On the stability of thermonuclear detonation in supernovae events

The stability of a plane stationary thermonuclear detonation in an exploding carbon white dwarf is investigated. It is shown that detonation is unstable in a wide range of densities of white dwarf matter from rho approximate to 2 X 10(7) g/cm(3) to rho = 3 X 10(9) g/cm(3). The detonation wave becomes stable at low densities rho less than or similar to 10(7) g/cm(3) typical for a pre-expanded white dwarf. An important feature of the obtained detonation stability spectrum is the presence of unstable modes of zero frequency, that may result in self-quenching of the detonation at the non-linear stage of the instability. Therefore, the detonation stability analysis suggests that detonation in white dwarfs cannot propagate at sufficiently high densities: rho greater than or equal to 2.1 X 10(7) g/cm(3). The effect of the detonation self-quenching at high densities of the carbon-oxygen fuel may provide the physical explanation for the delayed detonation triggering in the thermonuclear supernovae. (C) 1998 Elsevier Science B.V. All rights reserved.