Accuracy of relativistic Cowling approximation in protoneutron star asteroseismology

TL;DR

This paper assesses the relativistic Cowling approximation's accuracy in modeling protoneutron star oscillations, finding it provides qualitatively similar results within 20% accuracy and discussing implications for gravitational wave analysis.

Contribution

It systematically evaluates the Cowling approximation's validity in PNS asteroseismology, highlighting its limitations and applicability for gravitational wave studies.

Findings

Frequency predictions are within 20% accuracy using the approximation.

The fundamental mode is overestimated with the Cowling approximation.

Damping times vary before and after the avoided crossing, affecting gravitational wave analysis.

Abstract

The relativistic Cowling approximation, where the metric perturbations are neglected during the fluid oscillations, is often adopted for considering the gravitational waves from the protoneutron stars (PNSs) provided via core-collapse supernova explosions. In this study, we evaluate how the Cowling approximation works well by comparing the frequencies with the Cowling approximation to those without the approximation. Then, we find that the behavior of the frequencies with the approximation is qualitatively the same way as that without the approximation, where the frequencies with the approximation can totally be determined within $\sim 20\%$ accuracy. In particular, the fundamental mode with the Cowling approximation is overestimated. In addition, we also discuss the damping time of various eigenmodes in gravitational waves from the PNSs, where the damping time for the PNSs before the avoided crossing between the $f$- and $g_1$-modes, is quite different from that for cold neutron stars, but it is more or less similar to that for cold neutron stars in the later phase. The damping time is long enough compared to the typical time interval of short-Fourier transformation that often used in the analysis, and that ideally guarantees the validity of the transformation.