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Incomplete carbon-oxygen detonation in Type Ia supernovae

Incomplete carbon-oxygen detonation with reactions terminating after burning of 12C in the leading 12C + 12C reaction (C-detonation) may occur in the low density outer layers of white dwarfs exploding as Type Ia supernovae (SNIa). Previous studies of carbon-oxygen detonation structure and stability at low densities were performed under the assumption that the "velocity" of a detonation wave derives from complete burning of carbon and oxygen to iron. In fact, at densities <10^6 g/cm3 the detonation in SNIa 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 rho < 10^6 g/cm3 is estimated to be greater than the time-scale of a SNIa 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.