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

96 5. Ordered magnetic fields around radio galaxies
1. the pre-existing field cannot know anything about either the radio-source geometry or our
line-of-sight and
2. observations of Faraday rotation in other sources and the theoretical inference of turbulence
in the IGM both require disordered initial fields.
This suggests that the magnetic field must be aligned by rather than with the expansion of the radio
source. Indeed, the field configurations which generate straight bands look qualitatively like the
“draping” model proposed by Dursi & Pfrommer (2008), for some angles to the line-of-sight. The
analysis of Sections 5.2, 5.4 and 5.5 suggests that the magnetic fields causing the RM bands are
well-ordered, consistent with a stretching of the initial field that has erased much of the small-scale
structure while amplifying the large-scale component. I next attempt to constrain the geometry of
the resulting “draped” field.
5.7.2 Axisymmetric draped magnetic fields
A proper calculation of the RM from a draped magnetic-field configuration (Dursi & Pfrommer
2008) is outside the scope of this work, but we can start to understand the field geometry using
some simple approximations in which the field lines are stretched along the source axis. I assumed
initially that the field around the lobe is axisymmetric, with components along and radially
outwards from the source axis, so that the RM pattern is independent of rotation about the axis. It
is important to stress that such an axisymmetric field is not physical, as it requires a monopole and
unnatural reversals, it is nevertheless a useful benchmark for features of the field geometry that are
needed to account for the observed RM structure. I first considered field lines which are parabolae
with a common vertex on the axis ahead of the lobe. For field strength and density both decreasing
away from the vertex, I found that RM structures, with iso-contours similar to arcs, rather than
bands, were generated only for the approaching lobe of an inclined source. Such anisotropic RM
structures were not produced in the receding lobes, nor for sources in the plane of the sky. Indeed,
in order to generate any narrow, transverse RM structures such as arcs or bands, the line-of-sight
must pass through a foreground region in which the field lines show significant curvature, which
occurs only for an approaching lobe in case of a parabolic field geometry. This suggested to
consider field lines which are families of ellipses centred on the lobe, again with field strength and
density decreasing away from the leading edge. This indeed produced RM structures in both lobes
for any inclination, but the iso-RM contours were arcs, not straight lines. Because of the nonphysical
nature of these axisymmetric field models, the resulting RM images are deliberately not
shown. In order to quantify the departures from straightness of the iso-RM contours, I measured
the ratio of the predicted RM values at the centre and edge of the lobe at constant Y, at different
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