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

5.2. Analysis of RM and depolarization images 79
expanding lobes (Finoguenov et al. 2006).
5.2 Analysis of RM and depolarization images
The observational analysis is based on the following procedure. I first produced RM and Burn
law k images at two different angular resolutions for each source and searched for regions with
high k or correlated RM and k values, which could indicate the presence of internal Faraday
rotation and/or strong RM gradients across the beam (Secs. 3.2 and 3.3). In regions with low k
where the variations of RM are plausibly isotropic and random, I then used the structure function
(defined in Eq. 3.13) to derive the power spectrum of the RM fluctuations. Finally, to investigate
the depolarization in the areas of isotropic RM, and hence the magnetic field power on small scales,
I made numerical simulations of the Burn law k using the model power spectrum with different
minimum scales and compared the results with the data.
I assumed RM power spectra of the form:
Ĉ( f ⊥ ) = C 0 f −q
⊥ f ⊥ ≤ f max
= 0 f ⊥ > f max (5.1)
where f ⊥ is a scalar spatial frequency and fit the observed structure function (including the effect
of the observing beam) using the Hankel-transform method described by Laing et al. (2008) to
derive the amplitude, C 0 and the slope, q. To constrain the RM structure on scales smaller than the
beamwidth, I estimated the minimum scale of the best fitted field power spectrum,Λ min = 1/ f max ,
which predicts a mean value of k consistent with the observed one.
In this work, I am primarily interested in estimating the RM power spectrum over limited
areas, and I made no attempt to determine the outer scale of fluctuations.
5.3 Rotation measure images
The RM images and associated rms errors were produced by weighted least-squares fitting to
the observed polarization anglesΨ(λ) as a function ofλ 2 (Eq. 3.1) at three or four frequencies
(Table 5.3, see also the Appendix) using theRM task in theAIPS package.
Each RM map was calculated only at pixels with rms polarization-angle uncertainties