Fast Radio Bursts as Probes of Magnetic Fields in the Intergalactic Medium

We examine the proposal that the dispersion measures (DMs) and Faraday rotation measures (RMs) of extragalactic linearly-polarized fast radio bursts (FRBs) can be used to probe the intergalactic magnetic field (IGMF) in filaments of galaxies. The DM through the cosmic web is dominated by contributions from the warm-hot intergalactic medium (WHIM) in filaments and from the gas in voids. On the other hand, RM is induced mostly by the hot medium in galaxy clusters, and only a fraction of it is produced in the WHIM. We show that if one excludes FRBs whose sightlines pass through galaxy clusters, the line-of-sight strength of the IGMF in filaments, $B_{||}$, is approximately $C(\langle 1+z \rangle/f_{DM})(RM/DM)$, where $C$ is a known constant. Here, the redshift of the FRB is not required to be known; $f_{DM}$ is the fraction of total DM due to the WHIM, while $\langle 1+z \rangle$ is the redshift of interevening gas weighted by the WHIM gas density, both of which can be evaluated for a given cosmology model solely from the DM of an FRB. Using data on structure formation simulations and a model IGMF, we show that $C(\langle 1+z \rangle/f_{DM})(RM/DM)$ closely reproduces the density-weighted line-of-sight strength of the IGMF in filaments of the large-scale structure.