The reduction of the electron abundance during the pre-explosion simmering in white dwarf supernovae

Prior to the explosion of a carbon-oxygen white dwarf in a Type Ia supernova there is a long simmering,'' during which the C-12 + C-12 reaction gradually heats the white dwarf on a long (similar to 10(3) yr) timescale. Piro & Bildsten showed that weak reactions during this simmering set a maximum electron abundance Ye at the time of the explosion. We investigate the nuclear reactions during this simmering with a series of self-heating, at constant pressure, reaction network calculations. Unlike in AGB stars, p captures onto Ne-22 and heavier trace nuclei do not play a significant role. The C-12 abundance is sufficiently high that the neutrons preferentially capture onto C-12, rather than iron group nuclei. As an aid to hydrodynamical simulations of the simmering phase, we present fits to the rates of heating, electron capture, change in mean atomic mass, and consumption of C-12 in terms of the screened thermally averaged cross section for C-12 + C-12. Our evaluation of the net heating rate includes contributions from electron captures into the 3.68 MeVexcited state of C-13. This results in a slightly larger energy release, per C-12 consumed, than that found by Piro & Bildsten, but less than that released for a burn to only 20 Ne and Na-23. We compare our one-zone results to more accurate integrations over the white dwarf structure to estimate the amount of C-12 that must be consumed to raise the white dwarf temperature, and hence to determine the net reduction of Ye during simmering.