The Energy Function and Cosmic Formation Rate of Fast Radio Bursts

TL;DR

This study uses a model-independent method to determine the energy function and cosmic formation rate of FRBs from observational data, revealing different behaviors for samples from two telescopes and providing insights into their possible origins.

Contribution

First application of the Lynden-Bell C− method to derive FRB energy function and formation rate from observational data, revealing distinct patterns for different telescope samples.

Findings

Energy function is a broken power law for Parkes sample and a simple power law for ASKAP sample.

FRB formation rate roughly follows star formation rate up to certain redshift.

FRB formation rate evolves faster than star formation rate at lower redshifts.

Abstract

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.