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A binary neutron star (BNS) merger event has recently been observed ingravitational waves (GWs). As in the case of binary black holes, GWs generatedby BNS consist of inspiral, merger, and post-merger components. Detecting thelatter is important because it encodes information about the nuclear equationof state (EOS) in a regime that cannot be probed prior to merger. Thepost-merger signal, however, can be observed by current detectors only out to~10 Mpc. We carry out Monte-Carlo simulations showing that the dominantpost-merger signal (the 22 mode) from individual events will likely not beobservable even with the Einstein Telescope and Cosmic Explorer (CE), assuminga full year of operation, the latest merger rates, and a detection thresholdwith signal-to-noise ratio of 5. For this reason, we propose two methods thatstack the post-merger signal from multiple events to boost the detectionprobability. The first method follows a commonly-used practice of multiplyingthe Bayes factors of individual events. The second method relies on anassumption that the mode phase can be determined from the inspiral waveform, sothat coherent mode stacking of the data from different events becomes possible.Both methods significantly improve the chances of detecting the dominantpost-merger signal, making a detection very likely after a year of observationwith CE for certain EOS. We also show that in terms of detection, coherentstacking is more efficient in accumulating confidence. Moreover, assuming a 22mode is detected with CE via stacking, we estimate through a Fisher analysisthat the peak frequency can be measured to a statistical error of ~ 4-20 Hz forcertain equations of state. Such an error corresponds to a NS radiusmeasurement of ~ 15-56 m, a fractional relative error ~ 4 %, suggesting thatsystematic errors from theoretical modeling (~ 100 m) may dominate the errorbudget.

Gravitational wave spectroscopy of binary neutron star merger remnants with mode stacking