Redshift Estimation and Constraints on Intergalactic and Interstellar Media from Dispersion and Scattering of Fast Radio Bursts

A sample of 14 FRBs with measured redshifts and scattering times is used to assess contributions to dispersion and scattering from the intergalactic medium (IGM), galaxy halos, and the disks of host galaxies. The IGM and galaxy halos contribute significantly to dispersion measures but evidently not to scattering, which is then dominated by host galaxies. This enables usage of scattering times for estimating DM contributions from host galaxies and also for a combined scattering-dispersion redshift estimator. Redshift estimation is calibrated using scattering of Galactic pulsars after taking into account different scattering geometries for Galactic and intergalactic lines of sight. The DM-only estimator has a bias $\sim 0.1$ and RMS error $\sim 0.15$ in the redshift estimate for an assumed ad-hoc value of 50 pc cm$^{-3}$ for the host galaxy's DM contribution. The combined redshift estimator shows less bias by a factor of four to ten and a 20 to 40% smaller RMS error. We find that values for the baryonic fraction of the ionized IGM $f_{\rm igm} \sim 0.85 \pm 0.05$ optimize redshift estimation using dispersion and scattering. Our study suggests that two of the 14 candidate galaxy associations (FRB 20190523 and FRB~20190611B) should be reconsidered.