Luminosity Functions and Detectability of Binary Neutron Star Merger-nova Signals with Various Merger Remnants

With the rapid advancements in next-generation ground-based gravitational wave (GW) detectors, it is anticipated that $10^3$-$10^5$ binary neutron star (BNS) mergers per year will be detected, with a significant fraction accompanied by observable merger-nova signals through future sky surveys. Merger-novae are typically powered by the radioactive decay of heavy elements synthesized via the r-process. If the post-merger remnant is a long-lived rapid-rotating neutron star, the merger-nova can be significantly enhanced due to strong magnetized winds. In this paper, we generate mock BNS merger samples using binary population synthesis model and classify their post-merger remnants--black hole (BH) and magnetar, (i.e., long-lived supramassive NS and stable NS), based on results from numerical simulations. We then construct merger-nova radiation models to estimate their luminosity function. We find that the luminosity function may exhibit a distinctive triple-peak structure, with the relative positions and heights of these peaks depending on the equation of state (EOS) of the BNS. Furthermore, we estimate the average Target-of-Opportunity (ToO) detection efficiency $\langle f_{\rm eff} \rangle$ with the Chinese Space Station Telescope (CSST) and find that due to possible enhanced luminosity, the largest source redshift with $\langle f_{\rm eff} \rangle>0.1$ can be enlarged from $z_{\rm s}\sim 0.5$ to $z_{\rm s}\sim 1-1.5$. Besides, we also generate the detectable mass spectrum for merger-novae by $\langle f_{\rm eff}\rangle$, which may provide insights to the ToO searching strategy.