Modelling the energy distribution in CHIME/FRB Catalog-1

Abstract

We characterize the intrinsic properties of any FRB using its redshift $z$, spectral index $α$ and energy $E_{33}$ in units of $10^{33} \, {\rm J}$ emitted across $2128 - 2848\; {\rm MHz}$ in the FRB's rest frame. Provided that $z$ is inferred from the measured extra-galactic dispersion measure $DM_{\rm Ex}$, the fluence $F$ of the observed event defines a track in $(α, E_{33})$ 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 Catalog-1, and use these to determine $n(E_{33} \mid α)$ the conditional energy distribution i.e. the number of FRBs in the interval $ΔE_{33}$ given a value of $α$. Considering $-10 \le α\le 10$, we find that the entire energy scale shifts to higher energy values as $α$ is increased. 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.