On Numerical Considerations for Modeling Reactive Astrophysical Shocks

Abstract

Simulating detonations in astrophysical environments is often complicated by numerical approximations to shock structure. A common prescription to ensure correct detonation speeds and associated quantities is to prohibit burning inside the numerically broadened shock (Fryxell et al. 1989). We have performed a series of simulations to verify the efficacy of this approximation and to understand how resolution and dimensionality might affect its use. Our results show that, in one dimension, prohibiting burning in the shock is important wherever the carbon burning length is not resolved, in keeping with the results of Fryxell et al. (1989). In two dimensions, we find that the prohibition of shock burning effectively inhibits the development of cellular structure for all but the most highly-resolved cases. We discuss the possible impacts this outcome may have on sub-grid models and detonation propagation in models of Type Ia supernovae, including potential impacts on observables.

11 pages, 9 figures

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• The type Ia supernova SNLS-03D3bb from a super-Chandrasekhar-mass white dwarf star
• Double-detonation sub-Chandrasekhar supernovae: can minimum helium shell masses detonate the core?
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• Off-centre ignition of sub-Chandrasekhar white dwarfs does not resolve the tension with the observed $t_0$-$M_{\mathrm{Ni}56}$ relation of type Ia supernovae
• Numerical Treatment of Shock-Induced Nuclear Burning in Double Detonation Type Ia Supernovae
• Toward First-Principles Multi-Messenger Predictions: Coupling Nuclear Networks with GR Radiation-MHD in {\tt Gmunu}