Gravitational wave asteroseismology on cooling neutron stars

TL;DR

This paper investigates gravitational wave frequencies from cooling neutron stars using the relativistic Cowling approximation, revealing their strong dependence on stellar properties and deriving empirical formulas for key thresholds.

Contribution

It introduces a new analysis of gravitational wave modes during neutron star cooling, highlighting their dependence on stellar compactness and providing empirical formulas for the direct Urca threshold.

Findings

GW frequencies depend strongly on mass and EOS

Frequencies of fundamental and pressure modes relate to compactness

Empirical formula for the direct Urca threshold mass

Abstract

We examine the gravitational wave frequencies from neutron stars during thermal evolution, adopting the relativistic Cowling approximation. We particularly focus on the neutron star models, in which the direct Urca (rapid cooling process) does not work, without the superfluidity and superconductivity. For such models, the cooling curve hardly depends on the equation of state (EOS) as well as the mass of neutron star, while we show that the gravitational wave frequencies strongly depend on the both properties. Then, we find that the frequencies of the fundamental and the 1st pressure mode multiplied with the stellar mass are well expressed as a function of the stellar compactness almost independently of the EOS. We also find that the frequency of the 1st gravity mode in later phase of the thermal evolution is strongly correlated with the stellar compactness. In addition, we derive the empirical formula estimating the threshold mass for the onset of the direct Urca inside the neutron star as a function of the nuclear saturation parameter. This formula will give us a constraint on the neutron star properties, if it would be observationally found that the direct Urca occurs (or does not work) inside the neutron star.