The Dispersion of Fast Radio Bursts from a Structured Intergalactic Medium at Redshifts z < 1.5

We analyze the sources of free electrons that produce the large dispersion measures, $DM\approx 300\text{--}1600$ (in units of cm⁻³ pc), observed toward fast radio bursts (FRBs). Individual galaxies typically produce $DM\sim 25\text{--}60{cm}^{-3}pc$ from ionized gas in their disk, disk-halo interface, and circumgalactic medium. Toward an FRB source at redshift z, a homogeneous intergalactic medium (IGM) containing a fraction $f_{IGM}$ of cosmological baryons will produce $DM=\left(935{cm}^{-3}pc\right)f_{IGM}{h}_{70}^{-1}I\left(z\right)$, where $I{\left(z\right)=\left(2/3{\Omega }_m\right)\left[\right\{{\Omega }_m(1+z)}^3+{\Omega }_{\Lambda }\}{}^{1/2}-1]$. A structured IGM of photoionized Lyα absorbers in the cosmic web produces similar dispersion, modeled from the observed distribution, $f_b(N,z)$, of H i (Lyα-forest) absorbers in column density and redshift with ionization corrections and scaling relations from cosmological simulations. An analytic formula for DM(z) applied to observed FRB dispersions suggests that $z_{FRB}\approx 0.2\text{--}1.5$ for an IGM containing a significant baryon fraction, $f_{IGM}=0.6\pm 0.1$. Future surveys of the statistical distribution, DM($z)$, of FRBs identified with specific galaxies and redshifts can be used to calibrate the IGM baryon fraction and distribution of Lyα absorbers. Fluctuations in DM at the level ±10 cm⁻³ pc will arise from filaments and voids in the cosmic web.