Features of collisionless turbulence in the intracluster medium from
  simulated Faraday Rotation maps
  Observations of the intracluster medium (ICM) in galaxy clusters suggest for
the presence of turbulence and the magnetic fields existence has been proved
through observations of Faraday Rotation and synchrotron emission. The ICM is
also known to be filled by a rarefied weakly collisional plasma. In this work
we study the possible signatures left on Faraday Rotation maps by collisionless
instabilities. For this purpose we use a numerical approach to investigate the
dynamics of the turbulence in collisionless plasmas based on an
magnetohydrodynamical (MHD) formalism taking into account different levels of
pressure anisotropy. We consider models covering the sub/super-Alfv\'enic and
trans/supersonic regimes, one of them representing the fiducial conditions
corresponding to the ICM. From the simulated models we compute Faraday Rotation
maps and analyze several statistical indicators in order to characterize the
magnetic field structure and compare the results obtained with the
collisionless model to those obtained using standard collisional MHD framework.
We find that important imprints of the pressure anisotropy prevails in the
magnetic field and also manifest in the associated Faraday Rotation maps which
evidence smaller correlation lengths in the collisionless MHD case. These
points are remarkably noticeable for the case mimicking the conditions
prevailing in ICM. Nevertheless, in this study we have neglected the decrease
of pressure anisotropy due to the feedback of the instabilities that naturally
arise in collisionless plasmas at small scales. This decrease may not affect
the statistical imprint differences described above, but should be examined
elsewhere.
