Probing mass-radius relation of protoneutron stars from gravitational-wave asteroseismology

TL;DR

This paper demonstrates that gravitational-wave asteroseismology, specifically analyzing $w$- and $f$-modes, can reveal the evolving mass-radius relation of proto-neutron stars, offering insights into nuclear equations of state.

Contribution

It introduces universal relations between GW mode frequencies and PNS properties, enabling inference of PNS evolution from GW observations independent of nuclear EOS.

Findings

The $w_1$-mode frequency times PNS radius is linearly related to the mass-to-radius ratio.

The relation is insensitive to the nuclear equation of state.

Simultaneous detection of $f$- and $w_1$-modes can probe the PNS mass-radius evolution.

Abstract

The gravitational-wave (GW) asteroseismology is a powerful technique for extracting interior information of compact objects. In this work, we focus on spacetime modes, the so-called $w$-modes, of GWs emitted from a proto-neutron star (PNS) in the postbounce phase of core-collapse supernovae. Using results from recent three-dimensional supernova models, we study how to infer the properties of the PNS based on a quasi-normal mode analysis in the context of the GW asteroseismology. We find that the $w_1$-mode frequency multiplied by the PNS radius is expressed as a linear function with respect to the ratio of the PNS mass to the PNS radius. This relation is insensitive to the nuclear equation of state (EOS) employed in this work. Combining with another universal relation of the $f$-mode oscillations, we point out that the time dependent mass-radius relation of the PNS can be obtained by observing both the $f$- and $w_1$-mode GWs simultaneously. Our results suggest that the simultaneous detection of the two modes could provide a new probe into finite-temperature nuclear EOS that predominantly determines the PNS evolution.