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Inferences from the Distributions of Fast Radio Burst Pulse Widths, Dispersion Measures and Fluences

The widths, dispersion measures, dispersion indices and fluences of Fast Radio Bursts (FRB) impose coupled constraints that all models must satisfy. Observation of dispersion indices close to their low density limit of $-2$ sets a model-independent upper bound on the electron density and a lower bound on the size of any dispersive plasma cloud. The non-monotonic dependence of burst widths (after deconvolution of instrumental effects) on dispersion measure excludes the intergalactic medium as the location of scattering that broadens the FRB in time. Temporal broadening far greater than that of pulsars at similar high Galactic latitudes implies that scattering occurs close to the sources, where high densities and strong turbulence are plausible. FRB energetics are consistent with supergiant pulses from young, fast, high-field pulsars at cosmological distances. The distribution of FRB dispersion measures is inconsistent with expanding clouds (such as SNR). It excludes space-limited distributions (such as the local supercluster), but agrees with a homogeneous cosmological distribution with intergalactic dispersion. The FRB $\log{N}$--$\log{S}$ relation also indicates a cosmological distribution, aside from the anomalously bright Lorimer burst.