Simulated Faraday Rotation Measures toward High Galactic Latitudes
  We study the Faraday rotation measure (RM) due to the Galactic magnetic field
(GMF) toward high Galactic latitudes. The RM arises from the global, regular
component as well as from the turbulent, random component of the GMF. We model
the former based on observations and the latter using the data of
magnetohydrodynamic turbulence simulations. For a large number of different GMF
models, we produce mock RM maps around the Galactic poles and calculate various
statistical quantities with the RM maps. We find that the observed medians of
RMs toward the north and south Galactic poles, $\sim 0.0\pm 0.5 {\rm rad
m^{-2}}$ and $\sim +6.3\pm 0.5 {\rm rad m^{-2}}$, are difficult to explain with
any of our many alternate GMF models. The standard deviation of observed RMs,
$\sim 9 {\rm rad m^{-2}}$, is clearly larger than that of simulated RMs. The
second-order structure function of observed RMs is substantially larger than
that of simulated RMs, especially at small angular scales. We discuss other
possible contributions to RM toward high Galactic latitudes. Besides
observational errors and the intrinsic RM of background radio sources against
which RM is observed, we suggest that the RM due to the intergalactic magnetic
field may account for a substantial fraction of the observed RM. Finally we
note that reproducing the observed medians may require additional components
or/and structures of the GMF that are not present in our models.
