Kilonova and Optical Afterglow from Binary Neutron Star Mergers. II. Optimal Search Strategy for Serendipitous Observations and Target-of-opportunity Observations of Gravitational-wave Triggers

In the second work of this series, we explore the optimal search strategy for serendipitous and gravitational-wave-triggered target-of-opportunity (ToO) observations of kilonovae and optical short-duration gamma-ray burst (sGRB) afterglows from binary neutron star (BNS) mergers, assuming that cosmological kilonovae are AT2017gfo-like (but with viewing-angle dependence) and that the properties of afterglows are consistent with those of cosmological sGRB afterglows. A one-day cadence serendipitous search strategy with an exposure time of $\sim30\,$s can always achieve an optimal search strategy of kilonovae and afterglows for various survey projects. We show that the optimal detection rates of the kilonovae (afterglows) are $\sim0.3/0.6/1/20\,$yr$^{-1}$ ($\sim50/60/100/800\,$yr$^{-1}$) for ZTF/Mephisto/WFST/LSST, respectively A better search strategy for SiTian than the current design is to increase the exposure time. In principle, a fully built SiTian can detect $\sim7({2000})\,$yr$^{-1}$ kilonovae (afterglows). Population properties of electromagnetic (EM) signals detected via the serendipitous observations are studied in detail. For ToO observations, we predict that one can detect $\sim11\,{\rm{yr}}^{-1}$ BNS gravitational wave (GW) events during the fourth observing run (O4) by considering an exact duty cycle of the third observing run. The median GW sky localization area is expected to be $\sim10\,{\rm{deg}}^2$ for detectable BNS GW events. In O4, we predict that ZTF/Mephisto/WFST/LSST can detect $\sim5/4/3/3$ kilonovae ($\sim1/1/1/1$ afterglows) per year, respectively. The GW detection rates, GW population properties, GW sky localizations, and optimistic ToO detection rates of detectable EM counterparts for BNS GW events at the Advanced Plus, LIGO Voyager and ET\&CE eras are detailedly simulated in this paper.