Quasi-Normal Modes of General Relativistic Superfluid Neutron Stars

TL;DR

This paper develops a formalism for analyzing the linear oscillations of two-fluid neutron stars in general relativity, and computes their quasi-normal modes, revealing mode splitting and insights into spacetime oscillations.

Contribution

It introduces a general relativistic formalism for two-fluid neutron star oscillations and applies it to compute quasi-normal modes, including mode splitting effects.

Findings

Mode splitting occurs when fluid adiabatic indices differ.

W-modes are primarily due to spacetime oscillations.

Numerical computation of quasi-normal modes for simplified models.

Abstract

We develop a general formalism to treat, in general relativity, the linear oscillations of a two-fluid star about static (non-rotating) configurations. Such a formalism is intended for neutron stars, whose matter content can be described, as a first approximation, 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 other constituents (crust nuclei, protons, electrons, etc...). We obtain a system of equations which govern the perturbations both of the metric and of the matter variables, whatever the equation of state for the two fluids. As a first application, we consider the simplified case of two non-interacting fluids, each with a polytropic equation of state. We compute numerically the quasi-normal modes (i.e. oscillations with purely outgoing gravitational radiation) of the corresponding system. When the adiabatic indices of the two fluids are different, we observe a splitting for each frequency of the analogous single fluid spectrum. The analysis also substantiates the claim that w-modes are largely due to spacetime oscillations.