Radio Follow-Up of Einstein Probe Fast X-Ray Transients

Fast X-ray transients (FXTs) are brief, luminous bursts of soft X-ray emission whose physical origins remain uncertain. The Einstein Probe (EP) mission has recently enabled prompt discovery of these events, providing opportunities for rapid multi-wavelength follow-up. We present a coordinated radio observing campaign targeting 20 FXTs detected by the EP in 2024. The core consists of 59 epochs with the Allen Telescope Array (ATA), sampling post-burst timescales from $\sim$1 to $\sim$65 days and reaching typical $3\sigma$ sensitivities of 0.6--1.5\,mJy across 1--8\,GHz. Two FXTs---EP240315a and EP241021a---have radio counterparts. For EP241021a, AMI-LA monitoring at 15.5\,GHz reveals a light curve peaking at $\sim$30 days with $F_{\nu}\approx1.0$\,mJy; equipartition analysis implies a Newtonian equipartition energy of $\sim3\times10^{49}$\,erg and a mildly relativistic on-axis solution with $\Gamma_{\rm on}\approx1.3$. Multi-frequency modelling of EP240315a, combining new VLA measurements with published MeerKAT, ATCA, and eMERLIN data, indicates highly relativistic early emission ($\Gamma\gtrsim3$) that decelerates with time, consistent with jetted outflow. The detections and ATA non-detections span luminosities overlapping the brightest GRB and relativistic tidal disruption event (TDE) afterglows, suggesting FXTs comprise a heterogeneous population including both relativistic and non-relativistic explosions. Under a GRB-like redshift prior, our $3\sigma$ ATA limits correspond to observer-frame specific-luminosity thresholds of $\sim10^{32}$--$10^{33}\,\mathrm{erg\ s^{-1}\ Hz^{-1}}$; for nearby events ($z\lesssim0.2$), $L_{\nu}\lesssim10^{30\text{--}31}\,\mathrm{erg\ s^{-1}\ Hz^{-1}}$. Planned ATA upgrades and next-generation arrays (SKA, DSA, ngVLA) will enable sensitive, population-level radio studies of the FXT radio sky.