Alma Mater Studiorum Universit`a degli Studi di Bologna ... - Inaf

40 3. Intergalactic magnetic fields
(Simonetti, Cordes & Spangler 1984; Minter & Spangler 1996). It is related to the autocorrelation
function C(r ⊥ ) for a sufficiently large averaging region by S (r ⊥ )=2[C(r ⊥ )−C(0)].
Laing et al. (2008) also derived the effects of convolution with the observing beam on the
observed structure function. For the special case of a power-law power spectrum (their Eq.
B2), they showed that the observed structure function after convolution can be heavily modified
even at separations up to a few times the FWHM of the observing beam. Fig. 3.7 illustrates the
effects of the convolution in two different power-law power spectra and corresponding structure
function. After convolution the two power spectra are indistinguishable. This effect must
be taken into account when comparing observed and predicted structure functions. However,
because the suppression of power on high spatial frequencies due to the convolution, this analysis
only constrains the power spectrum of the fluctuations on scales larger than the beam-width.
Complementary information can be derived from numerical simulations of depolarization with
fine spatial sampling (Laing et al. 2008; Guidetti et al. 2008) which constrain fluctuations of RM
below the resolution limit. indeed, the use of the structure function together with the Burn law k
represents a powerful technique to investigate the RM power spectrum over a wide range of spatial
scales (Laing et al. 2008).
In this thesis we have derived very detailed images of Faraday rotation and depolarization
across radio galaxies. The next Chapters will show that all of our observations are consistent with
pure foreground Faraday rotation. Where the RM structures can be reasonably approximated
as isotropic, the statistics of the magnetic-field fluctuations have been quantified by deriving
rotation measure structure functions, fitted using models derived from theoretical power spectra.
The minimum scale of the magnetic field variations have been derived from depolarization
measurements. However, I will also show that not all Faraday rotation maps are consistent with
an isotropic magnetic field. This forms the most important part of my thesis and describes an
unexpected phenomenon in the RM world.
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