The Energy Function and Cosmic Formation Rate of Fast Radio Bursts

Fast radio bursts (FRBs) are intense radio transients whose physical origin remains unknown. Therefore, it is of crucial importance to use a model-independent method to obtain the energy function and cosmic formation rate directly from the observational data. Based on current samples from the Parkes and ASKAP telecsopes, we determine, for the first time, the energy function and formation rate of FRBs by using the Lynden-Bell $\rm C^{-}$ method. The energy function derived from the Parkes sample is a broken power law, however it is a simple power law for the ASKAP sample. For Parkes sample, we derive the formation rate which is roughly consistent with the star formation rate up to $z\sim1.7$, with a local formation rate of $\dot \rho (0) \simeq (3.2\pm 0.3)\; \times {10^4}\;{\rm{Gp}}{{\rm{c}}^{ - 3}}{\rm{y}}{{\rm{r}}^{ - 1}}$ above a detection threshold of $2\,{\rm{Jyms}}$. For ASKAP sample, we find that the formation rate evolves much faster than the star formation rate up to $z\sim0.7$, namely $\dot \rho (z) \propto {(1 + z)^{6.9 \pm 1.9}}$, with a local formation rate of $\dot \rho (0) \simeq (4.6\pm 0.8)\; \times {10^3}\;{\rm{Gp}}{{\rm{c}}^{ - 3}}{\rm{y}}{{\rm{r}}^{ - 1}}$ above a detection threshold of $51\,{\rm{Jyms}}$. This might be a important clue for the physical origin of FRBs.