On the possibility to detect gravitational waves from post-merger supermassive neutron stars with a kilohertz detector

The detection of a secular post-merger gravitational wave (GW) signal in a binary neutron star (BNS) merger serves as strong evidence for the formation of a long-lived post-merger neutron star (NS), which can help constrain the maximum mass of NSs and differentiate NS equations of state. We specifically focus on the detection of GW emissions from rigidly rotating NSs formed through BNS mergers, using several kilohertz GW detectors that have been designed. We simulate the BNS mergers within the detecting limit of LIGO-Virgo-KARGA O4 and attempt to find out on what fraction the simulated sources may have a detectable secular post-merger GW signal. For kilohertz detectors designed in the same configuration of LIGO A+, we find that the design with peak sensitivity at approximately 2 kHz is most appropriate for such signals. The fraction of sources that have a detectable secular post-merger GW signal would be approximately $0.94{\!-\!}11~{{ \rm per\ cent}}$ when the spin-downs of the post-merger rigidly rotating NSs are dominated by GW radiation, while it would be approximately $0.46{\!-\!}1.6~{{ \rm per\ cent}}$ when the contribution of electromagnetic (EM) radiation to the spin-down processes is non-negligible. We also estimate this fraction based on other well-known proposed kilohertz GW detectors and find that, with advanced design, it can reach approximately $12{\!-\!}45~{{ \rm per\ cent}}$ for the GW-dominated spin-down case and $4.7{\!-\!}16~{{\rm per\ cent}}$ when both the GW and EM radiations are considered.