The thermal index of neutron-star matter in the virial approximation

TL;DR

This paper investigates the thermal index of neutron-star matter using the virial expansion, revealing a nearly constant value in pure neutron matter and a smooth transition from electron- to neutron-dominated regimes, with implications for neutron star mergers.

Contribution

It provides an analytical expression for the thermal index in neutron-star matter and models its density and temperature dependence, including a simple parametrization of the transition between regimes.

Findings

Thermal index in pure neutron matter is nearly constant at ~5/3.

Transition from electron-dominated to neutron-dominated regimes occurs smoothly.

Virial approximation agrees with realistic models at high temperatures, with some discrepancies at lower temperatures.

Abstract

Motivated by gravitational wave observations of binary neutron-star mergers, we study the thermal index of low-density, high-temperature dense matter. We use the virial expansion to account for nuclear interaction effects. We focus on the region of validity of the expansion, which reaches $10^{-3}$ fm$^{-3}$ at $T=5$ MeV up to almost saturation density at $T=50$ MeV. In pure neutron matter, we find an analytical expression for the thermal index, and show that it is nearly density- and temperature-independent, within a fraction of a percent of the non-interacting, non-relativistic value of $\Gamma_\text{th} \approx 5/3$. When we incorporate protons, electrons and photons, we find that the density and temperature dependence of the thermal index changes significantly. We predict a smooth transition between an electron-dominated regime with $\Gamma_\text{th} \approx 4/3$ at low densities to a neutron-dominated region with $\Gamma_\text{th} \approx 5/3$ at high densities. This behavior is by and large independent of proton fraction and is not affected by nuclear interactions in the region where the virial expansion converges. We model this smooth transition analytically and provide a simple but accurate parametrization of the inflection point between these regimes. When compared to tabulated realistic models of the thermal index, we find an overall agreement at high temperatures that weakens for colder matter. The discrepancies can be attributed to the missing contributions of nuclear clusters. The virial approximation provides a clear and physically intuitive framework for understanding the thermal properties of dense matter, offering a computationally efficient solution that makes it particularly well-suited for the regimes relevant to neutron star binary remnants.