Oscillations of General Relativistic Superfluid Neutron Stars

Abstract

We develop a general formalism to treat, in general relativity, the nonradial oscillations of a superfluid neutron star about static (non-rotating) configurations. The matter content of these stars can, as a first approximation, be described by a two-fluid model: one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars; the other fluid is a conglomerate of all charged constituents. We use a system of equations that governs the perturbations both of the metric and of the matter variables, whatever the equation of state for the two fluids. The entrainment effect is explicitly included. We also allow for an outer envelope composed of ordinary fluid. We derive and implement the junction conditions for the metric and matter variables at the core/envelope interface. We investigate how the quasinormal modes of a superfluid star are affected by changes in the entrainment parameter, and unveil a series of avoided crossings between the various modes. We provide a proof that all modes of a two-fluid star must radiate gravitationally. We also discuss the future detectability of pulsations in a superfluid star and argue that it may be possible to use gravitational-wave data to constrain the parameters of superfluid neutron stars.