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The next generation gravitational wave (GW) detectors - Einstein Telescope(ET) and Cosmic Explorer (CE), will have distance horizons up to$\mathcal{O}(10)$ Gpc for detecting binary neutron star (BNS) mergers. Thiswill make them ideal for triggering high-energy neutrino searches from BNSmergers at the next generation neutrino detectors, such as IceCube-Gen2. Wecalculate the distance limits as a function of the time window of neutrinoanalysis, up to which meaningful triggers from the GW detectors can be used tominimize backgrounds and collect a good sample of high-energy neutrino eventsat the neutrino detectors, using the sky localization capabilities of the GWdetectors. We then discuss the prospects of the next generation detectors towork in synergy to facilitate coincident neutrino detections or to constrainthe parameter space in the case of non-detection of neutrinos. We show thatgood localization of GW events, which can be achieved by multiple thirdgeneration GW detectors, is necessary to detect a GW-associated neutrino eventor put a meaningful constraint ($\sim 3\sigma$ confidence level) on neutrinoemission models. Such a model independent analysis can also help constrainphysical models and hence provide insights into neutrino production mechanismsin binary neutron star mergers.

Gravitational wave triggered searches for high-energy neutrinos from binary neutron star mergers: prospects for next generation detectors