;Niemeyer & Hillebrandt 1995a;Khokhlov et al 1997;Gamezo et al 2005b;Ciaraldi-Schoolmann et al 2013). …”

The white dwarf’s carbon fraction as a secondary parameter of Type Ia supernovae

“…The rpc32 model has been run for all four DDT criteria of Table 1. For the 3D models, the treatment of initial composition is the same as for the 2D models (see above). The values used for the limits in the DDT criterion are 0.4 < X fuel < 0.6 and 0.6 < ρ/(10 7 g cm −3 ) < 0.9 (for details, see Ciaraldi-Schoolmann et al 2013) , where X fuel is the mass fraction of unburnt material in the cell. The parameter range around 0.5 ensures that a detonation is ignited only in cells where fuel and ashes are mixed.…”

“…Moreover, for larger C mass fractions, the transition density to burning to NSE 1 The DDT criterion chosen here requires high turbulent velocity fluctuations ≥10 8 cm s −1 to be present with a certain probability for at least half an eddy-turnover-time; this is the same criterion as used by Seitenzahl et al (2013). More details on the treatment of the criterion are described by Ciaraldi-Schoolmann et al (2013). Table 2.…”