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Statistical analysis of Faraday Rotation Measure (RM) maps of theintracluster medium (ICM) of galaxy clusters provides a unique tool to evaluatesome spatial features of the magnetic fields there. Its combination withnumerical simulations of magnetohydrodynamic (MHD) turbulence allows thediagnosis of the ICM turbulence. Being the ICM plasma weakly collisional, thethermal velocity distribution of the particles naturally develops anisotropiesas a consequence of the large scale motions and the conservation of themagnetic moment of the charged particles. A previous study (Paper I) analyzedthe impact of large scale thermal anisotropy on the statistics of RM mapssynthesized from simulations of turbulence; these simulations employed acollisionless MHD model which considered a tensor pressure with uniformanisotropy. In the present work, we extend that analysis to a collisionless MHDmodel in which the thermal anisotropy develops according to the conservation ofthe magnetic moment of the thermal particles. We also consider the effect ofanisotropy relaxation caused by the micro-scale mirror and firehoseinstabilities. We show that if the relaxation rate is fast enough to keep theanisotropy limited by the threshold values of the instabilities, the dispersionand power spectrum of the RM maps are indistinguishable from those obtainedfrom collisional MHD. Otherwise, there is a reduction in the dispersion andsteepening of the power spectrum of the RM maps (compared to the collisionalcase). Considering the first scenario, the use of collisional MHD simulationsfor modeling the RM statistics in the ICM becomes better justified.

Features of collisionless turbulence in the intracluster medium from simulated Faraday rotation maps II: the effects of instabilities feedback