Universal and approximate relations for the gravitational-wave damping timescale of $f$-modes in neutron stars

TL;DR

This paper develops highly accurate, empirically corrected formulas for the gravitational-wave damping timescale of f-modes in neutron stars, improving previous estimates and applicable to both nonrotating and rapidly rotating stars.

Contribution

It introduces a new empirical relation for damping timescales that is accurate across neutron star compactness ranges without requiring moment of inertia data.

Findings

Maximum relative error of 3% compared to full GR results.

Formulas extendable to rapidly rotating neutron stars.

Accurate across the entire expected compactness range.

Abstract

Existing estimates of the gravitational-wave damping timescale of the dominant quadrupole oscillation mode in the case of rapidly rotating stars are based on using a Newtonian estimate for the energy of the mode, in combination with the lowest-order post-Newtonian quadrupole formula for estimating the gravitational-wave luminosity. We investigate a number of other choices for estimating the gravitational-wave damping timescale in the nonrotating limit and construct a highly accurate, empirically corrected formula that has a maximum relative error of only 3% with respect to the perturbative result in full general relativity. The expressions involved are sufficiently general to be extended to the case of rapidly rotating stars. We also present a new higher-order empirical relation for the gravitational-wave damping timescale of quadrupole oscillations that is accurate in the whole range of expected values for the compactness of neutron stars, without the need for involving the moment of inertia.