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An advanced LIGO and Virgo’s third observing run brought another binary neutron star merger (BNS) and the first neutron-star black hole mergers. While no confirmed kilonovae were identified in conjunction with any of these events, continued improvements of analyses surrounding GW170817 allow us to project constraints on the Hubble Constant (H₀), the Galactic enrichment fromr-process nucleosynthesis, and ultra-dense matter possible from forthcoming events. Here, we describe the expected constraints based on the latest expected event rates from the international gravitational-wave network and analyses of GW170817. We show the expected detection rate of gravitational waves and their counterparts, as well as how sensitive potential constraints are to the observed numbers of counterparts. We intend this analysis as support for the community when creating scientifically driven electromagnetic follow-up proposals. During the next observing run O4, we predict an annual detection rate of electromagnetic counterparts from BNS of ${0.43}_{-0.26}^{+0.58}$( ${1.97}_{-1.2}^{+2.68}$) for the Zwicky Transient Facility (Rubin Observatory). 

Abstract During the first half of the fourth observing run (O4a) of the International Gravitational Wave Network, the Zwicky Transient Facility (ZTF) conducted a systematic search for kilonova (KN) counterparts to binary neutron star (BNS) and neutron star–black hole (NSBH) merger candidates. Here, we present a comprehensive study of the five high-significance (False Alarm Rate less than 1 yr⁻¹) BNS and NSBH candidates in O4a. Our follow-up campaigns relied on both target-of-opportunity observations and re-weighting of the nominal survey schedule to maximize coverage. We describe the toolkit we have been developing,Fritz, an instance ofSkyPortal, instrumental in coordinating and managing our telescope scheduling, candidate vetting, and follow-up observations through a user-friendly interface. ZTF covered a total of 2841 deg²within the skymaps of the high-significance GW events, reaching a median depth ofg≈ 20.2 mag. We circulated 15 candidates, but found no viable KN counterpart to any of the GW events. Based on the ZTF non-detections of the high-significance events in O4a, we used a Bayesian approach,nimbus, to quantify the posterior probability of KN model parameters that are consistent with our non-detections. Our analysis favors KNe with initial absolute magnitude fainter than −16 mag. The joint posterior probability of a GW170817-like KN associated with all our O4a follow-ups was 64%. Additionally, we use a survey simulation software,simsurvey, to determine that our combined filtered efficiency to detect a GW170817-like KN is 36%, when considering the 5 confirmed astrophysical events in O3 (1 BNS and 4 NSBH events), along with our O4a follow-ups. Following Kasliwal et al., we derived joint constraints on the underlying KN luminosity function based on our O3 and O4a follow-ups, determining that no more than 76% of KNe fading at 1 mag day⁻¹can peak at a magnitude brighter than −17.5 mag.