Polarization signatures of unresolved radio sources
  We investigate how the imprint of Faraday rotation on radio spectra can be
used to determine the geometry of radio sources and the strength and structure
of the surrounding magnetic fields. We model spectra of Stokes Q and U for
frequencies between 200 MHz and 10 GHz for Faraday screens with large-scale or
small-scale magnetic fields external to the source. These sources can be
uniform or 2D Gaussians on the sky with transverse linear gradients in rotation
measure (RM), or cylinders or spheroids with an azimuthal magnetic field. At
high frequencies the spectra of all these models can be approximated by the
spectrum of a Gaussian source; this is independent of whether the magnetic
field is large-scale or small-scale. A sinc spectrum in polarized flux density
is not a unique signature of a volume where synchrotron emission and Faraday
rotation are mixed. A turbulent Faraday screen with a large field coherence
length produces a spectrum which is similar to the spectrum of a partial
coverage model. At low and intermediate frequencies, such a Faraday screen
produces a significantly higher polarized signal than the depolarization model
by Burn, as shown by a random walk model of the polarization vectors. We
calculate RM spectra for four frequency windows. Sources are strongly
depolarized at low frequencies, but RMs can be determined accurately if the
sensitivity of the observations is sufficient. Finally, we show that RM spectra
can be used to differentiate between turbulent foreground models and partial
coverage models.
