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 approximate to 300-1600 (in units of cm(-3) pc), observed toward fast radio bursts (FRBs). Individual galaxies typically produce DM similar to 25-60cm(-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 = (935 cm(-3) pc)f(IGM) h(70)(-1)I(z), where I(z) = (2/Omega(m)) [{Omega(m)(1 + z)(3) + Omega(Lambda)}(1/2) - 1]. A structured IGM of photoionized Ly alpha absorbers in the cosmic web produces similar dispersion, modeled from the observed distribution, f(b) (N, z), of HI (Lya-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) approximate to 0.2-1.5 for an IGM containing a significant baryon fraction, f(IGM) = 0.6 +/- 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 Ly alpha absorbers. Fluctuations in DM at the level +/- 10 cm(-3). pc will arise from filaments and voids in the cosmic web.