Equation of state near β equilibrium for a collapsing stellar core

The composition and equation of state for the collapsing core of a massive star are calculated for temperatures in the range 5 x 109 to 5 x 1011 K and densities in the range 5 x 1010 to 5 x 1013 g cm-3. The core is approximated by a noninteracting gas, incorporating free nucleon degeneracy, high degrees of neutronization, and the thermal excitation of nuclei. The conditions prior to and at high degrees of neutronization, and the thermal excitation of nuclei. The conditions prior to and at β equilibrium are calculated, and analytic expressions for the inhibition of the electron capture rates by neutrino degeneracy are obtained. An estimate of probable collapse trajectories provides a general picture of core conditions during dynamical collapse. The results include a comparison of the effects of a Fermi gas partition function for the nuclei, and another form for the partition function which saturates at kTapprox. =10 MeV. The two approaches yield nearly identical results along the collapse trajectories, implying that the partition of nuclear states for heavy nuclei has a negligible role in the equation of state for kT>10 MeV. For kT< or approx. =5 MeV, the thermal excitation of nuclei pulls the adiabatic index below 4/3. It is also found that simple approximations to the nuclear composition do not work very well along the projected trajectories