Numerical models for stationary superfluid neutron stars in general relativity with realistic equations of state

We present a numerical model for uniformly rotating superfluid neutron stars in a fully general relativistic framework with, for the first time, realistic microphysics including entrainment. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a nondissipative interaction which in the case of a nonvanishing relative velocity between the fluids causes the fluid momenta to be not aligned with the respective fluid velocities. We extend the formalism put forth by Comer and Joynt in order to calculate the equation of state (EOS) and entrainment parameters for an arbitrary relative velocity as far as superfluidity is maintained. The resulting entrainment matrix fulfills all necessary sum rules, and in the limit of small relative velocity our results agree with Fermi liquid theory ones derived to lowest order in the velocity. This formalism is applied to two new nuclear equations of state which are implemented in the numerical model, which enables us to obtain precise equilibrium configurations. The resulting density profiles and moments of inertia are discussed employing both EOSs, showing the impact of entrainment and the dependence on the EOS.