Differences in Faraday Rotation Between Adjacent Extragalactic Radio
  Sources as a Probe of Cosmic Magnetic Fields
  Faraday rotation measures (RMs) of extragalactic radio sources provide
information on line-of-sight magnetic fields, including contributions from our
Galaxy, source environments, and the intergalactic medium (IGM). Looking at
differences in RMs, $\Delta$RM, between adjacent sources on the sky can help
isolate these different components. In this work, we classify adjacent
polarized sources in the NVSS as random or physical pairs. We recompute and
correct the uncertainties in the NVSS RM catalog, since these were
significantly overestimated. Our sample contains 317 physical and 5111 random
pairs, all with Galactic latitudes $|b|\ge20^{\circ}$, polarization fractions
$\ge2\%$, and angular separations between $1.^{'},$ and $20^{'}$. We find an
rms $\Delta$RM of $14.9\pm0.4\,$rad m$^{-2}$ and $4.6\pm1.1\,$rad m$^{-2}$ for
random and physical pairs, respectively. This means polarized extragalactic
sources that are close on the sky, but at different redshifts, have larger
differences in RM than two components of one source. This difference of
$\sim10\,$rad m$^{-2}$ is significant at $5\sigma$, and persists in different
data subsamples. While there have been other statistical studies of $\Delta$RM
between adjacent polarized sources, this is the first unambiguous demonstration
that some of this RM difference must be extragalactic, thereby providing a firm
upper limit on the RM contribution of the IGM. If the $\Delta$RMs originate
local to the sources, then the local magnetic field difference between random
sources is a factor of two larger than between components of one source.
Alternatively, attributing the difference in $\Delta$RMs to the intervening IGM
yields an upper limit on the IGM magnetic field strength of $40\,$nG.
