The Effects of Curvature and Expansion on Helium Detonations on White Dwarf Surfaces

Accreted helium layers on white dwarfs have been highlighted for many decades as a possible site for a detonation triggered by a thermonuclear runaway. In this paper, we find the minimum helium layer thickness that will sustain a steady laterally propagating detonation and show that it depends on the density and composition of the helium layer, specifically C12 and O16. Detonations in these thin helium layers have speeds slower than the Chapman-Jouget (CJ) speed from complete helium burning, v_cj=1.5e9 cm/s. Though gravitationally unbound, the ashes still have unburned helium (~ 80% in the thinnest cases) and only reach up to heavy elements such as Ca40, Ti44, Cr48, and Fe52. It is rare for these thin shells to generate large amounts of Ni56. We also find a new set of solutions that can propagate in even thinner helium layers when O16 is present at a minimum mass fraction of ~0.07. Driven by energy release from alpha captures on O16 and subsequent elements, these slow detonations only create ashes up to Si28 in the outer detonated He shell. We close by discussing how the unbound helium burning ashes may create faint and fast ".Ia" supernovae as well as events with virtually no radioactivity, and speculate on how the slower helium detonation velocities impact the off-center ignition of a carbon detonation that could cause a Type Ia supernova in the double detonation scenario.