Constraints on Relativistic Jets from the Fast X-ray Transient 210423 using Prompt Radio Follow-Up Observations

Fast X-ray Transients (FXTs) are a new observational class of phenomena with no clear physical origin. This is at least partially a consequence of limited multi-wavelength follow up of this class of transients in real time. Here we present deep optical ($g-$ and $i-$ band) photometry with Keck, and prompt radio observations with the VLA of FXT 210423 obtained at δ t ≈ 14-36 days since the X-ray trigger. We use these multi-band observations, combined with publicly available data sets, to constrain the presence and physical properties of on-axis and off-axis relativistic jets such as those that can be launched by neutron-star mergers and tidal disruption events, which are among the proposed theoretical scenarios of FXTs. Considering a wide range of possible redshifts z≤3.5, circumstellar medium (CSM) density n=10⁻⁶-10⁻¹\,cm⁻³, isotropic-equivalent jet kinetic energy Ek,iso=10⁴⁸-10⁵⁵\,erg, we find that we can rule out wide jets with opening angle θⱼ=15∘ viewed within 10∘ off-axis. For more collimated jets (θⱼ=3∘) we can only rule out on-axis (θⱼ=0∘) orientations. This study highlights the constraining power of prompt multi-wavelength observations of FXTs discovered in real time by current (e.g., Einstein Probe) and future facilities.