Statistical Analysis of Neutron Star Cooling: Implications for the Nuclear Equation of State and Nucleon Pairing

We perform a statistical analysis of the thermal evolution of isolated neutron stars by confronting theoretical cooling curves with luminosity-age measurements for 24 sources. For each object, we explore five purely nucleonic equations of state (APR4, FSU2R, DD2, IST, and NL3 ωρ) combined with representative models of neutron superfluidity and proton superconductivity, while varying the gravitational mass and envelope composition. The analysis spans approximately 10 5 cooling curves. Within this framework, we find that only the NL3 ωρ equation of state and, to a lesser extent, IST, both including neutron triplet pairing, provide an overall satisfactory description of the data. The remaining equations of state are in significant tension with the observations. These results demonstrate that NS cooling provides complementary constraints on dense matter, alongside nuclear structure, global NS observables, and gravitational-wave observations, while probing the interplay between the EoS and nucleon pairing.