Geometrical effects in off-center detonation of helium shells

The penetration of detonation waves from helium shells into C-O cores of accreting white dwarfs is studied. One-dimensional calculations using a Riemann solver show that for the spherically symmetric case the most relevant parameter for the formation of a double detonation is the location of the ignition surface. As long as ignition occurs at the interface, double detonation does not exist regardless of the accretion rates and the C-O core mass. A two-dimensional analysis, which resolves the interaction between a sliding Chapman-Jouguet front and adjacent medium, shows that the carbon near the interface is heated by the shock only slightly above 10 to the 9th K. Hence, some portion of the C-O core will burn and double detonation cannot be excluded. However, since rarefaction effects are not included in the analysis, detonation may not occur.