Clusters of galaxies, filled with hot magnetized plasma, are the largest bound objects in existence and an important touchstone in understanding the formation of structures in our Universe. In such clusters, thermal conduction follows field lines, so magnetic fields strongly shape the clusters thermal history; that some have not since cooled and collapsed is a mystery. In a seemingly unrelated puzzle, recent observations of Virgo cluster spiral galaxies imply ridges of strong, coherent magnetic fields offset from their centre. Here we demonstrate, using three-dimensional magnetohydrodynamical simulations, that such ridges are easily explained by galaxies sweeping up field lines as they orbit inside the cluster. This magnetic drape is then lit up with cosmic rays from the galaxies stars, generating coherent polarized emission at the galaxies leading edges. This immediately presents a technique for probing local orientations and characteristic length scales of cluster magnetic fields. The first application of this technique, mapping the field of the Virgo cluster, gives a startling result: outside a central region, the magnetic field is preferentially oriented radially as predicted by the magnetothermal instability. Our results strongly suggest a mechanism for maintaining some clusters in a non-cooling-core state.
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