The Cosmic Large-Scale Structure in X-rays (CLASSIX) Cluster Survey I. Probing galaxy cluster magnetic fields with line of sight rotation measures

To search for a signature of an intracluster magnetic field, we compare measurements of Faraday rotation of polarised extragalactic radio sources in the line of sight of galaxy clusters with those outside. To this end, we correlated a catalogue of 1383 rotation measures of extragalactic polarised radio sources with galaxy clusters from the CLASSIX survey (combining REFLEX II and NORAS II) detected by their X-ray emission in the ROSAT All-Sky Survey. The survey covers 8.25 ster of the sky at vertical bar b(II)vertical bar >= 20 degrees. We compared the rotation measures in the line of sight of clusters within their projected radii of r(500) with those outside and found a significant excess of the dispersion of the rotation measures in the cluster regions. Since the observed rotation measure is the result of Faraday rotation in several presumably uncorrelated magnetised cells of the intracluster medium, the observations correspond to quantities averaged over several magnetic field directions and strengths. Therefore the interesting quantity is the dispersion or standard deviation of the rotation measure for an ensemble of clusters. In the analysis of the observations we found a standard deviation of the rotation measure inside r500 of about 120 (+/- 21) rad m(-2). This compares to about 56 (+/- 8) rad m(-2) outside. Correcting for the effect of the Galaxy with the mean rotation measure in a region of 10 deg radius in the outskirts of the clusters does not change the outcome quoted above. We show that the most X-ray luminous and thus most massive clusters contribute most to the observed excess rotation measure. Modelling the electron density distribution in the intracluster medium with a self-similar model based on the REXCESS Survey, we found that the dispersion of the rotation measure increases with the column density, and we deduce a magnetic field value of about 2-6 (l/10 kpc)(-1/2) mu G assuming a constant magnetic field strength, where l is the size of the coherently magnetised intracluster medium cells. This magnetic field energy density amounts to a few percent of the average thermal energy density in clusters. On the other hand, when we allowed the magnetic field to vary such that the magnetic energy density is a constant fraction of the thermal energy density, we deduced a slightly lower value for this fraction of 3 10 (l/10 kpc)(-1/2) per mille. Compared to the situation in the Milky Way, where the ratio of the magnetic to thermal energy density is about unity, this ratio is much lower in galaxy clusters. The reason for this is most probably the different generation mechanism for the magnetic field, which is mostly powered by supernovae in the Galaxy and by turbulence from cluster mergers in galaxy clusters. The latter process sets a natural upper limit on the growth of the magnetic field.