Geometrical effects in off-center detonation of helium shells

An off-center detonation in helium shells which have been accreted on top of a white dwarf composed of a carbon and oxygen mixture (C-O core), is a candidate mechanism for Type Ib supernovae We examine the question, raised by Nomoto and Branch, whether such a process can ignite the carbon near the interface and form an ingoing detonation in the C-O core ("double-detonation" case). The problem is discussed both as a one-dimensional spherical problem and as a two-dimensional problem, using analytic and numerical methods We find that double detonation in the spherically symmetric case is possible only when ignition occurs at some distance above the interface. When helium is ignited at the base of the shell, double detonation is not possible regardless of the accretion rate. In the more realistic case of ignition at a single point our results are not conclusive. The shock entering the C-O core is strong enough to raise the carbon temperature onlv slightly above the ignition temperature (10⁹ K). Hence, some burning of carbon near the interface will certainly occur, but formation of a detonation appears marginal. Two-dimensional numerical simulations show that both double detonation and single detonation are possible under appropriate conditions.