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 |b _ { II } | \geq 20 ^ { o } .
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 r _ { 500 } of about 120 ( \pm 21 ) rad m ^ { -2 } .
This compares to about 56 ( \pm 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 .