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.