Self-similar energetics in large clusters of galaxies


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 shocks1, while residual transonic (near-sonic) flows create giant turbulent eddies and cascades2,3. Turbulence heats the intra-cluster medium4 and also amplifies magnetic energy by way of dynamo action5,6,7,8. 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 formation3,9. The permanent character of this hierarchy reflects yet another type of self-similarity in cosmology10,11,12,13, while its structure, consistent with current data14,15,16,17,18, encodes information about the efficiency of turbulent heating and dynamo action.

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Figure 1: High-resolution simulation of a galaxy cluster in fully cosmological context.
Figure 2: Temporal evolution of turbulence.
Figure 3: Temporal evolution of magnetic field.


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This work was supported by a grant from the Swiss National Supercomputing Center (CSCS) under project IDs S419 and S506.

Author information




F.M. carried out the cosmological simulations, computed the turbulence structure functions, derived equations (1), (2) and (3) and wrote most of the text. A.B. analysed the structure functions, testing the self-similar nature of second- and third-order structure functions within the inertial range and computing the dissipation rate. A.B. and F.M. computed the evolution of EB and LA.

Corresponding author

Correspondence to Francesco Miniati.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Generation and cascade of ICM hydromagnetic turbulence.

First the gravitational potential energy is converted into kinetic energy of accretion flows. These generate shear and shocks which, in addition to dissipation, produce fluid instabilities and a baroclinic term, respectively, leading to turbulent flows. Shocks also accelerate particles via the Fermi I mechanism. Shocks do not dissipate tangential flows, which will either generate turbulence, shear or shocks, or a combination thereof. The turbulence cascade includes dissipation of compressible modes at weak shocks, conversion of turbulent to magnetic energy via dynamo action, excitation of plasma waves accelerating relativistic particles via Fermi II mechanism, and viscous dissipation.

Extended Data Figure 2 Spectrum of ICM hydromagnetic turbulent cascade.

Characteristic spectrum of turbulent kinetic energy in the ICM. Solid and dashed lines correspond to the solenoidal (Kolmogorov-like) and the compressional (Burgers-like) velocity field, respectively. On the x axis, from left to right, we have marked the virial scale, Rvir, the injection scale, L, the Ozmidov’s scale, LO, the Alfvén scale, LA, and Kolmogorov’s dissipation scale, diss. All quantities are time dependent and Ozmidov’s scale is comparable to the injection scale, so at times turbulence in the radial direction could be suppressed by stratification.

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Miniati, F., Beresnyak, A. Self-similar energetics in large clusters of galaxies. Nature 523, 59–62 (2015).

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