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—that 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.