A universal energy distribution for FRB 121102

Abstract: Fast radio bursts (FRBs) are milliseconds radio transients with large dispersion measures (DMs). An outstanding question is the relation between repeating FRBs and those with a single burst. In this paper, we study the energy distribution of the repeating FRB 121102. For a power-law distribution of energy $dN/dE\propto E^{-\alpha_E}$, we show that the value of $\alpha_E$ is in a narrow range $1.6-1.8$ for bursts observed by different telescopes at different frequencies, which indicates a universal energy distribution for FRB 121102. Interestingly, similar power-law index of energy distribution for non-repeating FRBs observed by Parkes and ASKAP is also found. However, if low-energy bursts below completeness threshold of Arecibo are discarded for FRB 121102, the slope could be up to 2.2. Implications of such a universal energy distribution are discussed.