Identification of the optical counterpart of the fast X-ray transient EP240414a

Fast X-ray transients (FXTs) are extragalactic bursts of X-rays first identified in archival X-ray data, and now routinely discovered by the Einstein Probe in real time, which is continuously surveying the night sky in the soft ($0.5 - 4$ keV) X-ray regime. In this Letter, we report the discovery of the second optical counterpart (AT2024gsa) to an FXT (EP240414a). EP240414a is located at a projected radial separation of 27 kpc from its likely host galaxy at $z = 0.4018 \pm 0.0010$. The optical light curve of AT2024gsa displays three distinct components. The initial decay from our first observation is followed by a re-brightening episode, displaying a rapid rise in luminosity to an absolute magnitude of $M_r \sim -21$ after two rest-frame days. While the early optical luminosity and decline rate is similar to luminous fast blue optical transients, the colour temperature of AT2024gsa is distinctly red and we show that the peak flux is inconsistent with a thermal origin. The third component peaks at $M_i \sim -19$ at $\gtrsim 16$ rest-frame days post-FXT, and is compatible with an emerging supernova. We fit the $riz$-band data with a series of power laws and find that the decaying components are in agreement with gamma-ray burst afterglow models, and that the re-brightening may originate from refreshed shocks. By considering EP240414a in context with all previously reported known-redshift FXT events, we propose that Einstein Probe FXT discoveries may predominantly result from (high-redshift) gamma-ray bursts, and thus appear to be distinct from the previously discovered lower redshift, lower luminosity population of FXTs.