Exploring the potential for detecting rotational instabilities in binary neutron star merger remnants with gravitational wave detectors

We explore the potential for detecting rotational instabilities in the postmerger phase of binary neutron star mergers using different network configurations of upgraded and next-generation gravitational wave detectors. Our study employs numerically generated postmerger waveforms, which reveal the reexcitation of the $l=m=2$ $f$-mode at a time of $O(10)\text{ }\text{ }\mathrm{ms}$ after merger. We evaluate the detectability of these signals by injecting them into colored Gaussian noise and performing a reconstruction as a sum of wavelets using Bayesian inference. Computing the overlap between the reconstructed and injected signal, restricted to the instability part of the postmerger phase, we find that one could infer the presence of rotational instabilities with a network of planned third-generation detectors, depending on the total mass and distance to the source. For a recently suggested high-frequency detector design, we find that the instability part would be detectable even at 200 Mpc, significantly increasing the anticipated detection rate. For a network consisting of the existing HLV detectors, but upgraded to twice the $\mathrm{A}+$ sensitivity, we confirm that the peak frequency of the whole postmerger gravitational wave emission could be detectable with a network signal-to-noise ratio of 8 at a distance of 40 Mpc.