Tidal Love numbers of neutron stars

TL;DR

This paper calculates the relativistic tidal Love number k2 for neutron star models using polytropic equations of state, providing results that differ from Newtonian predictions and are relevant for gravitational wave observations.

Contribution

It presents a numerical method to compute the relativistic tidal Love number k2 for neutron stars with realistic equations of state, extending previous Newtonian analyses.

Findings

Relativistic Love numbers differ from Newtonian values by up to ~24%.

Results agree with Newtonian limits in weak gravity.

Potential measurability of Love numbers in gravitational wave signals.

Abstract

For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k2. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n~0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l=2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second order differential equation for the perturbation to the metric coefficient g_tt, and matching the exterior solution to the asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to ~24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.