Universality in oscillation modes of superfluid neutron stars?

TL;DR

This paper investigates whether the oscillation modes of superfluid neutron stars exhibit universal scaling laws similar to ordinary-fluid stars, revealing that the ordinary mode does, but the superfluid mode's behavior is more complex and affected by fluid coupling.

Contribution

The study extends the understanding of oscillation mode universality to superfluid neutron stars, analyzing decoupled and coupled fluid models and deriving analytical expressions for mode shifts.

Findings

The ordinary fluid $f$-mode follows established universal scaling laws.

The superfluid $f$-mode obeys a different scaling law, derived analytically.

Fluid coupling breaks the universality in superfluid neutron star oscillations.

Abstract

It has been well established that the $f$-mode of relativistic ordinary-fluid neutron stars displays a universal scaling behavior. Here we study whether the "ordinary" $f_{\rm o}$- and "superfluid" $f_{\rm s}$-modes of superfluid neutron stars also show similar universal behavior. We first consider a simple case where the neutron superfluid and normal fluid are decoupled, and with each fluid modeled by a polytropic equation of state. We find that the $f_{\rm o}$-mode obeys the same scaling laws as established for the $f$-mode of orindary-fluid stars. However, the oscillation frequency of the $f_{\rm s}$-mode obeys a different scaling law, which can be derived analytically from a homogenous two-fluid stellar model in Newtonian gravity. Next the coupling effect between the two fluids is studied via a parameterized model of entrainment. We find that the coupling in general breaks the universal behavior seen in the case of decoupled fluids. Based on a relativistic variational principle, an approximated expression is derived for the first-order shift of the $f_{\rm s}$-mode squared frequency due to the entrainment.