SUBMITTED TO APJ Preprint typeset using LATEX style emulateapj v. 5/2/11 THE IGNITION OF CARBON DETONATIONS VIA CONVERGING SHOCK WAVES IN WHITE DWARFS

The progenitor channel responsible for the majority of Type Ia supernovae is still uncertain. One emergent scenario involves the detonation of a He-rich layer surrounding a C/O white dwarf, which sends a shock wave into the core. The quasi-spherical shock wave converges and strengthens at an off-center location, forming a second, C-burning, detonation that disrupts the whole star. In this paper, we examine this second detonation of the double detonation scenario using a combination of analytic and numeric techniques. We perform a spatially resolved study of the imploding shock wave and outgoing detonation and calculate the critical imploding shock strengths needed to achieve a core C detonation. We find that He detonations in recent two-dimensional simula-tions yield converging shock waves that are strong enough to ignite C detonations in C/O cores, with the caveat that a truly robust answer requires multi-dimensional detonation initiation calculations. We also find that, due to the greatly increased difficulty of igniting O-burning, convergence-driven detonations in O/Ne cores are far harder to achieve and are perhaps unrealized in standard binary evolution. Subject headings: binaries: close — nuclear reactions, nucleosynthesis, abundances — shock waves — super-novae: general — white dwarfs 1