We investigate the thermal properties of the potential model equation of state of Akmal, Pandharipande and Ravenhall. This equation of state approximates the microscopic model calculations of Akmal and Pandharipande, which feature a neutral pion condensate. We treat the bulk homogeneous phase for isospin asymmetries ranging from symmetric nuclear matter to pure neutron matter and for temperatures and densities relevant for simulations of core-collapse supernovae, proto-neutron stars, and neutron star mergers. Numerical results of the state variables are compared with those of a typical Skyrme energy density functional with similar properties at nuclear densities, but which differs substantially at supra-nuclear densities. Analytical formulas, which are applicable to non-relativistic potential models such as the equations of state we are considering, are derived for all state variables and their thermodynamic derivatives. A highlight of our work is its focus on thermal response functions in the degenerate and non-degenerate situations, which allow checks of the numerical calculations for arbitrary degeneracy. These functions are sensitive to the density dependent effective masses of neutrons and protons, which determine the thermal properties in all regimes of degeneracy. We develop the "thermal asymmetry free energy" and establish its relation to the more commonly used nuclear symmetry energy. We also explore the role of the pion condensate at supra-nuclear densities and temperatures. Tables of matter properties as functions of baryon density, composition (i.e., proton fraction) and temperature are being produced which are suitable for use in astrophysical simulations of supernovae and neutron stars.Comment: 44 pages, 40 figures, 6 table

We explore the thermal properties of hot and dense matter using a model that reproduces the empirical properties of isospin symmetric and asymmetric bulk nuclear matter, optical model fits to nucleon-nucleus scattering data, heavy-ion flow data in the energy range 0.5-2 GeV/A, and the largest well-measured neutron star mass of 2 M . This model, which incorporates finite range interactions through a Yukawa-type, finite-range force, is contrasted with a conventional zero-range Skyrme model. Both models predict nearly identical zero-temperature properties at all densities and proton fractions, including the neutron star maximum mass, but differ in their predictions for heavy-ion flow data. We contrast their predictions of thermal properties, including their specific heats, and provide analytical formulas for the strongly degenerate and non-degenerate limits. We find significant differences in the results of the two models for quantities that depend on the density derivatives of nucleon effective masses. We show that a constant value for the ratio of the thermal components of pressure and energy density expressed as Γ th = 1 + (P th /ε th ), often used in simulations of proto-neutron stars and merging compact object binaries, fails to adequately describe results of either nuclear model. The region of greatest discrepancy extends from sub-saturation densities to a few times the saturation density of symmetric nuclear matter. Our results suggest alternate approximations for the thermal properties of dense matter that are more realistic.

Differences in the equation of state (EOS) of dense matter translate into differences in astrophysical simulations and their multimessenger signatures. Thus, extending the number of EOSs for astrophysical simulations allows us to probe the effect of different aspects of the EOS in astrophysical phenomena. In this work, we construct the EOS of hot and dense matter based on the Akmal, Pandharipande, and Ravenhall (APR) model and thereby extend the open-source SROEOS code which computes EOSs of hot dense matter for Skyrme-type parametrizations of the nuclear forces. Unlike Skrme-type models, in which parameters of the interaction are fit to reproduce the energy density of nuclear matter and/or properties of heavy nuclei, the EOS of APR is obtained from potentials resulting from fits to nucleon-nucleon scattering and properties of light nuclei. In addition, this EOS features a phase transition to a spin-isospin ordered state of nucleons, termed a neutral pion condensate, at supranuclear densities. We show that differences in the effective masses between EOSs have consequences for the properties of nuclei in the subnuclear inhomogeneous phase of matter. We also test the new EOS of APR in spherically symmetric core-collapse of massive stars with 15 M and 40 M , respectively. We find that the phase transition in the EOS of APR speeds up the collapse of the star. However, this phase transition does not generate a second shock wave or another neutrino burst as reported for the hadron-to-quark phase transition. The reason for this difference is that the width of the coexistence region and the latent heat in the EOS of APR are substantially smaller than in the quark-to-hadron transition employed earlier, which results in a significantly smaller softening of the high density EOS.

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of nonrelativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic mean-field theoretical models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects, but in the case of finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Numerical computations are performed to compare results from our analytical formulas with the exact results for zero-and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid.

No abstract