Understanding the Geometry of Astrophysical Magnetic Fields
  Faraday rotation measurements have provided an invaluable technique with
which to measure the properties of astrophysical magnetized plasmas.
Unfortunately, typical observations provide information only about the
density-weighted average of the magnetic field component parallel to the line
of sight. As a result, the magnetic field geometry along the line of sight, and
in many cases even the location of the rotating material, is poorly
constrained. Frequently, interpretations of Faraday rotation observations are
dependent upon underlying models of the magnetic field being probed (e.g.,
uniform, turbulent, equipartition). However, we show that at sufficiently low
frequencies, specifically below roughly 13 (RM/rad m^-2)^(1/4) (B/G)^(1/2) MHz,
the character of Faraday rotation changes, entering what we term the
``super-adiabatic regime'' in which the rotation measure is proportional to the
integrated absolute value of the line-of-sight component of the field. As a
consequence, comparing rotation measures at high frequencies with those in this
new regime provides direct information about the geometry of the magnetic field
along the line of sight. Furthermore, the frequency defining the transition to
this new regime, nu_SA, depends directly upon the local electron density and
magnetic field strength where the magnetic field is perpendicular to the line
of sight, allowing the unambiguous distinction between Faraday rotation within
and in front of the emission region. Typical values of nu_SA range from 10 kHz
to 10 GHz, depending upon the details of the Faraday rotating environment. In
particular, for resolved AGN, including the black holes at the center of the
Milky Way (Sgr A*) and M81, nu_SA ranges from roughly 10 MHz to 10 GHz, and
thus can be probed via existing and up-coming ground-based radio observatories.
