Thermal properties of hot and dense matter with finite range interactions

Abstract

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.

The equation of state of hot, dense matter and neutron stars

“…Independent calculations by Danielewicz [20,21], who also used a momentum-dependent single-particle potential, have confirmed the need for the momentum dependence to saturate at high momenta to describe heavy-ion data. In addition, the cold EOS implied by such a mean field is also consistent with the recently discovered 2 M neutron star [22,23]. Much of the credit for the resolution of the thorny problem mentioned above belongs to Gerry who gave the team he built much impetus.…”

“…(Note that there is no minimum value for p 1 based on this condition, due to the presence of the polytropic regions 2 and 3.) These limits must be found numerically from TOV integrations, which indicate that 23 We note that the causality boundaries differ from those shown in Ref. [85].…”

“…For non-relativistic models with finite-range interactions, a method involving next-to-leading order steepest descent approach for the calculation of all the state variables has been developed in Ref. [23]. For relativistic mean-field theoretical (MFT) models, the appropriate formulas in the dilute gas limit can be found in Ref.…”

Exploring properties of high-density matter through remnants of neutron-star mergers

“…See e.g. [19] and [37] for a motivation of this value. One should keep in mind that the exact choice of Γ th introduces an ambiguity and thus an uncertainty of the numerical values of certain quantities extracted from simulations.…”

Enforcing causality in nonrelativistic equations of state at finite temperature

“…Finite-range forces introduce momentum dependences (other than p 2 ) to the single-particle potential which in turn cause it to acquire a temperature dependence [52]. The effects of these interactions can still be collected in a density-and temperature-dependent function m * (n, T ) which, however, can no longer be identified with the Landau effective mass.…”