We analyze the sources of free electrons that produce the large dispersion measures , DM \approx 300 - 1600 ( in units cm ^ { -3 } pc ) , observed toward fast radio bursts ( FRBs ) .
Individual galaxies typically produce DM \sim 25 - 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 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 / 3 \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 H i ( Ly \alpha -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 - 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 Ly \alpha absorbers .
Fluctuations in DM at the level \pm 10 cm ^ { -3 } pc will arise from filaments and voids in the cosmic web .