Title: Late-time Radio Flares in Tidal Disruption Events

Abstract: Radio monitoring unveiled late (hundreds to a thousand days) radio flares in a significant fraction of tidal disruption events. We propose that these late-time radio flares are a natural outcome if the surrounding density profile flattens outside the Bondi radius. At the Bondi radius, the outflow is optically thin (above a few GHz) to synchrotron self-absorption. As more and more material is swept up, the radio emission rises asymptotically as $\propto t^3$ until the outflow begins to decelerate. A Detection of such a rise and a late-time maximum constrains the black hole mass and the mass and energy of the radio-emitting outflow. We show that this model can give reasonable fits to some observed light curves, leading to reasonable estimates of the black hole and outflow masses. We also find that the slope of the density profile within the Bondi radius determines whether an early-time ($\sim10^2\,\rm days$) radio peak exists.