Neutron-star seismology with realistic, finite-temperature nuclear matter

The oscillation spectrum of a neutron star is notably rich and intrinsically dependent on the equation of state of nuclear matter. With recent advancements in gravitational-wave and electromagnetic astronomy, we are nearing the capability to perform neutron-star asteroseismology and probe the complex physics of neutron stars. With this in mind, we explore the implementation of three-parameter finite-temperature matter models in the computation of neutron-star oscillations. We consider in detail the thermodynamics of nuclear matter and show how this information enters the problem. Our realistic treatment takes into account entropy and composition gradients that exist in the nuclear matter, giving rise to buoyant $g$-mode oscillations. To illustrate the implementation, we determine the oscillation spectrum of a low-temperature neutron star. In addition to the expected compositional and thermal $g$-modes, we find perturbations sourced by phase transitions in the equation of state. We also examine two thermal models, comparing the results for constant redshifted temperature with those for uniform entropy per baryon.