The structure of detonation waves in supernovae revisited

TL;DR

This paper accurately models thermonuclear detonation wave structures in supernovae, providing benchmarks, revealing that CO detonations are pathological across densities, and confirming He detonations as CJ type, with new insights into nuclear reactions at high densities.

Contribution

It offers precise detonation structure calculations for CO and He, introduces a density-independent condition for CJ detonations, and uncovers new nuclear reaction roles at high densities.

Findings

CO detonations are pathological at all densities.

He detonations are confirmed as CJ type.

Reactions involving $^{11}$B+p are significant at high densities.

Abstract

The structure of a thermonuclear detonation wave can be solved accurately and, thus, may serve as a test bed for studying different approximations that are included in multidimensional hydrodynamical simulations of supernova. We present the structure of thermonuclear detonations for the equal mass fraction of $^{12}$C and $^{16}$O (CO) and for pure $^{4}$He (He) over a wide range of upstream plasma conditions. The lists of isotopes we constructed allow us to determine the detonation speeds, as well as the final states for these detonations, with an uncertainty of the percent level (obtained here for the first time). We provide our results with a numerical accuracy of $\sim0.1\%$, which provides an efficient benchmark for future studies. We further show that CO detonations are pathological for all upstream density values, which differs from previous studies, which concluded that for low upstream densities CO detonations are of the Chapman-Jouget (CJ) type. We provide an approximate condition, independent of reaction rates, that allows to estimate whether arbitrary upstream values will support a detonation wave of the CJ type. Using this argument, we are able to show that CO detonations are pathological and to verify that He detonations are of the CJ type, as was previously claimed for He. Our analysis of the reactions that control the approach to nuclear statistical equilibrium, which determines the length-scale of this stage, reveals that at high densities, the reactions $^{11}$B$+p\leftrightarrow3^{4}$He plays a significant role, which was previously unknown.