Empirical relations for gravitational-wave asteroseismology of binary neutron star mergers

TL;DR

This paper develops empirical relations linking gravitational wave frequencies to neutron star properties, enabling more accurate measurements of neutron star radii and tidal deformabilities from post-merger signals.

Contribution

It introduces new multivariate empirical relations that connect post-merger gravitational wave frequencies with neutron star radii and deformabilities, using data from simulations and machine learning.

Findings

Empirical relations accurately determine neutron star radii and tidal deformabilities.

Good agreement between different simulation data sets for frequency extraction.

Spectral classification scheme can be reproduced with machine learning.

Abstract

We construct new, multivariate empirical relations for measuring neutron star radii and tidal deformabilities from the dominant gravitational wave frequency in the post-merger phase of binary neutron star mergers. The relations determine neutron star radii and tidal deformabilities for specific neutron star masses with consistent accuracy and depend only on two observables: the post-merger peak frequency $f_{\rm peak}$ and the chirp mass $M_{\rm chirp}$. The former could be measured with good accuracy from gravitational waves emitted in the post-merger phase using next-generation detectors, whereas the latter is already obtained with good accuracy from the inspiral phase with present-day detectors. Our main data set consists of a gravitational wave catalogue obtained with CFC/SPH simulations. We also extract the $f_{\rm peak}$ frequency from the publicly available CoRe data set, obtained through grid-based GRHD simulations and find good agreement between the extracted frequencies of the two data sets. As a result, we can construct empirical relations for the combined data sets. Furthermore, we investigate empirical relations for two secondary peaks, $f_{2-0}$ and $f_{\rm spiral}$, and show that these relations are distinct in the whole parameter space, in agreement with a previously introduced spectral classification scheme. Finally, we show that the spectral classification scheme can be reproduced using machine-learning techniques.