Correlation of the magnetic field and the intra-cluster gas density in galaxy clusters

We present a correlation between X-ray surface brightness and Faraday rotat ion measure in galaxy clusters, both, from radio and X-ray observations as well as from modeling of the intra-cluster medium. The observed correlation rules out a magnetic field of constant strength throughout the cluster. Co smological, magnetohydrodynamic simulations of galaxy clusters are used to show that for a magnetic field of cosmic origin this correlation is expecte d and excellently reproduces the observations showing that the rms scatter of the Faraday rotation increases linearly with the X-ray surface brightnes s. From the correlation between the observable quantities, rotation measure and X-ray surface brightness, we infer a relation between the physical qua ntities: magnetic field and gas density. For the best available observation s, those of A119, we find B proportional to n(e)(0.9).