Papers › The thermal index of neutron-star matter in the virial approximation
The thermal index of neutron-star matter in the virial approximation
Giuseppe Rivieccio, Adriana Nadal-Matosas, Arnau Rios, Milton Ruiz
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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 Γₜₕ ≈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 Γₜₕ ≈4/3 at low densities to a neutron-dominated region with Γₜₕ ≈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.
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