The launch of the \textit{Einstein Probe} unleashed a new era of high-energy transient discovery in the largely unexplored soft X-ray band. The \textit{Einstein Probe} has detected a significant number of fast X-ray transients that display no gamma-ray emission, complicating their robust association to more common gamma-ray bursts. To explore their possible connection, we analyzed the redshift distribution of both \textit{Einstein Probe} fast X-ray transients and long duration gamma-ray bursts. A comparative analysis of their cumulative redshift distributions using non-parametric two-sample tests, namely the Kolmogorov-Smirnov and Anderson-Darling tests, finds no statistically significant difference. These tests favor that their redshifts are drawn from the same underlying distribution. This empirical connection between \textit{Einstein Probe} transients and long gamma-ray bursts is further supported by their agreement with the so-called ``Amati relation'' between the spectral peak energy and the isotropic-equivalent energy. Together, these results indicate that most extragalactic \textit{Einstein Probe} fast X-ray transients are closely related to long gamma-ray bursts and originate from a massive star (collapsar) progenitor channel. Our findings highlight the role of the \textit{Einstein Probe} in uncovering the missing population of failed jets and dirty fireballs that emit primarily at soft X-ray wavelengths.
@article{arxiv.2509.07141,
title = {The redshift distribution of Einstein Probe transients supports their relation to gamma-ray bursts},
author = {Brendan O'Connor and Paz Beniamini and Eleonora Troja and Malte Busmann and Simone Dichiara and Ramandeep Gill and Jonathan Granot and Michael Moss and Xander Hall and Antonella Palmese and Niccolo Passaleva and Yu-Han Yang},
journal= {arXiv preprint arXiv:2509.07141},
year = {2025}
}