Magnetic Fields in Cluster Cores: Faraday Rotation in A400 and A2634

We present Faraday rotation data for radio sources in the centers of the Abell clusters A400 and A2634. These clusters contain large (> 100 kpc), tailed radio sources, each attached to the central cD galaxy. These clusters do not have strong cooling cores. Our data extend previous work on rotation measure in cluster centers to larger scales and non-cooling clusters. The rotation measure, and thus the magnetic field, is ordered on scales 10-20 kpc in both clusters. The geometry of the rotation measure appears to be determined by the distribution of the X-ray emitting gas, rather than by the radio tails themselves. We combine our data with previously published X-ray and radio data in order to analyze the magnetic fields in all 12 clusters whose central radio sources have been imaged in rotation measure. We find that the fields are dynamically significant in most clusters. We argue that the Faraday data measure fields in the intracluster medium, rather than in a skin of the radio source. Finally, we consider the nature and maintenance of the magnetic fields in these clusters, and conclude that either the cluster-wide field exists at similar levels, or that a weaker cluster-wide field is amplified by effects in the core.