Dense matter equation of state for neutron star mergers.

In simulations of binary neutron star mergers, the dense matter equation of state (EOS) is required over wide ranges of density and temperature as well as under conditions in which neutrinos are trapped, and the effects of magnetic fields and rotation prevail. Here we assess the status of dense matter theory and point out the successes and limitations of approaches currently in use. A comparative study of the excluded volume (EV) and virial approaches for the $np\alpha$ system using the equation of state of Akmal, Pandharipande and Ravenhall for interacting nucleons is presented in the sub-nuclear density regime. Owing to the excluded volume of the $\alpha$-particles, their mass fraction vanishes in the EV approach below the baryon density 0.1 fm$^{-3}$, whereas it continues to rise due to the predominantly attractive interactions in the virial approach. The EV approach of Lattimer et al. is extended here to include clusters of light nuclei such as d, $^3$H and $^3$He in addition to $\alpha$-particles. Results of the relevant state variables from this development are presented and enable comparisons with related but slightly different approaches in the literature. We also comment on some of the sweet and sour aspects of the supra-nuclear EOS. The extent to which the gravitational and baryon masses vary due to thermal effects, neutrino trapping, magnetic fields and rotation are summarized from earlier studies in which the effects from each of these sources were considered separately. Increases of about 25\% (50\%) occur for rigid (differential) rotation with comparable increases occurring in the presence of magnetic fields only for fields in excess of $10^{18}$ Gauss. Comparatively smaller changes occur due to thermal effects and neutrino trapping. Some future studies to gain further insight into the outcome of dynamical simulations are suggested.