Gravitational-wave asteroseismology with f-modes from neutron star binaries at the merger phase

TL;DR

This paper demonstrates a close correspondence between the gravitational-wave frequency at neutron star merger and the fundamental oscillation mode of isolated neutron stars, enabling direct insights into neutron star properties from merger signals.

Contribution

It establishes that the merger gravitational-wave frequency closely matches the neutron star f-mode frequency, linking isolated star oscillations to merger signals and explaining universal relations with tidal deformability.

Findings

$f_{max}$ and $f_{2f}$ differ by about 1% across systems.

Tidal resonance condition $|m|\, ext{Omega} = f_{2f}$ is satisfied near merger.

Relation between $f_{2f}$ and tidal deformability explains universal $f_{max}$-deformability relation.

Abstract

Gravitational-wave signals from coalescing binary neutron stars can yield important information about the properties of nuclear-matter equation of state from the early part of the signal through tidal effects to the properties and oscillation frequencies of the merger product. We investigate a direct link between the properties of isolated neutron stars and their merger, by comparing the frequency of the fundamental oscillation mode ($f$-mode) of neutron stars with the gravitational-wave frequency associated with the merger of two neutron stars. We calculate the quadrupolar ($l=2$) $f$-mode oscillation ($f_{2f}$) of non-rotating and rotating neutron stars using a nonlinear hydrodynamics code in the conformally-flat approximation and obtain the gravitational-wave frequency associated with the peak amplitude ($f_{\rm max}$) of binary-neutron stars from a set of publicly available simulations. We find that $f_{\rm max}$ and $f_{2f}$ differ by about 1\%, on average, across forty-five equal-mass systems with different total mass and equations of state. Assuming that the gravitational-wave frequency is still approximately equal to twice the orbital frequency $\Omega$ near the merger, the result indicates that the condition for tidal resonance $|m|\Omega = f_{2f}$ is satisfied to high accuracy near the merger, where $m=2$ is the azimuthal quantum number. Moreover, the well established universal relation between $f_{\rm max}$ and the tidal deformability of equal-mass binary systems can now be explained by a similar relation between $f_{2f}$ and the tidal deformability of isolated neutron stars, which has been demonstrated to be associated with the nearly incompressible properties of neutron stars. Our findings suggest that it is possible to relate the gravitational-wave signal at the merger of a binary neutron star system directly to the fundamental oscillation modes and the mass ratio.