The Fast Radio Burst Population Energy Distribution

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 ($V\mathrm{/}{V}_{\mathrm{m}\mathrm{a}\mathrm{x}}$) 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 $\gamma =-1.96\pm 0.15$, and a Schechter function with $\gamma =-1.82\pm 0.12$ and downturn energy $E_{\mathrm{m}\mathrm{a}\mathrm{x}}\sim 6.3\cdot {10}^{25}$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.