Evolving turbulence and magnetic fields in galaxy clusters

We discuss, using simple analytical models and magnetohydrodynamic (MHD) simulations, the origin and parameters of turbulence and magnetic fields in galaxy clusters. Any pre-existing tangled magnetic field must decay in a few hundred million years by generating gas motions even if the electric conductivity of the intracluster gas is high. We argue that turbulent motions can be maintained in the intracluster gas and its dynamo action can prevent such a decay and amplify a random seed magnetic field by a net factor of typically 10(4) in 5 Gyr. Three physically distinct regimes can be identified in the evolution of turbulence and magnetic field in galaxy clusters. First, the fluctuation dynamo will produce microgauss (mu G)-strong, random magnetic fields during the epoch of cluster formation and major mergers. At this stage pervasive turbulent flows with rms velocity of about 300 km s(-1)can be maintained at scales of 100-200 kpc. The magnetic field is intermittent, has a smaller scale of 20-30 kpc and average strength of 2 mu G. Secondly, turbulence will decay after the end of the major merger epoch; we discuss the dynamics of the decaying turbulence and the behaviour of magnetic field in it. Magnetic field and turbulent speed undergo a power-law decay, decreasing by a factor of 2 during this stage, whereas their scales increase by about the same factor. Thirdly, smaller-mass subclusters and cluster galaxies will produce turbulent wakes where magnetic fields will be generated as well. Although the wakes plausibly occupy only a small fraction of the cluster volume, we show that their area-covering factor can be close to unity, and thus they can produce some of the signatures of turbulence along virtually all lines of sight. The latter could potentially allow one to reconcile the possibility of turbulence with ordered filamentary gas structures, as in the Perseus cluster. The turbulent speeds and magnetic fields in the wakes are estimated to be of the order of about 300 km s-(1) and 2 mu G, respectively, whereas the turbulent scales are of the order of 200 kpc for wakes behind subclusters of a mass 3 x 10(13) M-circle dot and about 10 kpc in the galactic wakes. Magnetic field in the wakes is intermittent and has the scale of about 30 and 1 kpc in the subcluster and galactic wakes, respectively. Random Faraday rotation measure is estimated to be typically 100-200 rad m(-2), in agreement with observations. We predict detectable polarization of synchrotron emission from cluster radio haloes at wavelengths 3-6 cm, if observed at sufficiently high resolution.