Predictions for electromagnetic counterparts to Neutron Star mergers discovered during LIGO-Virgo-KAGRA observing runs 4 and 5

We present a comprehensive, configurable open-source software framework for estimating the rate of electromagnetic detection of kilonovae (KNe) associated with gravitational wave detections of binary neutron star (BNS) mergers. We simulate the current LIGO-Virgo-KAGRA (LVK) observing run (O4) using current sensitivity and uptime values as well as using predicted sensitivites for the next observing run (O5). We find the number of discoverable kilonovae during LVK O4 to be 1 ⁺ _-1 ⁴ or 2 ⁺ _-2 ³, (at 90 per cent confidence) depending on the distribution of NS masses in coalescing binaries, with the number increasing by an order of magnitude during O5 to 19 ⁺ _-11 ²⁴. Regardless of mass model, we predict at most five detectable KNe (at 95 per cent confidence) in O4. We also produce optical and near-infrared light curves that correspond to the physical properties of each merging system. We have collated important information for allocating observing resources for search and follow-up observations, including distributions of peak magnitudes in several broad-bands and time-scales for which specific facilities can detect each KN. The framework is easily adaptable, and new simulations can quickly be produced in response to updated information such as refined merger rates and NS mass distributions. Finally, we compare our suite of simulations to the thus-far completed portion of O4 (as of 2023, October 14), finding a median number of discoverable KNe of 0 and a 95 percentile upper limit of 2, consistent with no detections so far in O4.