Empirical relations for gravitational-wave asteroseismology of binary neutron star mergers
Stamatis Vretinaris, Nikolaos Stergioulas, Andreas Bauswein
Abstract
We construct new, multivariate empirical relations for measuring neutron star radii and tidal deformabilities from the dominant gravitational wave frequency in the postmerger 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 postmerger peak frequency ${f}_{\text{peak}}$ and the chirp mass ${M}_{\text{chirp}}$. The former could be measured with good accuracy from gravitational waves emitted in the postmerger phase using next-generation detectors, whereas the latter is already obtained with good accuracy from the inspiral phase with present-day detectors. Our main dataset consists of a gravitational wave catalog obtained with smoothed-particle hydrodynamics simulations within the spatial conformal flatness approximation. We also extract the ${f}_{\text{peak}}$ frequency from the publicly available CoRe data set, obtained through grid-based general-relativistic hydrodynamical simulations and find good agreement between the extracted frequencies of the two datasets. As a result, we can construct empirical relations for the combined datasets. Furthermore, we investigate empirical relations for two secondary peaks, ${f}_{2\ensuremath{-}0}$ and ${f}_{\text{spiral}}$, 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.