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Gravitational-wave signals from coalescing binary neutron stars can yieldimportant information about the properties of nuclear-matter equation of statefrom the early part of the signal through tidal effects to the properties andoscillation frequencies of the merger product. We investigate a direct linkbetween the properties of isolated neutron stars and their merger, by comparingthe frequency of the fundamental oscillation mode ($f$-mode) of neutron starswith the gravitational-wave frequency associated with the merger of two neutronstars. We calculate the quadrupolar ($l=2$) $f$-mode oscillation ($f_{2f}$) ofnon-rotating and rotating neutron stars using a nonlinear hydrodynamics code inthe conformally-flat approximation and obtain the gravitational-wave frequencyassociated with the peak amplitude ($f_{\rm max}$) of binary-neutron stars froma 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 systemswith different total mass and equations of state. Assuming that thegravitational-wave frequency is still approximately equal to twice the orbitalfrequency $\Omega$ near the merger, the result indicates that the condition fortidal resonance $|m|\Omega = f_{2f}$ is satisfied to high accuracy near themerger, where $m=2$ is the azimuthal quantum number. Moreover, the wellestablished universal relation between $f_{\rm max}$ and the tidaldeformability of equal-mass binary systems can now be explained by a similarrelation between $f_{2f}$ and the tidal deformability of isolated neutronstars, which has been demonstrated to be associated with the nearlyincompressible properties of neutron stars. Our findings suggest that it ispossible to relate the gravitational-wave signal at the merger of a binaryneutron star system directly to the fundamental oscillation modes and the massratio.

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