The I-Love-Q Relations for Superfluid Neutron Stars

Cheung-Hei Yeung,Greg Comer,Nils Andersson,Lap-Ming Lin

doi:10.3390/universe7040111

Cheung-Hei Yeung, Greg Comer + Show 2 more

Open Access

https://doi.org/10.3390/universe7040111

Copy DOI

Abstract

The I-Love-Q relations are approximate equation-of-state independent relations that connect the moment of inertia, the spin-induced quadrupole moment, and the tidal deformability of neutron stars. In this paper, we study the I-Love-Q relations for superfluid neutron stars for a general relativistic two-fluid model: one fluid being the neutron superfluid and the other a conglomerate of all charged components. We study to what extent the two-fluid dynamics might affect the robustness of the I-Love-Q relations by using a simple two-component polytropic model and a relativistic mean field model with entrainment for the equation-of-state. Our results depend crucially on the spin ratio Ωn/Ωp between the angular velocities of the neutron superfluid and the normal component. We find that the I-Love-Q relations can still be satisfied to high accuracy for superfluid neutron stars as long as the two fluids are nearly co-rotating Ωn/Ωp≈1. However, the deviations from the I-Love-Q relations increase as the spin ratio deviates from unity. In particular, the deviation of the Q-Love relation can be as large as O(10%) if Ωn/Ωp differ from unity by a few tens of percent. As Ωn/Ωp≈1 is expected for realistic neutron stars, our results suggest that the two-fluid dynamics should not affect the accuracy of any gravitational waveform models for neutron star binaries that employ the relation to connect the spin-induced quadrupole moment and the tidal deformability.

Highlights

The groundbreaking detection of the first gravitational wave signal from a binary neutron star system GW170817 [1] has opened up a powerful channel to study the internal structures of neutron stars and the poorly understood supranuclear equation-of-state (EOS)
As Ωn/Ωp ≈ 1 is expected for realistic neutron stars, our results suggest that the two-fluid dynamics should not affect the accuracy of any gravitational waveform models for neutron star binaries that employ the relation to connect the spin-induced quadrupole moment and the tidal deformability
We have studied the I-Love-Q relations for superfluid neutron stars based on a general relativistic two-fluid formulation

Summary

Introduction

The groundbreaking detection of the first gravitational wave signal from a binary neutron star system GW170817 [1] has opened up a powerful channel to study the internal structures of neutron stars and the poorly understood supranuclear equation-of-state (EOS). It is quite surprising that various approximately EOS-insensitive relations connecting different neutron star properties have been discovered in the past decade [11,12,13,14,15,16,17,18,19,20,21,22,23,24] These relations are “universal” in the sense that they are insensitive to the EOS models to the O(1%) level (see [25,26] for reviews). By making use of the universal relation for the f -modes of neutron stars [12], the mass and radius of an isolated neutron star can be inferred accurately if gravitational waves emitted from the f -mode oscillations of the star can be detected

Objectives

Results

Conclusion