\times 10^{9}\,\mathrm{g}\,
\mathrm{cm}^{-3}$. In the hydrodynamic explosion simulations, burning was treated in a simplified way. Only five species (carbon, oxygen, alpha-particles, a representative for iron-peak elements, and a representative for intermediate mass elements) were followed. The deflagration and detonation fronts were modeled with the level-set approach (Reinecke et al. 1999b; Golombek & Niemeyer 2005; Roepke & Niemeyer 2007c). After passage of the zero-level set representing the combustion waves, the material was converted from the carbon/oxygen fuel mixture to an approximate nuclear ash composition. At high densities, NSE is reached and the ash was modeled as a temperature- and density-dependent mixture of iron-peak elements and alpha-particles. In the NSE region, electron captures neutronizing the ashes were followed. In the hydrodynamic simulations, $512 \times 512$ cells are used for C-DEF and C-DDT models, and $1024 \times 512$ cells are used for O-DDT model.

In the delayed detonation models, we assumed the deflagration-to-detonation transition to take place once the flame enters the distributed burning regime (e.g., Röpke & Niemeyer 2007c) at a fuel density of $\le 1 \times 10^{7}\,\mathrm{g}\,
\mathrm{cm}^{-3}$ (hereafter $\rho_{\rm DDT}$). We emphasize that in contrast to the classical 1D models, the DDT is not exclusively parameterized by $\rho_{\rm DDT}$, but 