The delayed-detonation model of a Type Ia supernovae. I. The deflagration phase

The nature of the "delayed detonation" mechanism of Khokhlov for the explosion of Type Ia supernovae is investigated by using two-dimensional numerical hydrodynamics simulations. A new algorithm is used to treat the deflagration front. Assuming that it propagates locally at the laminar flame speed, the deflagration is insufficient to unbind the star. Expansion shuts off the flame; much of this small production of iron group nuclei occurs at lower densities, which reduces the electron-capture problem. The burning front does become wrinkled, but the wavelength of the instability is much larger than the computational grid size and is resolved; this is consistent with previous analysis. Because the degenerate star has an adiabatic exponent only slightly above 4/3, the energy released by deflagration drives a pulsation of large amplitude. During the first expansion phase, adiabatic cooling shuts off the burning, and a Rayleigh-Taylor instability then gives mixing of high-entropy ashes with low-entropy fuel. During the first contraction phase, compressional heating reignites the material. This paper deals with the deflagration phase, from the onset of burning, through expansion and quenching of the flame, to the first contraction.