Can a binary neutron star merger in the vicinity of a supermassive black hole enable a detection of a post-merger gravitational wave signal?

The post-merger gravitational-wave (GW) signal of a binary neutron star (BNS) merger is expected to contain valuable information that could shed light on the equation of state (EOS) of NSs, the properties of the matter produced during the merger, as well as the nature of any potential intermediate merger product such as hypermassive or supramassive NSs. However, the post-merger lies in the high frequency regime (greater than or similar to 1000 Hz) where current LIGO-Virgo detectors are insensitive. While proposed detectors such as NEMO, Cosmic Explorer and Einstein Telescope could potentially detect the post-merger for BNSs within O(10 Mpc), such events are likely to be rare. In this work, we speculate on the possibility of detecting the post-merger from BNSs coalescing in the vicinity of supermassive black holes (SMBHs). The redshift produced by the gravitational field of the SMBH, as well as the BNS's proper motion around the SMBH, could effectively 'stretch' the post-merger signal into the band of the detectors. We demonstrate, using a phenomenological model, that such BNS coalescences would enable constraints on the peak of the post-merger signal that would otherwise have not been possible, provided the degree of redshifting due to the SMBH can be independently acquired. Further, using numerical simulations of binary neutron stars, we show how such mergers would improve EOS model selection using the post-merger signal. We discuss the mechanisms that might deliver such events and the limitations of this work.