THE CONDUCTIVE PROPAGATION OF NUCLEAR FLAMES .1. DEGENERATE C+O AND O+NE+MG WHITE-DWARFS

The physical properties-speed, width, and density structure-of conductive burning fronts in degenerate carbon-oxygen (C + O) and oxygen-neon-magnesium (O + Ne + Mg) compositions are determined for a grid of initial densities and compositions. Assuming a subsonic, isobaric nuclear flame, these properties are computed by four independent methods: a numerical radiation transport code which includes implicit hydrodynamics; a moving mesh diffusion code; an eigenvalue method; and a quasi-analytical, integral expression. The dependence of the physical properties of the flame on the assumed values of nuclear reaction rates, the nuclear reaction network employed, the thermal conductivity, and the choice of coordinate system are all investigated. The new results have implications for the formation of neutron stars by the accretion-induced collapse (AIC) of a white dwarf and for the production of Type Ia supernovae. The occurrence of AIC is critically dependent on the velocity of the nuclear conductive burning front and the growth rate of hydrodynamic instabilities. However, electron capture in nuclear statistical equilibrium behind the flame causes the density to increase (at constant pressure), restoring the density to its initial value some distance behind the front. There consequently exists a maximum length scale for the development of hydrodynamic instabilities. Treating the expanding area of the turbulent burning region as a fractal whose tile size is identical to the minimum unstable Rayleigh-Taylor wavelength, we find, for all reasonable values of the fractal dimension, that for initial C + O or 0 + Ne + M densities above about 9 x 10(9) cm-3 the white dwarf should colla se to a neutron star.