INCOMPLETE CARBON–OXYGEN DETONATION IN TYPE Ia SUPERNOVAE
Incomplete carbon–oxygen detonation with reactions terminating after burning of C12 in the leading C12 + C12 reaction (C-detonation) may occur in the low-density outer layers of white dwarfs exploding as Type Ia supernovae (SNe Ia). Previous studies of carbon–oxygen detonation structure and stability at low densities were performed under the assumption that the velocity of a detonation wave is derived from complete burning of carbon and oxygen to iron. In fact, at densities ρ ⩽ 106 g cm−3 the detonation in SNe Ia may release less than a half of the available nuclear energy. In this paper, we study basic properties of such detonations. We find that the length of an unsupported steady-state C-detonation is ≃30–100 times greater than previously estimated and that the decreased energy has a drastic effect on the detonation stability. In contrast to complete detonations which are one-dimensionally stable, C-detonations may be one-dimensionally unstable and propagate by periodically re-igniting themselves via spontaneous burning. The re-ignition period at ρ ⩽ 106 g cm−3 is estimated to be greater than the timescale of an SN Ia explosion. This suggests that propagation and quenching of C-detonations at these densities could be affected by the instability. Potential observational implications of this effect are discussed.