Effects of Finite-Temperature Gradients on the Mass, Radius, and Love of Neutron Stars

Neutron stars are most often modeled at zero temperature, and existing efforts to implement finite-temperature effects have used uniform temperature profiles. Recent developments in small finite-temperature expansions of thermodynamic variables now enable a self-consistent and dynamical treatment of the neutron star equation of state. In this work, we implement a non-zero radial temperature gradient assuming beta-equilibrium in neutron stars, utilizing the finite-temperature expansion, to determine the effects on observable parameters such as the mass-radius relation and tidal-deformability. Our formulation allows for the equation of state to strictly depend on chemical potential and temperature, which extends beyond the barotropic assumption and does not rely on speed-of-sound relations. We present a general derivation of the tidal deformability equations valid for such non-barotropic equations of state, and discuss the resulting thermal modifications to neutron star structure and observables.