Probing magnetic turbulence by synchrotron polarimetry: statistics and
  structure of magnetic fields from Stokes correlators
  We describe a technique for probing the statistical properties of cosmic
magnetic fields based on radio polarimetry data. Second-order magnetic field
statistics like the power spectrum cannot always distinguish between magnetic
fields with essentially different spatial structure. Synchrotron polarimetry
naturally allows certain 4th-order magnetic field statistics to be inferred
from observational data, which lifts this degeneracy and can thereby help us
gain a better picture of the structure of the cosmic fields and test
theoretical scenarios describing magnetic turbulence. In this work we show that
a 4th-order correlator of physical interest, the tension-force spectrum, can be
recovered from the polarized synchrotron emission data. We develop an estimator
for this quantity based on polarized-emission observations in the
Faraday-rotation-free frequency regime. We consider two cases: a statistically
isotropic field distribution, and a statistically isotropic field superimposed
on a weak mean field. In both cases the tension force power spectrum is
measurable; in the latter case, the magnetic power spectrum may also be
obtainable. The method is exact in the idealized case of a homogeneous
relativistic-electron distribution that has a power-law energy spectrum with a
spectral index p=3, and assumes statistical isotropy of the turbulent field. We
carry out tests of our method using synthetic data generated from numerically
simulated magnetic fields. We show that the method is valid, that it is not
prohibitively sensitive to the value of the electron spectral index, and that
the observed tension-force spectrum allows one to distinguish between, e.g., a
randomly tangled magnetic field (a default assumption in many studies) and a
field organized in folded flux sheets or filaments.
