Revisiting the $I$-Love-$Q$ relations for superfluid neutron stars

TL;DR

This paper refines the understanding of the $I$-Love-$Q$ relations for rotating superfluid neutron stars by incorporating boundary effects and second-order mass contributions, revealing deviations from universality and extending previous models.

Contribution

It introduces a corrected perturbative matching approach for superfluid neutron stars and establishes an augmented set of universal relations including second-order mass effects.

Findings

Significant deviations from universality when boundary conditions are not properly applied.

Development of an extended set of universal relations including $ ext{delta} M$.

Numerical models spanning three equations of state demonstrate these effects.

Abstract

We study the tidal problem and the resulting $I$-Love-$Q$ approximate universal relations for rotating superfluid neutron stars in the Hartle-Thorne formalism. Superfluid stars are described in this work by means of a two-fluid model consisting of superfluid neutrons and all other charged constituents. We employ a stationary and axisymmetric perturbation scheme to second order around a static and spherically symmetric background. Recently, we used this scheme to study isolated rotating superfluid stars. In this paper it is applied to analyze the axially symmetric sector of the tidal problem in a binary system. We show that a consistent use of perturbative matching theory amends the original two-fluid formalism for the tidal problem to account for the possible non-zero value of the energy density at the boundary of the star. This is exemplified by building numerically different stellar models spanning three equations of state. Significant departures from universality are found when the correct matching relations are not taken into account. We also present an augmented set of universal relations for superfluid neutron stars which includes the contribution to the total mass of the star at second order, $\delta M$. Therefore, our results complete the set of universal relations for rotating superfluid stars, generalizing our previous findings in the perfect fluid case.