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 ${\delta t \approx 14-36}$ 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 $z\le3.5$, circumstellar medium (CSM) density $n={10^{-6}-10^{-1}\,\rm{cm^{-3}}}$, isotropic-equivalent jet kinetic energy $E_{k,iso}={10^{48}-10^{55}\,\rm{erg}}$, we find that we can rule out wide jets with opening angle ${\theta_{j}=15^{\circ}}$ viewed within ${10^{\circ}}$ off-axis. For more collimated jets (${\theta_{j}=3^{\circ}}$) we can only rule out on-axis (${\theta_{obs}=0^{\circ}}$) 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.