Radio Emission from Fast Blue Optical Transients Powered by Trans-relativistic Shocks in Confined Circumstellar Material

Abstract: Fast blue optical transients (FBOTs) are luminous, rapidly evolving explosions whose radio emission provides a sensitive probe of shock interaction and the circumstellar material (CSM) surrounding the progenitor. However, the origin of their diverse radio light-curve morphologies, especially the very steep post-peak declines seen in several well-sampled events, remains unclear. We present a forward-shock synchrotron model in which mildly relativistic ejecta interact with a dense but radially confined CSM. The CSM is described by a broken power-law density profile, and the radio emission is modeled by including both synchrotron self-absorption and external free-free absorption. Applying this framework to multi-frequency radio observations of a representative sample of FBOTs, we show that their radio diversity can be explained by shock propagation through a finite CSM shell. The early radio evolution is regulated by absorption, while the rapid post-peak fading marks the forward shock's transition from the dense inner CSM into a more tenuous outer environment. The inferred shock velocities are trans-relativistic, $v_{\rm sh}\sim0.1$--$0.5c$. The radio-emitting CSM requires high mass-loading rates, $\dot{M}\sim10^{-4}$--$10^{-3}\,M_{\odot}\,{\rm yr}^{-1}$, but modest total CSM masses, $M_{\rm CSM}\sim10^{-4}$--$10^{-2}\,M_{\odot}$. These properties point to brief episodes of enhanced mass loss in the final years to decades before explosion, rather than long-lived steady winds. Our results provide a dynamically consistent interpretation of FBOT radio emission and establish radio light curves as a diagnostic of the immediate pre-explosion mass-loss history of FBOT progenitors.