Simplified Hydrostatic Carbon Burning in White Dwarf Interiors
  We introduce two simplified nuclear networks that can be used in hydrostatic
carbon burning reactions occurring in white dwarf interiors. They model the
relevant nuclear reactions in carbon-oxygen white dwarfs (COWDs) approaching
ignition in Type Ia supernova (SN Ia) progenitors, including the effects of the
main e-captures and \beta-decays that drive the convective Urca process. They
are based on studies of a detailed nuclear network compiled by the authors and
are defined by approximate sets of differential equations whose derivations are
included in the text. The first network, N1, provides a good first order
estimation of the distribution of ashes and it also provides a simple picture
of the main reactions occurring during this phase of evolution. The second
network, N2, is a more refined version of N1 and can reproduce the evolution of
the main physical properties of the full network to the 5% level. We compare
the evolution of the mole fraction of the relevant nuclei, the neutron excess,
the photon energy generation and the neutrino losses between both simplified
networks and the detailed reaction network in a fixed temperature and density
parcel of gas.
