Hot and dense matter in supernovae and binary mergers
The equation of state (EOS) of dense matter at zero and finite temperature is essential in the description of neutron stars, core-collapse supernovae, and binary mergers. Its cold component is relevant in the determination of the structure of old neutron stars and in the pre-merger evolution of a binary system. Its thermal properties are important in the hydrodynamical modeling of supernovae, during a merger when mass transfer can lead to shock heating, and in the post-event fate of the remnant.
We review different methods used in the construction of the EOS for conditions appropriate to the aforementioned phenomena. We begin with a discussion of the constraints on the EOS from terrestrial experiments and astrophysical observations. We then turn to the supranuclear, uniform nucleonic phase of matter where the various approaches can be broadly classified as microscopic (e.g. Green's functions, variational, Brueckner-Hartree-Fock, chiral effective theory) or phenomenological (e.g. nonrelativistic potential models based on the Skyrme or the Gogny forces, relativistic mean-field theory, etc). Finally, the subnuclear regime is addressed. Here, matter is an inhomogeneous mixture of nucleons, nuclei, and other structures (``pasta''), and several techniques (such as nuclear statistical equilibrium, single-nucleus approximation, virial expansion, and molecular dynamics) at varying degrees of sophistication have been employed in its description.