The I-Love-Q Relations for Superfluid Neutron Stars

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 ${\Omega }_{\mathrm{n}}/{\Omega }_{\mathrm{p}}$ 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 ${\Omega }_{\mathrm{n}}/{\Omega }_{\mathrm{p}}\approx 1$. 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 ${\Omega }_{\mathrm{n}}/{\Omega }_{\mathrm{p}}$ differ from unity by a few tens of percent. As ${\Omega }_{\mathrm{n}}/{\Omega }_{\mathrm{p}}\approx 1$ 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.

Invited contribution to Universe's Special Issue "Superfluidity and Superconductivity in Neutron Stars" (Guest Editor: Nicolas Chamel)

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• Rotating Love: The dynamical tides of spinning Newtonian stars
• Dynamical tides in superfluid neutron stars
• Universal relations for anisotropic interacting quark stars
• Fully general relativistic simulations of rapidly rotating quark stars: Oscillation modes and universal relations
• Universal Relations For Generic Family Of Neutron Star Equations Of State
• A revised formalism for slowly-rotating superfluid neutron stars in general relativity
• I-C-Q relations for rapidly rotating stable hybrid stars
• Equation-of-State Independent Relations in Rapidly Rotating Hybrid Stars
• Mass-radius relation, moment of inertia, and tidal love numbers of anisotropic neutron stars in f (R,T) gravity
• Rotation-dependent $I$-Love-$Q$-$\delta M$ relations in perturbation theory
• I-Love-Q Relations of Fermion-Boson Stars