### Fast Radio Burst Pulse Widths, Scattering and Distances

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By comparing the dispersion measures and pulse widths of two fast radio bursts (FRB) for which pulse widths were measured we show that if the dispersion measures resulted from propagation through the intergalactic medium at cosmological distances and the widths were a consequence of scattering by single thin screens, then the screens’ electron densities were $\gtrsim 20$/cm$^3$, $10^8$ times the intergalactic density. This problem is resolved if the radiation scattered close to its source, where high densities are possible. 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 the dispersive plasma cloud, excluding terrestrial or Solar System origin. Much of the dispersion measures may be attributed to scattering regions about 1 AU from the sources, with electron densities $\sim 3 \times 10^8$/cm$^3$. Transparency to inverse bremsstrahlung requires that scattering occurred in regions with temperature $\gtrsim 10^{7\,\circ}$K, consistent with the environment of an energetic outburst. The inferred parameters are only marginally consistent and suggest re-examination of the assumed relation between dispersion measure and distance. Origin in an ionized starburst or protogalaxy is suggested, but statistical arguments exclude compact young SNR in the Galactic neighborhood.