Paper detail

The Differences between Analytical and Numerical Ignition Curve of He-C-O Mixture

In this paper, we use large reaction networks to find ignition conditions of single-zone nuclear fuel with compositions typical of white dwarf (WD) matter. The necessary but, possibly not sufficient condition for initiation of detonation is that the nuclear burning proceeds on smaller timescale than the sound-crossing timescale. Under typical white dwarf thermodynamic conditions, the nuclear timescale depends sensitively on the chosen nuclear reaction network, and widely-used analytical formulae are not sufficient to accurately determine unstable ignition conditions the answer to which lies in the fully compressible reactive turbulent simulations. We model the nuclear reactions in the numerical simulation using the astrophysical code TORCH. We report the differences introduced due to the size of the nuclear reaction network. Our findings have implications for numerical results obtained using the popular 19-species network in multidimensional simulations of WD of Chandrasekhar and sub-Chandrasekhar masses. We present a sufficiently accurate general criterion in temperature-density ($T-ρ$) plane for a given initial fuel to ignite in an unstable fashion.