Ultrahigh-energy neutrino searches using next-generation gravitational wave detectors at radio neutrino detectors: GRAND, IceCube-Gen2 Radio, and RNO-G

Binary neutron star mergers can be sources of ultrahigh-energy (UHE) cosmic rays and potential emitters of UHE neutrinos. The upcoming and current radio neutrino detectors like the Giant Radio Array for Neutrino Detection (GRAND), IceCube-Gen2 Radio, and the Radio Neutrino Observatory in Greenland are projected to reach the required sensitivities to search for these neutrinos. In particular, in conjunction with the next-generation of gravitational wave (GW) detectors like Cosmic Explorer (CE) and Einstein Telescope (ET), GW-triggered stacking searches can be performed with the UHE neutrino detectors. In this work, we explore the prospects of such searches by implementing in our analysis an upper distance limit based on the sky-localization capabilities of the GW detectors from which meaningful triggers can be collected. We find that if each GW burst is associated with a total isotropic-equivalent energy of $\ensuremath{\sim}{10}^{50}--{10}^{51}\text{ }\text{ }\mathrm{erg}$ emitted in UHE neutrinos, along with a corresponding beaming fraction of 1%, GRAND and IceCube-Gen2 Radio have a large probability ($\ensuremath{\sim}99%$) to detect a coincident neutrino event using the joint combination of $\mathrm{CE}+\mathrm{ET}$ in a timescale of less than 15 years of operation for our fiducial choice of parameters. In case of nondetections, the parameter spaces can be constrained at $3\ensuremath{\sigma}$ level in similar timescales of operation. We also highlight and discuss the prospects of such joint radio neutrino detector network, their importance, and their role in facilitating synergic GW and neutrino observations in the next era of multimessenger astrophysics.