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 12C + 12C reaction gradually heats the white dwarf on a long (~ 1000 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, proton captures onto 22Ne and heavier trace nuclei do not play a significant role. The 12C abundance is sufficiently high that the neutrons preferentially capture onto 12C, 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 12C in terms of the screened thermally averaged cross section for 12C + 12C. Our evaluation of the net heating rate includes contributions from electron captures into the 3.68 MeV excited state of 13C. This results in a slightly larger energy release, per 12C consumed, than that found by Piro & Bildsten, but less than that released for a burn to only 20Ne and 23Na. We compare our one-zone results to more accurate integrations over the white dwarf structure to estimate the amount of 12C that must be consumed to raise the white dwarf temperature, and hence to determine the net reduction of Ye during simmering.