Degenerate limit thermodynamics beyond leading order for models of dense matter

Abstract

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.

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

“…To illustrate this advantage, models that are widely used in nuclear and neutron star phenomenology were chosen in Ref. [26] for demonstration purposes.…”

“…[26] with a conventional zero-range Skyrme model known as SkO [143]. Both models predict nearly identical zero-temperature properties (energy density and pressure) at all densities and proton fractions, and thus the neutron star maximum mass [23], but differ in their predictions for heavy-ion flow data [15].…”

“…(109) contributions from two-loop contributions [26]. Although such contributions do not lend themselves to analytical forms, straightforward numerical derivatives are easily calculated.…”

“…Recently, analytical formulas valid to next-to-leading order (NLO) effects in T /T F for all of the thermal state variables have been developed in Ref. [26], and are summarized below.…”

“…Constantinos (now a post-doc at Juelich with Ulf-Meissner, another of Gerry's wards) has worked on thermal effects in dense matter relevant to the astrophysics of compact objects, a subject that was close to Gerry's heart. This article contains a brief review of Constantinos's work [23,25,26], which would have pleased Gerry immensely especially as Landau's Fermi Liquid theory (another subject close to Gerry's heart) was put to good use.…”