  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.
