Statistical Techniques for Detecting the Intergalactic Magnetic Field
  from Large Samples of Extragalactic Faraday Rotation Data
  Rotation measure (RM) grids of extragalactic radio sources have been widely
used for studying cosmic magnetism. But their potential for exploring the
intergalactic magnetic field (IGMF) in filaments of galaxies is unclear, since
other Faraday-rotation media such as the radio source itself, intervening
galaxies, and the interstellar medium of our Galaxy are all significant
contributors. We study statistical techniques for discriminating the Faraday
rotation of filaments from other sources of Faraday rotation in future
large-scale surveys of radio polarization. We consider a 30 degree times 30
degree field-of-view toward the south Galactic pole, while varying the number
of sources detected in both present and future observations. We select sources
located at high redshifts and toward which depolarization and optical
absorption systems are not observed, so as to reduce the RM contributions from
the sources and intervening galaxies. It is found that a high-pass filter can
satisfactorily reduce the RM contribution from the Galaxy, since the angular
scale of this component toward high Galactic latitudes would be much larger
than that expected for the IGMF. Present observations do not yet provide a
sufficient source density to be able to estimate the RM of filaments. However,
from the proposed approach with forthcoming surveys, we predict significant
residuals of RM that should be ascribable to filaments. The predicted structure
of the IGMF down to scales of 0.1 degree should be observable with data from
the SKA, if we achieve selections of sources toward which sight lines do not
contain intervening galaxies and RM errors are less than a few rad m-2.
