Quantifying How Density Gradients and Front Curvature Affect Carbon Detonation Strength During Type Ia Supernovae

Accurately reproducing the physics behind the detonations of Type Ia supernovae and the resultant nucleosynthetic yields is important for interpreting observations of spectra and remnants. The scales of the processes involved span orders of magnitudes, making the problem computationally impossible to ever fully resolve in full star simulations in the present and near future. In the lower density regions of the star, the curvature of the detonation front will slow the detonation, affecting the production of intermediate mass elements. We find that shock strengthening due to the density gradient present in the outer layers of the progenitor is essential for understanding the nucleosynthesis there, with burning extending well below the density at which a steady-state detonation is extinct. We show that a complete reaction network is not sufficient to obtain physical detonations at high densities and modest resolution due to numerical mixing at the unresolved reaction front. At low densities, below 6$\times$10$^{5}$ g cm$^{-3}$, it is possible to achieve high enough resolution to separate the shock and the reaction region,and the abundance structure predicted by fully resolved quasi-steady-state calculations is obtained. For our best current benchmark yields, we utilize a method in which the unresolved portion of Lagrangian histories are reconstructed based on fully resolved quasi-steady-state detonation calculations. These computations demonstrate that under-resolved simulations agree approximately, $\sim$10\% in post-shock values of temperature, pressure, density, and abundances, with expected detonation structures sufficiently far from the under-resolved region, but that there is still room for some improvement in the treatment of subgrid reactions in the hydrodynamics to before better than 1$\%$ can be achieved at all densities.