Equation of State of Dense Matter: Pauli Degeneracy, Pairing Correlations, and Implications for Neutron Stars

TL;DR

This paper presents a unified model of dense fermionic matter, highlighting how Pauli degeneracy, interactions, and pairing influence the equation of state and neutron star properties.

Contribution

It introduces a comprehensive framework that incorporates multiple physical effects into the EOS and applies it to neutron star structure analysis.

Findings

Pauli degeneracy dominates the pressure in dense matter.

Interactions significantly affect the EOS stiffness.

Pairing correlations provide subleading but important corrections, especially in quark matter.

Abstract

We develop a unified description of dense fermionic matter that consistently incorporates Pauli degeneracy, interaction effects, and pairing correlations. The condition that the temperature is much smaller than the Fermi energy leads to a natural separation between Sommerfeld, Fermi-liquid, and pairing regimes, and how these contributions enter the equation of state. The resulting EOS is applied to the Tolman-Oppenheimer-Volkoff equations to analyze neutron-star structure. We demonstrate that Pauli degeneracy provides the dominant pressure, interactions determine the stiffness of the EOS, and pairing correlations produce subleading but potentially significant corrections, especially in quark matter. Implications for mass--radius constraints and modern observations are discussed.