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Register a new userComparison of statistical treatments for the equation of state for core-collapse supernovae
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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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We construct the equation of state (EOS) of dense matter covering a wide range of temperature, proton fraction, and density for the use of core-collapse supernova simulations. The study is based on the relativistic mean-field (RMF) theory, which can provide an excellent description of nuclear matter and finite nuclei. The Thomas--Fermi approximation in combination with assumed nucleon distribution functions and a free energy minimization is adopted to describe the non-uniform matter, which is composed of a lattice of heavy nuclei. We treat the uniform matter and non-uniform matter consistently using the same RMF theory. We present two sets of EOS tables, namely EOS2 and EOS3. EOS2 is an update of our earlier work published in 1998 (EOS1), where only the nucleon degree of freedom is taken into account. EOS3 includes additional contributions from $Lambda$ hyperons. The effect of $Lambda$ hyperons on the EOS is negligible in the low-temperature and low-density region, whereas it tends to soften the EOS at high density. In comparison with EOS1, EOS2 and EOS3 have an improved design of ranges and grids, which covers the temperature range $T=0.1$--$10^{2.6}$ MeV with the logarithmic grid spacing $Delta log_{10}(T/rm{[MeV]})=0.04$ (92 points including T=0), the proton fraction range $Y_p=0$--0.65 with the linear grid spacing $Delta Y_p = 0.01$ (66 points), and the density range $rho_B=10^{5.1}$--$10^{16},rm{g,cm^{-3}}$ with the logarithmic grid spacing $Delta log_{10}(rho_B/rm{[g,cm^{-3}]}) = 0.1$ (110 points).
We study the evolution of supernova core from the beginning of gravitational collapse of a 15Msolar star up to 1 second after core bounce. We present results of spherically symmetric simulations of core-collapse supernovae by solving general relativistic neutrino-radiation-hydrodynamics in the implicit time-differencing. We aim to explore the evolution of shock wave in a long term and investigate the formation of protoneutron star together with supernova neutrino signatures. These studies are done to examine the influence of equation of state (EOS) on the postbounce evolution of shock wave in the late phase and the resulting thermal evolution of protoneutron star. We make a comparison of two sets of EOS, that is, by Lattimer and Swesty (LS-EOS) and by Shen et al.(SH-EOS). We found that, for both EOSs, the core does not explode and the shock wave stalls similarly in the first 100 milliseconds after bounce. The revival of shock wave does not occur even after a long period in either cases. However, the recession of shock wave appears different beyond 200 milliseconds after bounce, having different thermal evolution of central core. A more compact protoneutron star is found for LS-EOS than SH-EOS with a difference in the central density by a factor of ~2 and a difference of ~10 MeV in the peak temperature. Resulting spectra of supernova neutrinos are different to the extent that may be detectable by terrestrial neutrino detectors.
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.
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}).
In this review article we discuss selected developments regarding the role of the equation of state (EOS) in simulations of core-collapse supernovae. There are no first-principle calculations of the state of matter under supernova conditions since a wide range of conditions is covered, in terms of density, temperature and isospin asymmetry. Instead, model EOS are commonly employed in supernova studies. These can be divided into regimes with intrinsically different degrees of freedom: heavy nuclei at low temperatures, inhomogeneous nuclear matter where light and heavy nuclei coexist together with unbound nucleons, and the transition to homogeneous matter at high densities and temperatures. In this article we discuss each of these phases with particular view on their role in supernova simulations.
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