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In this paper, we use large reaction networks to find ignition conditions ofsingle-zone nuclear fuel with compositions typical of white dwarf (WD) matter.The necessary but, possibly not sufficient condition for initiation ofdetonation is that the nuclear burning proceeds on smaller timescale than thesound-crossing timescale. Under typical white dwarf thermodynamic conditions,the nuclear timescale depends sensitively on the chosen nuclear reactionnetwork, and widely-used analytical formulae are not sufficient to accuratelydetermine unstable ignition conditions the answer to which lies in the fullycompressible reactive turbulent simulations. We model the nuclear reactions inthe numerical simulation using the astrophysical code TORCH. We report thedifferences introduced due to the size of the nuclear reaction network. Ourfindings have implications for numerical results obtained using the popular19-species network in multidimensional simulations of WD of Chandrasekhar andsub-Chandrasekhar masses. We present a sufficiently accurate general criterionin temperature-density ($T-\rho$) plane for a given initial fuel to ignite inan unstable fashion.

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