Pre-merger alert to detect prompt emission in very-high-energy gamma-rays from binary neutron star mergers: Einstein Telescope and Cherenkov Telescope Array synergy

The current generation of very-high-energy gamma-ray (VHE; E > 30 GeV) detectors (MAGIC and H.E.S.S.) have recently demonstrated the ability to detect the afterglow emission of gamma-ray bursts (GRBs). However, the GRB prompt emission, typically observed in the 10 keV-10 MeV band, is still undetected at higher energies. Here, we investigate the perspectives of multi-messenger observations to detect the earliest VHE emission from short GRBs. Considering binary neutron star mergers as progenitors of short GRBs, we evaluate the joint detection efficiency of the Cherenkov Telescope Array (CTA) observing in synergy with the third generation of gravitational-wave detectors, such as the Einstein Telescope (ET) and Cosmic Explorer (CE). In particular, we evaluate the expected capabilities to detect and localize gravitational-wave events in the inspiral phase and to provide an early warning alert able to drive the VHE search. We compute the amount of possible joint detections by considering several observational strategies, and demonstrate that the sensitivity of CTA make the detection of the VHE emission possible even if it is several orders fainter than that observed at 10 keV-10 MeV. We discuss the results in terms of possible scenarios of the production of VHE photons from binary neutron star mergers.