Binary Neutron Star Mergers: Multi-Messenger Systematics and Prospects with Next-Generation Facilities

Multi-messenger astronomy was galvanized by the detection of gravitational waves (GWs) from the binary neutron star (BNS) merger GW170817 and electromagnetic (EM) emission from the subsequent kilonova and short gamma ray burst. Maximizing multi-messenger constraints on these systems requires combining models of the progenitors and products of BNS mergers within a single framework. Motivated by GW170817, we create a combined model that relate the progenitor astrophysics of a BNS population with their GW observability and localizability, kilonova light curves, gamma-ray burst afterglow flux, and kilonova remnant evolution. We compute the BNS merger rate by convolving metallicity-dependent star-formation history with population-synthesis predictions, and we sample realistic populations to evaluate their GW and EM observables and joint detection rates. We find that next-generation detectors will typically observe BNS mergers with GW network signal-to-noise ratios of $\sim$ 10 to 20, 90th-percentile sky areas of order $\sim$ 10 deg$^2$, and kilonova $i$-band magnitudes spanning $\sim$ 23 to 33. The variation of the merger rate with respect to the common-envelope efficiency is shown in the GW and EM observables and the resulting multi-messenger detection yield, demonstrating how uncertainties propagate into all stages of joint GW+EM forecasting. Across the models examined, no more than $\sim$ 4% of BNS mergers are detectable simultaneously by a two-Cosmic-Explorer plus one-Einstein-Telescope network and by both Roman (in a $K$-like band) and Rubin ($i$ and $g$ bands). These results show that assumptions underlying the combination of progenitor evolution and source observables will constitute key multi-messenger modeling systematics for inference of astrophysical, nuclear, and fundamental physics from future datasets.