Thermal properties of supernova matter: The bulk homogeneous phase

Abstract

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

Enforcing causality in nonrelativistic equations of state at finite temperature

“…In this section, we present results pertaining to the speed of sound for the PNM models of APR [18,47], LS [45], and SLy4 [46] and the alterations our causalityenforcing scheme causes to the properties of the neutron stars in their maximum-mass configurations. This configuration reaches the largest central density and therefore it is the setting where the effects of causality implementation will be most apparent.…”

“…That the different curves appear to be causally fixed at the same density is a consequence of the (accidental) fact that, for APR, n f (β f = 0.9) n X . As a caution we point out that the problematic implementation of [18] will appear correct if one chooses β f = β f (n X ).…”

“…While such a method is available in the literature for zero temperature [18,43,44], a method to encompass the influence of temperature on c s has not received much attention (the method presented in Appendix E of our earlier work in Ref. [18] contained an inadvertent error, which is corrected in this work). We illustrate the application of the method using a few chosen models [45][46][47] that become acausal at high density and temperature.…”

“…The method outlined in Ref. [18] for T = 0 was flawed in that Eq. (E18) there defining the chemical potential lacked a term involving T S, that is, µ was taken to be ∂ε/∂n| S,N instead of the correct ∂ε/∂n| S,V where n = N/V .…”

“…For EOS's with only nucleonic components, S nuc of up to 4-5 is not uncommon. In the homogeneous phase (n ≥ 0.1 fm −3 ) and using the EOS of APR [18], S ≤ 30 with nucleons contributing about 5, leptons 15, and photons 10. The highest density at which S ∼ 200 is about 0.01 fm −3 (at T =200 MeV) with 95% of the contributions coming from leptons and photons.…”