Kilonova Emission from Black Hole-Neutron Star Mergers. II. Luminosity Function and Implications for Target-of-opportunity Observations of Gravitational-wave Triggers and Blind Searches

We present detailed simulations of the kilonova and gamma-ray burst (GRB) afterglow and kilonova luminosity function from black hole-neutron star (BH-NS) mergers, and discuss the detectability of an electromagnetic (EM) counterpart in connection with gravitational wave (GW) detections, GW-triggered target-of-opportunity observations, and time-domain blind searches. The predicted absolute magnitude of BH-NS kilonovae at 0.5 days after the merger falls in the range [-10, -15.5]. The simulated luminosity function contains potential information on the viewing-angle distribution of the anisotropic kilonova emission. We simulate the GW detection rates, detectable distances, and signal duration for future networks of 2nd/2.5th/3rd generation GW detectors. BH-NSs tend to produce brighter kilonovae and afterglows if the BH has a higher aligned spin, and a less massive NS with a stiffer equation of state. The detectability of kilonovae is especially sensitive to the BH spin. If BHs typically have low spins, the BH-NS EM counterparts are hard to discover. For 2nd generation GW detector networks, a limiting magnitude of m_limit ~ 23-24 mag is required to detect kilonovae even if high BH spin is assumed. Thus, a plausible explanation for the lack of BH-NS-associated kilonova detection during LIGO/Virgo O3 is that either there is no EM counterpart (plunging events) or the current follow-ups are too shallow. These observations still have the chance to detect the on-axis jet afterglow associated with a short GRB or an orphan afterglow. Follow-up observations can detect possible associated short GRB afterglows, from which kilonova signatures may be studied. For time-domain observations, a high-cadence search in redder filters is recommended to detect more BH-NS-associated kilonovae and afterglows.