An Archival Optical Counterpart Search for Extragalactic Fast X-Ray Transients Discovered by Einstein Probe

Extragalactic fast X-ray transients (eFXTs) represent a rapidly growing class of high-energy phenomena, whose physical origins remain poorly understood. With its wide-field, sensitive all-sky monitoring, the Einstein Probe (EP) has greatly increased the discovery rate of eFXTs. The search and identification of the optical counterparts of eFXT are vital for understanding their classification and constraining their physical origin. Yet, a considerable fraction of eFXTs still lack secure classifications due to the absence of timely follow-up observations. We carry out a systematic search of publicly available optical survey data and transient databases (including the Zwicky Transient Facility, ZTF, and the Transient Name Server, TNS) for optical counterparts to eFXT candidates detected by EP. In this paper, we describe our ongoing program and report the first results. Specifically, we identified the eFXT EP240506a to be associated with a UV/optical counterpart, AT 2024ofs. Spectroscopy of its host galaxy with VLT yields a redshift of $z = 0.120 \pm 0.002$. By combining archival survey data with early-time multiwavelength observations, we find that the luminosity and light-curve evolution of AT~2024ofs are consistent with a core-collapse supernova origin. From detectability simulations, we estimate a local event rate density $\rho_{0}=8.8^{+21.2}_{-3.9}\ \mathrm{yr^{-1}\, Gpc^{-3}}$ for EP240506a-like events, and completeness-corrected rate of about $36$--$78\ \mathrm{yr^{-1}\ Gpc^{-3}}$ for EP-detected X-ray transients associated with supernovae. Our results demonstrate the potential of EP to uncover prompt high-energy emission from core-collapse supernovae and underscore the critical importance of timely follow-up of future eFXT events.