Implications from ASKAP Fast Radio Burst Statistics

Although there has recently been tremendous progress in studies of fast radio bursts (FRBs), the nature of their progenitors remains a mystery. A fundamental question associated with this is the relation between FRBs that are observed to repeat and those that have only shown a single burst. We study the current FRB population to better understand their energetics and statistics. For a power-law volumetric rate per unit isotropic energy $dN/dE \propto E^{-\gamma}$, we show that the observed cumulative distribution of dispersion measure (DM) scales $N(>\mathrm{DM}) \propto \mathrm{DM}^{5-2\gamma}$ for $\gamma>1$. Comparing this with the observed distribution of the ASKAP sample, we find a good fit for a power-law index of $\gamma \simeq 1.7$. The similarity of this value to that of repeating FRBs argues that single bursts may share the same underlying physical mechanism with the repeaters. We also discuss the fluence distribution of the ASKAP sample, which allows us to estimate a maximum isotropic burst energy of $2\times10^{33}\,$erg/Hz as well as the volumetric rate of FRBs as a function of their energies. We provide fitting functions that can be applied to the much larger FRB samples expected in the near future to study their distributions, energetics, and rates.

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