Alma Mater Studiorum Universit`a degli Studi di Bologna ... - Inaf
Alma Mater Studiorum Universit`a degli Studi di Bologna ... - Inaf
Alma Mater Studiorum Universit`a degli Studi di Bologna ... - Inaf
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130 6. Summary and conclusions<br />
with the observed properties only when the field is wrapped around the ra<strong>di</strong>o lobes in a two<strong>di</strong>mensional<br />
geometry. In order to create RM bands with multiple reversals, more complex<br />
field geometries such as two-<strong>di</strong>mensional ed<strong>di</strong>es are needed.<br />
4. Magnetic field power spectrum: functional form and range of scales<br />
Recent observational work on galaxy clusters has led to claims that the intra-cluster<br />
magnetic field has a Kolmogorov-like power spectrum (i.e. a power law with slope q =<br />
11/3). Kolmogorov turbulence would be expected over some inertial range if the turbulence<br />
is primarily hydrodynamic (Kolmogorov 1941) or for the MHD cascade investigated<br />
by Goldreich & Sridhar (1997). However, the assumptions on which the Kolmogorov<br />
turbulence relies (homogeneity, isotropic and lack of magnetization) are not satisfied in the<br />
intergalactic me<strong>di</strong>um. Numerical simulations pre<strong>di</strong>ct a wide range of spectral slopes (albeit<br />
with some preference for the Kolmogorov value; Dolag 2006), and a comparison between<br />
theory and observation therefore seems premature.<br />
None of the RM <strong>di</strong>stributions stu<strong>di</strong>ed in this thesis show fluctuations compatible with a<br />
Kolmogorov power spectrum over the full range of observed scales. Instead, they are<br />
consistent with flatter power-law power spectra (q≤3). A Kolmogorov form on scales<br />
below the resolution limit cannot be excluded, although this is not the case on linear scales<br />
as low as 60 pc in M 87. Power spectra with slopes flatter than 11/3 have also been found<br />
by other authors (Murgia et al. 2004; Govoni et al. 2006; Laing et al. 2008). Similar results<br />
come from the analysis of magnetic turbulence in the Galaxy. For example, Regis (2011)<br />
found a flatter index (q=2.7) by analysing the fluctuations in the Galactic synchrotron<br />
emission (see also Minter & Spangler 1996).<br />
It is worth noting that the power spectra for sources in this thesis appear to be steeper in<br />
richer environments. The slopes range from q≈2 in groups (0755+37, 0206+35) up to<br />
q≈3 in clusters (3C 353, M 87). The flatter slopes are found in sources showing anisotropic<br />
RM’s, but this might be a selection effect. The idea of that the index of the power spectrum<br />
is determined by the richness of the environment is probably oversimplified.<br />
In 3C 449, the power spectrum cannot be a single power law, but rather steepens on smaller<br />
scales. A broken power law gives a good representation of the data, as found for 3C 31<br />
(Laing et al. 2008), but is not unique: a smoother function would fit just as well. The<br />
precise location of the break in the broken power law may not be physically significant, but<br />
a change in slope might occur at the typical field reversal scale if the field is produced by a<br />
fluctuation dynamo (Schekochihin & Cowley 2006; Eilek & Owen 2002).<br />
It is not clear what determines the minimum and the maximum scales of the magnetic field.<br />
Reconnection of field lines is expected to occur on much smaller scales than those sampled<br />
130