Temporal Smearing of Transient Radio Sources by the Intergalactic Medium

The temporal smearing of impulsive radio events at cosmological redshifts probes the properties of the ionized Inter-Galactic Medium (IGM). We relate the degree of temporal smearing and the profile of a scattered source to the evolution of turbulent structure in the IGM as a function of redshift. We estimate the degree of scattering expected by analysing the contributions to the Scattering Measure (SM) of the various components of baryonic matter embedded in the IGM, including the diffuse IGM, intervening galaxies and intracluster gas. These estimates predict that the amount of temporal smearing expected at 300\,MHz is typically as low as ~1 ms and suggests that these bursts may be detectable with low frequency widefield arrays. A generalization of the DM-SM relation observed for Galactic scattering to the densities and turbulent conditions relevant to the IGM suggests that scattering measures of order 10^{-6} kpc m {-20/3} would be expected at z ~ 1. This scattering is sufficiently low that its effects would, for most lines of sight, not be manifest in existing observations of the scattering broadening in images of extragalactic compact sources. The redshift dependence of the temporal smearing discriminates between scattering that occurs in the host galaxy of the burst and the IGM, with tau_host \propto (1+z)^{-3} if the scattering probes length scales below the inner scale of the turbulence or tau_host \propto (1+z)^{-17/5} if the turbulence follows a Kolmogorov spectrum. This differs strongly from the expected IGM scaling tau_{IGM} ~ z^2 for z < 1 and (1+z)^{0.2-0.5} for z >> 1.