Deep Optical Follow-up Observations to IceCube Cosmic Neutrinos: a case for IC230724A with Subaru/HSC and prospects with Rubin/LSST

IceCube has been detecting cosmic high-energy neutrinos for more than 10 years, but their major sources are still under debate. To identify them, IceCube is issuing neutrino alerts, which enable us to perform electromagnetic follow-up observations. In this paper, we present our Subaru/HSC deep optical follow-up observations down to 25.5 mag to a well-localized neutrino event, IceCube 230724A. We conduct a dedicated analysis with extensive evaluation of background rates and true positive rates adopting the blind analysis policy to identify or disfavor tidal disruption events (TDEs) as cosmic neutrino sources. Our analysis found no TDE candidate in the region of interest. Rubin/LSST survey will enable us to constrain their fractional contribution to the cosmic high-energy neutrino background, either $\lesssim 60\mathrm{\%}$ or $\gtrsim 30\mathrm{\%}$ for non-detection and detection, respectively, if Rubin covers the error regions of 10 neutrino events.