Single and multiple detonations in white dwarfs

A currently favored model for Type Ia supernovae consists of a carbon-oxyge n (CO) white dwarf (similar to 0.6-1.0 M.), surrounded by a thick layer of helium (similar to 0.2-0.3 M.), which explodes as a consequence of successi ve detonations in the helium layer and the CO core. Previous studies, carri ed out in one and two dimensions, have shown that this model is capable of providing light curves and late-time spectra in agreement with observations , though the peak light spectrum may be problematic. These same studies als o highlighted a key uncertainty in the model. When properly considered in t hree dimensions, will the helium detonation actually succeed in igniting a corresponding detonation in the carbon core? In this paper we follow the hy drodynamic evolution of a representative case calculated in three dimension s using the smoothed particle (SPH) approach to multi-dimensional hydrodyna mical modeling. Several fine zoned simulations are also carried out in one dimension to elucidate shock hydrodynamics that cannot be resolved in a cal culation that carries the whole star. Consistent with the previous results by Bent (1997) and Livne & Arnett (1995), our calculations show that the in itial stages of helium ignition strongly influence the development of the e xplosion. In particular, the altitude above the core boundary at which the first hot spots appear will determine the character of detonation in the co re. This altitude is sensitive to the carbon mass fraction in the CO core a nd to the pre-explosive mixing between the CO core and helium layer. We als o find, for a given helium layer and CO core mass, that the number and geom etrical distribution of these hot spots influences the evolution of the exp losion and the nucleosynthetic yield. A model in which the ignition begins at five distinct points produces more intermediate mass elements than anoth er model in which the ignition commences at a single point. Nevertheless, g iven that a successful double detonation occurs, the energetics and gross f eatures of the explosion are not very different from what is seen in one- o r two-dimensional simulations.