Constraining Galaxy Haloes from the Dispersion and Scattering of Fast
  Radio Bursts and Pulsars
  Fast radio bursts (FRBs) can be scattered by ionized gas in their local
environments, host galaxies, intervening galaxies along their lines-of-sight,
the intergalactic medium, and the Milky Way. The relative contributions of
these different media depend on their geometric configuration and the internal
properties of the gas. When these relative contributions are well understood,
FRB scattering is a powerful probe of density fluctuations along the
line-of-sight. The precise scattering measurements for FRB 121102 and FRB
180916 allow us to place an upper limit on the amount of scattering contributed
by the Milky Way halo to these FRBs. The scattering time $\tau\propto(\tilde{F}
\times {\rm DM}^2) A_\tau$, where ${\rm DM}$ is the dispersion measure,
$\tilde{F}$ quantifies electron density variations with $\tilde{F}=0$ for a
smooth medium, and the dimensionless constant $A_\tau$ quantifies the
difference between the mean scattering delay and the $1/e$ scattering time
typically measured. A likelihood analysis of the observed scattering and halo
DM constraints finds that $\tilde{F}$ is at least an order of magnitude smaller
in the halo than in the Galactic disk. The maximum pulse broadening from the
halo is $\tau\lesssim12$ $\mu$s at 1 GHz. We compare our analysis of the Milky
Way halo with other galaxy haloes by placing limits on the scattering
contributions from haloes intersecting the lines-of-sight to FRB 181112 and FRB
191108. Our results are consistent with haloes making negligible or very small
contributions to the scattering times of these FRBs.
