Supernovae, the equation of state and phase transitions

The role of the equation of state (EOS) in supernova collapse is investigated. Improvements are made to the BCK parameterization, incorporating a new symmetry energy and prevention of superluminal behaviour, and first-order phase transitions are included by specifying the location and width of the mixed-phase region and high density limiting behaviour. The resulting EOS make neutron stars sufficiently massive to satisfy observations and may be used to follow the evolution of a supernova through the formation of a neutron star. Numerical simulations using a new completely implicit hydrodynamical code are carried out. An unphysically soft EOS used with a small iron core leads to a direct explosion, while a stiff EOS falters with an accretion shock. The region near the accretion shock is remarkably similar in either case. Phase transitions are then included and have important consequences. The presence of a mixed-phase region softens the EOS and leads to a direct explosion, with the EOS being sufficiently stiff to construct a neutron star compatible with observations. Due to the presence of electrons which do not participate in the phase transition, the phase change is muted and secondary shocks do not develop.