The equation of state and composition of hot, dense matter in core-collapse supernovae

Abstract

The equation of state (EOS) and composition of matter are calculated for conditions typical for pre-collapse and early collapse stages in core-collapse supernovae. The composition is evaluated under the assumption of nuclear statistical equilibrium, when the matter is considered as an "almost" ideal gas with corrections owing to thermal excitations of nuclei, to free nucleon degeneracy, and to Coulomb and surface-energy corrections. The account of these corrections allows us to obtain the composition for densities that are slightly below the nuclear matter density. Through comparisons with the EOS developed by Shen et al., which is used in most of recent supernova simulations, we examine the differences of our EOS in the multi-composition with the EOS in the approximation of one representative nucleus. We find that widely distributed compositions in the nuclear chart are different because of the different mass formulae we used, while the thermodynamical quantities are quite close to those in Shen's EOS.

Extended equation of state for core-collapse simulations

“…Although this should not have a large impact on the purely thermodynamic properties [6], it is important to correctly describe the composition of matter to determine the electron capture rates and neutrino interactions. Therefore, in the last years, several groups have started to build EOSs mainly using statistical approaches to improve the low-density part of the EOS (see, e.g., [7][8][9][10][11][12][13]). It has been shown that especially the 1 We work here exclusively with baryon number densities, because the baryon number is a conserved quantity, notably throughout a hydrodynamic simulation, contrary to the mass density which is not conserved.…”

Ensemble inequivalence in supernova matter within a simple model

“…The presence of metastable solutions was never discussed in the framework of NSE models [19,[25][26][27][28]] to our knowledge. It can be understood from the fact that, for chemical potentials higher than the Fermi energy of dense uniform matter µ ≥ e F ≈ −16M eV , the equilibrium condition can be obtained either as a mixture of clusters and homogeneously distributed nucleons µ a>1 = µ a=1 = µ, or alternatively letting the clusterized component to vanish (µ a=1 = µ and ρ cl = 0).…”

“…As a first approximation, one can consider that the the system of interacting nucleons is equivalent to a system of non-interacting clusters, nuclear interaction being completely exhausted by clusterization [24]. This classical model of clusterized nuclear matter is known in the literature as nuclear statistical equilibrium (NSE) [25][26][27][28]. This simple model can only describe diluted matter at ρ ≪ ρ 0 as it can be found in the outer crust of neutron stars, while nuclear interaction among nucleons and clusters has to be included for applications at higher density, when the average inter-particle distance becomes comparable to the range of the force.…”

“…Conversely in a grandcanonical formulation, as the widely used nuclear statistical equilibrium (NSE) [25][26][27][28], these partitions are simply not accessible as they fall in the phase transition region. An approach consisting in taking the metastable grandcanonical prediction and considering only the nuclei of size such that the chosen total density is obtained, as in Ref.…”

Magicity quenching in neutron-rich nuclei and its consequences on electron-capture rates during core collapse

“…Quite recently a number of N(uclear) S(tatistical) E(quilibrium) models has been proposed as alternative to model finite-temperature nuclear matter at sub-saturation densities [5,6,7,8,9,10,11]. All these models depict nuclear matter as a mixture of light and heavy nuclei treated as an ideal gas and a uniform distribution of self-interacting nucleons.…”