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 (~10³ yr) timescale. Piro & Bildsten showed that weak reactions during this simmering set a maximum electron abundance Y_e 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 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 Y_e during simmering.