On the Sensitivity of Deflagrations in Chandrasekhar Mass White Dwarf to Initial Conditions

We analyze the sensitivity of the flame propagation in a Chandrasekhar mass white dwarf to initial conditions during the subsonic burning phase, using 2D simulations of the full WD. Results are presented for a wide variety of initial flame distributions including central and off-center single point and multi-point, simultaneous and non-simultaneous, ignitions. We also examine the effects of convective velocity field which should exist at the core before the thermo-nuclear runaway. Our main conclusion suggests that the amounts of burning products and their distributions through the deflagration phase are extremely sensitive to initial conditions, much more sensitive than presented in previous studies. In particular, we find that more complex configurations such as even slight off-center ignitions, non-simultaneous multi-point ignitions and velocity fields tend to favor solutions in which individual plumes rise faster than the bulk of a typical Rayleigh-Taylor driven, unstable burning front. The difference to previous calculations for an octant of a WD may be understood as a consequence of the suppression of l=1,2 modes. Our results are consistent with full star calculations by the Chicago group. Moreover, the total amount of nuclear burning during the phase of subsonic burning depends sensitively on the initial conditions and may cause the WD to pulsate or to become unbound. We discuss the implications of the results on current models for Type Ia SNe, limitations imposed by the 2-D nature of our study, and suggest directions for further study.