The Equation of State , Supernovae , and Neutron

The role of the nuclear equation of state in supernovae and in neutron star cooling is elaborated. The equation of state is derived from a nuclear liquid droplet model using a parametrized, phe-nomenological nuclear force. The parameters are adjustable to t the as yet poorly determined properties of bulk nuclear and neutron matter. While some nuclear force parameters are well-constrained by nuclear energies and other experiments, other parameters, like the nuclear incompressibility and symmetry energy parameters are not. However, experiments can determine interesting correlations between these parameters, and the equation of state should include these correlations. The results of the early phases of supernova evolution with this adjustable nuclear equation of state are described. They show that the \bounce-shock" mechanism for supernovae cannot succeed, and that some other, \long-term" mechanism must be involved. The parameters of the nuclear force aaect the light curves of the emitted neutrinos, and, in turn, observations might themselves constrain the nuclear parameters. The equation of state is also important in determining how neutron stars cool. It has recently been proposed that neutron stars may rapidly cool without the intervention of exotic phases of matter like meson condensates and quarks. If the proton fraction of matter is large enough, or if hyperons appear, the direct Urca process, which is over 10 6 times as rapid as standard cooling processes, will rapidly cool the star. It is shown that observations of the rapid cooling epoch could uniquely determine the neutron star radius and x the equation of state above nuclear density.