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We present sets of equation of state (EOS) of nuclear matter including hyperons using an SU_f(3) extended relativistic mean field (RMF) model with a wide coverage of density, temperature, and charge fraction for numerical simulations of core collapse supernovae. Coupling constants of Sigma and Xi hyperons with the sigma meson are determined to fit the hyperon potential depths in nuclear matter, U_Sigma(rho_0) ~ +30 MeV and U_Xi(rho_0) ~ -15 MeV, which are suggested from recent analyses of hyperon production reactions. At low densities, the EOS of uniform matter is connected with the EOS by Shen et al., in which formation of finite nuclei is included in the Thomas-Fermi approximation. In the present EOS, the maximum mass of neutron stars decreases from 2.17 M_sun (Ne mu) to 1.63 M_sun (NYe mu) when hyperons are included. In a spherical, adiabatic collapse of a 15$M_odot$ star by the hydrodynamics without neutrino transfer, hyperon effects are found to be small, since the temperature and density do not reach the region of hyperon mixture, where the hyperon fraction is above 1 % (T > 40 MeV or rho_B > 0.4 fm^{-3}).
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Extensive calculations of properties of supernova matter are presented, using the extended Nuclear Statistical Equilibrium model of PRC92 055803 (2015) based on a statistical distribution of Wigner-Seitz cells modeled using realistic nuclear mass and level density tables, complemented with a non-relativistic Skyrme functional for unbound particles and beyond drip-line nuclei. Both thermodynamic quantities and matter composition are examined as a function of baryonic density, temperature, and proton fraction, within a large domain adapted for applications in supernova simulations. The results are also provided in the form of a table, with grid mesh and format compatible with the CompOSE platform [http://compose.obspm.fr/] for direct use in supernova simulations. Detailed comparisons are also presented with other existing databases, all based on relativistic mean-field functionals, and the differences between the different models are outlined. We show that the strongest impact on the predictions is due to the different hypotheses used to define the cluster functional and its modifications due to the presence of a nuclear medium.
The equation of state 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 due 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 a bit below the nuclear matter density. Through comparisons with the equation of state (EOS) developed by Shen et al. we examine the approximation of one representative nucleus used in most of recent supernova EOSs. We find that widely distributed compositions in the nuclear chart are different, depending on the mass formula, while the thermodynamical quantities are quite close to those in the Shens EOS.
We report a new equation of state (EoS) of cold and hot hyperonic matter constructed in the framework of the quark-meson-coupling (QMC-A) model. The QMC-A EoS yields results compatible with available nuclear physics constraints and astrophysical observations. It covers the range of temperatures from T=0 to 100 MeV, entropies per particle S/A between 0 and 6, lepton fractions from Y$_L$=0.0 to 0.6, and baryon number densities n$_B$=0.05-1.2 fm$^{-3}$. Applications of the QMC-A EoS are made to cold neutron stars (NS) and to hot proto-neutron stars (PNS) in two scenarios, (i) lepton rich matter with trapped neutrinos and (ii) deleptonized chemically equilibrated matter. We find that the QMC-A model predicts hyperons in amounts growing with increasing temperature and density, thus suggesting not only their presence in PNS but also, most likely, in NS merger remnants. The nucleon-hyperon phase transition is studied through the adiabatic index and the speed of sound c$_s$. It is shown that the lowering of (c$_s$/c)$^2$ to and below the conformal limit of 1/3 is a general consequence of instabilities due to any phase transition and is not a unique fingerprint of the hadron-quark matter transition. Rigid rotation of cold and hot stars, their moments of inertia and Kepler frequencies are also explored. The QMC-A model results are compared with two relativistic models, the chiral mean field model (CMF), and the generalized relativistic density functional with hyperons (GRDF-Y). Similarities and differences are discussed.
Electron capture rates on neutron-rich nuclei (A>65) were calculated within the Random Phase Approximation with partial number formalism, including allowed and forbidden transitions. The partial occupation numbers were provided as a function of temperature by Shell-Model Monte Carlo calculations, including an pairing+quadrupole interaction. Capture rates on relevent nuclei were calculated for density and temperature conditions during the core collapse of a massive star. It was found that electron captures on nuclei can compete with electron captures on free protons. Furthermore, they produce neutrinos with average energies lower than neutrinos emitted from captures on free protons, with possible consequences on the cooling of the core.
Neutrinos emitted during the collapse, bounce and subsequent explosion provide information about supernova dynamics. The neutrino spectra are determined by weak interactions with nuclei and nucleons in the inner regions of the star, and thus the neutrino spectra are determined by the composition of matter. The composition of stellar matter at temperature ranging from $T=1-3$ MeV and densities ranging from $10^{-5}$ to 0.1 times the saturation density is explored. We examine the single-nucleus approximation commonly used in describing dense matter in supernova simulations and show that, while the approximation is accurate for predicting the energy and pressure at most densities, it fails to predict the composition accurately. We find that as the temperature and density increase, the single nucleus approximation systematically overpredicts the mass number of nuclei that are actually present and underestimates the contribution from lighter nuclei which are present in significant amounts.
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