New Evidence for Extragalactic Einstein Probe Transients associated with Long Gamma-ray Bursts

Abstract: The origin of extragalactic fast X-ray transients (EFXTs) remains a fundamental open question in high-energy astrophysics. The Einstein Probe (EP) mission provides a transformative opportunity to investigate their nature. While mounting observations of EP-discovered EFXTs (EP-EFXTs) suggest a possible connection to long gamma-ray bursts (lGRBs), an in-depth comparative analysis between them remains lacking. Here, we present a comparative analysis of their cosmic formation histories, revealing that EP-EFXTs and lGRBs share a similar evolutionary trend-showing a marked decline at $z<1.0$ and a plateau beyond $1.0<z<5$-which clearly distinguishes them from short GRBs. This result is derived from a rigorously selected sample of EP-EFXTs, using Lynden-Bell's $c^{-}$ method to reconstruct, for the first time, the luminosity function and formation rate of EP-EFXTs without any assumptions. Our findings provide independent evidence that EP-EFXTs and lGRBs may originate from a common progenitor channel.