A Generic Model for Persistent Radio Source around Fast Radio Bursts

The repeated fast radio burst FRB 121102A and FRB 190520B has been reported, along with a spatially coincident, compact, persistent radio emission. In this paper, we present a parameterized one-zone model, with a 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 electron filled between the forward shock and the termination shock. We show that via appropriate adjustment of the model parameters, we can obtain the synchrotron radio emission properties from the one-zone model bright enough to account for observation, simply and analytically fitting the observed spectra well. Through dynamical evolution of the model, we can also obtain time-varying of relevant properties. This parameterized model does not depend on concrete physical models such as central engine, instead we can constraint physical model via comparison between parameters and observation, 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 on the counterparts at other waveband.