Gravitational wave asteroseismology with protoneutron stars

TL;DR

This paper investigates how gravitational wave frequencies from protoneutron stars evolve post-bounce, revealing their dependence on mass and radius, and proposes these signals as probes for stellar evolution using ground-based detectors.

Contribution

It demonstrates that gravitational wave frequencies from protoneutron stars depend mainly on their average density, providing a new method to infer stellar properties from gravitational wave observations.

Findings

Frequencies depend on mass and radius, not on internal profiles.

Frequencies scale with the square root of the average density.

Expected frequencies are around a few hundred Hz, suitable for ground-based detectors.

Abstract

We examine the time evolution of the frequencies of the gravitational wave after the bounce within the framework of relativistic linear perturbation theory using the results of one dimensional numerical simulations of core-collapse supernovae. Protoneutron star models are constructed in such a way that the mass and radius of protoneutron star become equivalent to the results obtained from the numerical simulations. Then, we find that the frequencies of gravitational waves radiating from protoneutron stars strongly depend on the mass and radius of protoneutron stars, but almost independently of the profiles of electron fraction and entropy per baryon inside the star. Additionally, we find that the frequencies of gravitational waves can be characterized by the square root of the average density of protoneutron star irrespectively the progenitor models, which are completely different from the empirical formula for cold neutron stars. The dependence of the spectra on the mass and radius is different from that of the $g$-mode: the oscillations around the surface of protoneutron stars due to the convection and the standing accretion-shock instability. Careful observations of the these modes of gravitational waves can determine the evolution of the mass and radius of protoneutron stars after core-bounce. Furthermore, the expected frequencies of gravitational waves are around a few hundred hertz in the early stage after bounce, which must be a good candidate for the ground-based gravitational wave detectors.