Prospects for multi-messenger detection of binary neutron star mergers in the fourth LIGO-Virgo-KAGRA observing run

The joint detection of GW170817 and GRB 170817A opened the era of multimessenger astronomy with gravitational waves (GWs) and provided the first direct probe that at least some binary neutron star (BNS) mergers are progenitors of short gamma-ray bursts (S-GRBs). In the next years, we expect to have more multimessenger detections of BNS mergers, thanks to the increasing sensitivity of GW detectors. Here, we present a comprehensive study on the prospects for joint GW and electromagnetic observations of merging BNSs in the fourth Laser Interferometer Gravitational-wave Observatory (LIGO)-Virgo-Kamioka Gravitational Wave Detector (KAGRA) observing run with Fermi Gamma-ray Space Telescope (Fermi), Neil Gehrels Swift Observatory (Swift), INTErnational Gamma-Ray Astrophysics Laboratory (INTEGRAL), and Space Variable Objects Monitor (SVOM). This work combines accurate population synthesis models with simulations of the expected GW signals and the associated S-GRBs, considering different assumptions about the gamma-ray burst (GRB) jet structure. We show that the expected rate of joint GW and electromagnetic detections could be up to similar to 6 yr(-1) when Fermi/Gamma-ray Burst Monitor (GBM) is considered. Future joint observations will help us to better constrain the association between BNS mergers and S-GRBs, as well as the geometry of the GRB jets.