Implications of Fast Radio Burst Pulse Widths
  The pulse widths, dispersion measures and dispersion indices of Fast Radio
Bursts (FRB) impose coupled constraints that all models must satisfy. We show
that if the dispersion measures resulted from propagation through the
intergalactic medium at cosmological distances and the pulse widths were a
consequence of scattering by single thin screens, then the screens' electron
densities were $\gtrsim 20$/cm$^3$, $10^8$ times the mean 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. The scattering and 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$^3$. The inferred
parameters are only marginally consistent; re-examination of the assumed
relation between dispersion measure and distance is warranted. Origin in an
ionized starburst or protogalaxy is suggested, but statistical arguments
exclude compact young SNR in the Galactic neighborhood. An appendix applies
these arguments to PSR J1745-2900 at the Galactic Center. We suggest that its
pulse width and angular broadening may be reconciled if we are near a caustic
or focal point produced by refraction, rather than by the classic thin sheet
scattering model.
