The Fast Radio Burst Population Energy Distribution

Abstract

We examine the energy distribution of the fast radio burst (FRB) population using a well-defined sample of 63 FRBs from the ASKAP radio telescope, 28 of which are localised to a host galaxy. We apply the luminosity-volume ($V/V_{\max }$) test to examine the distribution of these transient sources, accounting for cosmological and instrumental effects, and determine the energy distribution for the sampled population over the redshift range $0.01\lesssim z\lesssim 1.02$. We find the distribution between $10^{23}$ and $10^{26}$J Hz${}^{-1}$ to be consistent with both a pure power-law with differential slope ${\hat{I}}^3=-1.96\pm 0.15$, and a Schechter function with ${\hat{I}}^3=-1.82\pm 0.12$ and downturn energy $E_{\max }\sim 6.3\cdot 10^{25}$J Hz${}^{-1}$. We identify systematic effects which currently limit our ability to probe the luminosity function outside this range and give a prescription for their treatment. Finally, we find that with the current dataset, we are unable to distinguish between the evolutionary and spectral models considered in this work.

23 pages, 10 figures, submitted to PASA