Relativistic Equation of State for Core-Collapse Supernova Simulations

Abstract

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 Λ hyperons. The effect of Λ hyperons on the EOS is negligible in the lowtemperature 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 ∆ log 10 (T /[MeV]) = 0.04 (92 points including T = 0), the proton fraction range Y p = 0-0.65 with the linear grid spacing ∆Y p = 0.01 (66 points), and the density range ρ B = 10 5.1 -10 16 g cm −3 with the logarithmic grid spacing ∆ log 10 (ρ B /[g cm −3 ]) = 0.1 (110 points).

Equation of State of Hyperonic Nuclear Matter at Zero and Finite Temperatures with the Variational Method

“…In the SN explosion, the weak equilibrium could be achieved by the neutrino trapping in the central high-density region, where Λ hyperon mixing is not negligible. In fact, other SN-EOSs including Λ hyperons [10,12] provide thermodynamic quantities under this equilibrium condition at fixed n B , Y p , and T . We note that, in this study, the contribution from Λ hyperons is included when the Λ-hyperon fraction x Λ exceeds 10 −4 .…”

“…The other type was constructed by Shen et al [8] with use of a relativistic mean field theory for uniform matter and a Thomas-Fermi approximation for non-uniform matter. Recently, new nuclear EOSs including hyperon mixing [9][10][11][12], have been developed for the numerical simulations of SNe, but the number of SN-EOSs is still limited, especially for hyperonic nuclear matter. Furthermore, even for purely nucleonic matter without hyperons, these SN-EOSs are based on phenomenological models for uniform matter.…”

Variational Study of the Supernova Equation of State with Hyperons

“…Moreover, we extended the cluster variational method to obtain the EOS of neutron star matter taking into account hyperon mixing at zero temperature. In this study, we extend this research so as to construct a new variational EOS for hot hyperonic nuclear matter composed of nucleons and Λ hyperons, and discuss the properties of the obtained EOS as compared with the Shen EOS with Λ hyperon mixing [2].…”

“…Various nuclear EOSs for SN simulations have been proposed so far (e.g., [1,2]), but those nuclear EOSs are based on phenomenological models for uniform matter. Under these circumstances, we recently constructed a new type of SN-EOS for purely nucleonic matter based on a realistic nuclear Hamiltonian comprising the Argonne v18 two-body and Urbana IX three-body potentials using the cluster variational method for uniform matter [3].…”

Finite-Size Effects on Equation of State for Supernovae and Neutron Stars

“…The EOS for supernova matter should cover wide ranges in baryon number density, temperature, and isospin asymmetry. During the past few decades, great efforts have been made to study the EOS of dense matter [1][2][3][4][5][6]. At densities below saturation and temperatures lower than ∼ 20 MeV, stellar matter may be in a liquid-gas mixed phase which plays a crucial role in supernova explosions and neutron-star formation [5].…”