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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. We study the
fluence and dispersion measure (DM) distributions of the ASKAP sample to better
understand their energetics and statistics. We first consider a simplified
model of a power-law volumetric rate per unit isotropic energy dN/dE ~
E^{-gamma} with a maximum energy E_max in a uniform Euclidean Universe. This
provides analytic insights for what can be learnt from these distributions. We
find that the observed cumulative DM distribution scales as N(>DM) ~
DM^{5-2*gamma} (for gamma > 1) until a maximum value DM_max above which bursts
near E_max fall below the fluence threshold of a given telescope. Comparing
this model with the observed fluence and DM distributions, we find a reasonable
fit for gamma ~ 1.7 and E_max ~ 10^{33} erg/Hz. We then carry out a full
Bayesian analysis based on a Schechter rate function with cosmological factor.
We find roughly consistent results with our analytical approach, although with
large errors on the inferred parameters due to the small sample size. The
power-law index and the maximum energy are constrained to be gamma = 1.6 +/-
0.3 and log(E_max) [erg/Hz] = 34.1 +1.1 -0.7 (68% confidence), respectively.
From the survey exposure time, we further infer a cumulative local volumetric
rate of log N(E > 10^{32} erg/Hz) [Gpc^{-3} yr^{-1}] = 2.6 +/- 0.4 (68%
confidence). The methods presented here will be useful for the much larger FRB
samples expected in the near future to study their distributions, energetics,
and rates.Comment: ApJ accepted. Expanded beyond the scope of the earlier version into 8
pages, 7 figures. Following referees' comments, we included a full Bayesian
analysis based on a Schechter rate function with cosmological factor. The PDF
of the inferred model parameters are presented by MCMC sampling in Figure 4
(the most important result). We also discussed the completeness of ASKAP
sample in Section
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