Induced scattering limits on fast radio bursts from stellar coronae

The origin of fast radio bursts remains a puzzle. Suggestions have been made that they are produced within the Earth atmosphere, in stellar coronae, in other galaxies or at cosmological distances. If they are extraterrestrial, the implied brightness temperature is very high, and therefore, the induced scattering places constraints on possible models. In this paper, constraints are obtained on flares from coronae of nearby stars. It is shown that the radio pulses with the observed power could not be generated if the plasma density within and in the nearest vicinity of the source is as high as it is necessary in order to provide the observed dispersion measure. However, one cannot exclude a possibility that the pulses are generated within a bubble with a very low density and pass through the dense plasma only in the outer corona.