Modelling the energy distribution in CHIME/FRB catalogue-1

We characterize the intrinsic properties of any FRB using its redshift z , spectral index α and energy E₃₃ in units of $10^{33} \, {\rm J}$ emitted across 2128-2848 MHz in the FRB's rest frame. Provided that z is inferred from the measured extra-galactic dispersion measure DM_Ex, the fluence F of the observed event defines a track in (α, E₃₃) space which we refer to as the 'energy track'. Here, we consider the energy tracks for a sample of 254 non-repeating low dispersion measure FRBs from the CHIME/FRB catalogue-1, and use these to determine the conditional energy distribution, n(E₃₃∣α), i.e. the number of FRBs in the interval ΔE₃₃ given a value of α. For all values of α, we can identify two distinct energy ranges indicating that there are possibly two distinct FRB populations. At high energies, the distribution is well fitted by a modified Schechter function whose slope and characteristic energy both increase with α. At low energies, the number of FRBs are in excess of the predictions of the modified Schechter function indicating that we may have a distinctly different population of low-energy FRBs. We have checked that our main findings are reasonably robust to the assumptions regarding the Galactic Halo and Host galaxy contributions to the dispersion measure.