Multi-messenger Observations of Binary Neutron Star Mergers in the O4 Run

We present realistic expectations for the number and properties of neutron star binary mergers to be detected as multi-messenger sources during the upcoming fourth observing run (O4) of the LIGO-Virgo-KAGRA gravitational-wave (GW) detectors, with the aim of providing guidance for the optimization of observing strategies. Our predictions are based on a population synthesis mode, which includes the GW signal-to-noise ratio, the kilonova (KN) optical and near-infrared light curves, the relativistic jet gamma-ray burst (GRB) prompt emission peak photon flux, and the afterglow light curves in radio, optical, and X-rays. Within our assumptions, the rate of GW events to be confidently detected during O4 is 7.7(-5.7)(+11.9) yr(-1) (calendar year), 78% of which will produce a KN, and a lower 52% will also produce a relativistic jet. The typical depth of current optical electromagnetic search and follow-up strategies is still sufficient to detect most of the KNae in O4, but only for the first night or two. The prospects for detecting relativistic jet emission are not promising. While closer events (within z less than or similar to 0.02) will likely still have a detectable cocoon shock breakout, most events will have their GRB emission (both prompt and afterglow) missed unless seen under a small viewing angle. This reduces the fraction of events with detectable jets to 2% (prompt emission, serendipitous) and 10% (afterglow, deep radio monitoring), corresponding to detection rates of 0.17(-0.13)(+0.26) and 0.78(-0.58)(+1.21) yr(-1), respectively. When considering a GW subthreshold search triggered by a GRB detection, our predicted rate of joint GW+GRB prompt emission detections increases up to a more promising 0.75(-0.55)(+1.16) yr(-1).