A Generic Model for a Persistent Radio Source around Fast Radio Bursts

The repeated fast radio bursts FRB 121102A and FRB 190520B have been reported, along with a spatially coincident, compact, persistent radio emission. In this paper, we present a parameterized one-zone model, with the basic scenario that a relativistic magnetized wind from the pulsar sweeps up the surroundings, e.g., freely expanding supernova ejecta, giving rise to a power-law distribution of electrons between the forward shock and the termination shock. We show that via appropriate adjustment of the model parameters, we can obtain synchrotron radio emission properties from the one-zone model bright enough to account for the observation, simply and analytically fitting the observed spectra well. Through dynamical evolution of the model, we can also obtain time-varying relevant properties. This parameterized model does not depend on concrete physical models such as a central engine; instead, we can constraint the physical model via comparison between parameters and observations, indicating the information about the central engine and surroundings. We also discuss the synchrotron self-Compton emission in our scenario in the end but find no clue about the counterparts at other wave bands.