The curious case of EP241021a: Unraveling the mystery of its exceptional rebrightening

Fast X-ray transients (FXTs) are a rare and poorly understood phenomenon with a variety of possible progenitors. The launch of the Einstein Probe (EP) mission has facilitated a rapid increase in the real-time discovery and follow-up of FXTs. We focus on the recent EP discovered transient EP241021a, which shows a peculiar panchromatic behavior, with the aim of understanding its origin. We obtained optical and near-infrared multiband imaging and spectroscopy with the Fraunhofer Telescope at Wendelstein Observatory, the Hobby-Eberly Telescope, and the Very Large Telescope of the newly discovered EP transient EP241021a over the first 100 days of its evolution. EP241021a was discovered by EP as a soft X-ray trigger, but was not detected at gamma-ray frequencies. The observed soft X-ray prompt emission spectrum is consistent with nonthermal radiation, which requires at least a mildly relativistic outflow with a bulk Lorentz factor Γ,≳,$4$. The optical and near-infrared light curve displays a two-component behavior, where an initially fading component, ∼,t^-1, transitions to a rise steeper than ∼,t^3 after a few days, before peaking at an absolute magnitude of M_r,≈,-21.8 mag and quickly returning to the initial decay. Standard supernova models are unable to reproduce either the absolute magnitude or the rapid timescale ($<$,$2$ d) of the rebrightening. The X-ray, optical and near-infrared spectral energy distributions display a red color, r,-,J,≈,$0.8$ mag, and point to a nonthermal origin (∼,ν^-1) for the broadband emission. Considering a gamma-ray burst as a plausible scenario, we favor a refreshed shock as the cause of the rebrightening. This is consistent with the inference of an at least mildly relativistic outflow based on the prompt trigger. Our results suggest a link between EP-discovered FXTs and gamma-ray bursts, despite the lack of gamma-ray detections for the majority of EP transients.