  Massive galaxy clusters are filled with a hot, turbulent and magnetized
intra-cluster medium. Still forming under the action of gravitational
instability, they grow in mass by accretion of supersonic flows. These flows
partially dissipate into heat through a complex network of large-scale shocks
[1], while residual transonic flows create giant turbulent eddies and cascades
[2,3]. Turbulence heats the intra-cluster medium [4] and also amplifies
magnetic energy by way of dynamo action [5-8]. However, the pattern regulating
the transformation of gravitational energy into kinetic, thermal, turbulent and
magnetic energies remains unknown. Here we report that the energy components of
the intra-cluster medium are ordered according to a permanent hierarchy, in
which the ratio of thermal to turbulent to magnetic energy densities remains
virtually unaltered throughout the cluster's history, despite evolution of each
individual component and the drive towards equipartition of the turbulent
dynamo. This result revolves around the approximately constant efficiency of
turbulence generation from the gravitational energy that is freed during mass
accretion, revealed by our computational model of cosmological structure
formation [3,9]. The permanent character of this hierarchy reflects yet another
type of self-similarity in cosmology [10-13], while its structure, consistent
with current data [14-18], encodes information about the efficiency of
turbulent heating and dynamo action.
