Equation-of-state dependence of the gravitational-wave signal from the ring-down phase of neutron-star mergers

Neutron star (NS) merger simulations are conducted for 38 representative microphysical descriptions of high-density matter in order to explore the equation-of-state (EoS) dependence of the postmerger ring-down phase. The formation of a deformed, oscillating, differentially rotating very massive NS is the typical outcome of the coalescence of two stars with 1.35M_ for most candidate EoSs. The oscillations of this object imprint a pronounced peak in the gravitational wave (GW) spectra, which is used to characterize the emission for a given model. The peak frequency of this postmerger GW signal correlates very well with the radii of nonrotating NSs, and thus allows us to constrain the high-density EoS by a GW detection. In the case of 1.35-1.35M_ mergers the peak frequency scales particularly well with the radius of an NS with 1.6M_, where the maximum deviation from this correlation is only 60 m for fully microphysical EoSs which are compatible with NS observations. Combined with the uncertainty in the determination of the peak frequency it appears likely that a GW detection can measure the radius of a 1.6M_ NS with an accuracy of about 100--200 m. We also uncover relations of the peak frequency with the radii of nonrotating NSs with 1.35M_ or 1.8M_, with the radius or the central energy density of the maximum-mass Tolman-Oppenheimer-Volkoff configuration, and with the pressure or sound speed at a fiducial rest mass density of about twice the nuclear saturation density. Furthermore, it is found that a determination of the dominant postmerger GW frequency can provide an upper limit for the maximum mass of nonrotating NSs. The effect of variations of the binary setup are investigated and corresponding functional dependences between the peak frequency and radii of nonrotating NSs are derived. With higher total binary masses, correlations are tighter for radii of nonrotating NSs with higher masses. The prospects for a detection of the postmerger GW signal and a determination of the dominant GW frequency are estimated to be in the range of 0.015--1.2 events per year with the upcoming Advanced Laser Interferometer Gravitational Wave Observatory detector.