We review the present theoretical and numerical understanding of magnetic field amplification in cosmic large-scale structure, on length scales of galaxy clusters and beyond. Structure formation drives compression and turbulence, which amplify tiny magnetic seed fields to the microGauss values that are observed in the intracluster medium. This process is intimately connected to the properties of turbulence and the microphysics of the intra-cluster medium. Additional roles are played by merger induced shocks that sweep through the intra-cluster medium and motions induced by sloshing cool cores. The accurate simulation of magnetic field amplification in clusters still poses a serious challenge for simulations of cosmological structure formation. We review the current literature on cosmological simulations that include magnetic fields and outline theoretical as well as numerical challenges.

We present the first high-resolution magnetohydrodynamic simulation of cosmic-ray electron re-acceleration by turbulence in cluster mergers. We use an idealized model for cluster mergers, combined with a numerical model for the injection, cooling and re-acceleration of cosmic-ray electrons, to investigate the evolution of cluster-scale radio emission in these objects. In line with theoretical expectations, we for the first time show in a simulation that re-acceleration of cosmic-ray electrons has the potential to reproduce key observables of radio haloes. In particular, we show that clusters evolve being radio loud or radio quiet, depending on their evolutionary stage during the merger. We thus recover the observed transient nature of radio haloes. In the simulation, the diffuse emission traces the complex interplay between the spatial distribution of turbulence injected by the halo infall and the spatial distribution of the seed electrons to re-accelerate. During the formation and evolution of the halo, the synchrotron emission spectra show the observed variety: from power laws with spectral index of 1–1.3 to curved and ultra-steep spectra with index >1.5.

Previous studies have shown that CIZA J2242.8+5301 (the ‘Sausage’ cluster, z = 0.192) is a massive merging galaxy cluster that hosts a radio halo and multiple relics. In this paper, we present deep, high-fidelity, low-frequency images made with the LOw-Frequency Array (LOFAR) between 115.5 and 179 MHz. These images, with a noise of 140 μJy beam^{− 1} and a resolution of θ_beam = 7.3 arcsec × 5.3 arcsec, are an order of magnitude more sensitive and five times higher resolution than previous low-frequency images of this cluster. We combined the LOFAR data with the existing Giant Metrewave Radio Telescope (GMRT) (153, 323, 608 MHz) and Westerbork Synthesis Radio Telescope (WSRT) (1.2, 1.4, 1.7, 2.3 GHz) data to study the spectral properties of the radio emission from the cluster. Assuming diffusive shock acceleration (DSA), we found Mach numbers of |$\mathcal {M}_{n}=2.7{}_{-0.3}^{+0.6}$| and |$\mathcal {M}_{s}=1.9_{-0.2}^{+0.3}$| for the northern and southern shocks. The derived Mach number for the northern shock requires an acceleration efficiency of several percent to accelerate electrons from the thermal pool, which is challenging for DSA. Using the radio data, we characterized the eastern relic as a shock wave propagating outwards with a Mach number of |$\mathcal {M}_{e}=2.4_{-0.3}^{+0.5}$|⁠, which is in agreement with |$\mathcal {M}_{e}^{X}=2.5{}_{-0.2}^{+0.6}$| that we derived from Suzaku data. The eastern shock is likely to be associated with the major cluster merger. The radio halo was measured with a flux of 346 ± 64 mJy at 145 MHz. Across the halo, we observed a spectral index that remains approximately constant (⁠|$\alpha ^{\text{145 MHz-2.3 GHz}}_{\rm {across \sim 1\ Mpc}^2}=-1.01\pm 0.10$|⁠) after the steepening in the post-shock region of the northern relic. This suggests a generation of post-shock turbulence that re-energies aged electrons.

Particle acceleration by turbulence plays a role in many astrophysical environments. The non-linear evolution of the underlying cosmic ray spectrum is complex and can be described by a Fokker–Planck equation, which in general has to be solved numerically. We present here an implementation to compute the evolution of a cosmic ray spectrum coupled to turbulence considering isotropic particle pitch-angle distributions and taking into account the relevant particle energy gains and losses. Our code can be used in runtime and post-processing to very large astrophysical fluid simulations. We also propose a novel method to compress cosmic ray spectra by a factor of 10, to ease the memory demand in very large simulations. We show a number of code tests, which firmly establish the correctness of the code. In this paper, we focus on relativistic electrons, but our code and methods can be easily extended to the case of hadrons. We apply our pipeline to the relevant problem of particle acceleration in galaxy clusters. We define a sub-grid model for compressible magnetohydrodynamic (MHD) turbulence in the intracluster medium and calculate the corresponding reacceleration time-scale from first principles. We then use a MHD simulation of an isolated cluster merger to follow the evolution of relativistic electron spectra and radio emission generated from the system over several Gyr.

The giant radio relic in CIZA J2242.8+5301 provides clear evidence of a Mpc sized shock in a massive merging galaxy cluster. Here we present idealized SPH hydrodynamical and collisionless Dark Matter simulations, aiming to find a model that is consistent with that large range of observations of this galaxy cluster. We first show that in the northern shock, the observed radio spectral index profile and integrated radio spectrum are consistent with the observed upstream X-ray temperature. Using simulations, we first find that only a cool-core versus non-cool-core merger can lead to the observed elongated X-ray morphology. We then carry out simulations for two merging clusters assuming a range of NFW and β-model density profiles and hydrostatic equilibrium. We find a fiducial model that mimics the overall morphology of the shock structures, has a total mass of 1.6 × 10¹⁵M_⊙ and a mass ratio of 1.76. For this model the derived Mach number for the northern shock is 4.5. This is almost a factor 2 higher compared to observational determination of the Mach number using X-ray observations or measurements of the radio injection spectral index. We could not find numerical models that both fit the X-ray properties and yielded such low Mach numbers. We discuss various ways of understanding this difference and argue that deep X-ray observations of CIZA J2242.8+5301 will be able to test our model and reconcile the differences.

We present a new code for astrophysical magnetohydrodynamics specifically designed and optimized for high performance and scaling on modern and future supercomputers. We describe a novel hybrid OpenMP/MPI programming model that emerged from a collaboration between Cray, Inc. and the University of Minnesota. This design utilizes MPI-RMA optimized for thread scaling, which allows the code to run extremely efficiently at very high thread counts ideal for the latest generation of multi-core and many-core architectures. Such performance characteristics are needed in the era of “exascale” computing. We describe and demonstrate our high-performance design in detail with the intent that it may be used as a model for other, future astrophysical codes intended for applications demanding exceptional performance.