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 numeri
cally. 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 run time and post-processing to very large astrophysical fluid simulations. We also propose a novel method to compress cosmic- ray spectra by a factor of ten, 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 MHD-turbulence in the intra- cluster-medium and calculate the corresponding reacceleration timescale from first principles. We then use a magneto-hydrodynamic simulation of an isolated cluster merger to follow the evolution of relativistic electron spectra and radio emission generated from the system over several Gyrs.
Simulations of isolated binary mergers of galaxy clusters are a useful tool to study the evolution of these objects. For exceptionally massive systems they even represent the only viable way of simulation, because these are rare in typical cosmologic
al simulations. We present a new practical model for these simulations based on the Hernquist dark matter profile. The hydrostatic equation is solved for a beta-model with $beta$ = 2/3 in this potential and approximate expressions for X-ray brightness and Compton-y parameter are derived. We show in detail how to setup such a system using SPH. The theoretical and several numerical models are compared to observed scaling relations of galaxy clusters and satisfactory agreement with the self-similar relations is found. The model is then applied to investigate the observed cluster ACT-CT J0102-4915 (El Gordo), a particularly massive merging high redshift cluster. We are able to reproduce the X-ray luminosity, SZ-effect and dark matter core distance as well as the rough shape of the observed cluster for reasonable model parameters. The lack of substruc- ture prevents us from obtaining the fluctuations observed in the wake of the system and we argue that the parent cluster of the system was highly disturbed even before the main merger observed today.
We review models for giant radio halos in clusters of galaxies, with a focus on numerical and theoretical work. After summarising the most important observations of these objects, we present an introduction to the theoretical aspects of hadronic mode
ls. We compare these models with observations using simulations and find severe problems for hadronic models. We give a short introduction to reacceleration models and show results from the first simulation of CRe reaccel- eration in cluster mergers. We find that in-line with previous theoretical work, reacceleration models are able to elegantly explain main observables of giant radio halos.
We present the first high resolution MHD simulation of cosmic-ray electron reacceleration by turbulence in cluster mergers. We use an idealised model for cluster mergers, combined with a numerical model for the injection, cooling and reacceleration o
f 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 reacceleration of CRe has the potential to reproduce key observables of radio halos. 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 halos. In the simulation the diffuse emission traces the complex interplay between spatial distribution of turbulence injected by the halo infall and the spatial distribution of the seed electrons to reaccelerate. During the formation and evolution of the halo the synchrotron emission spectra show the observed variety: from power-laws with spectral index of 1 to 1.3 to curved and ultra-steep spectra with index $> 1.5$.
We use results from a constrained, cosmological MHD simulation of the Local Universe to predict radio halos and their evolution for a volume limited set of galaxy clusters and compare to current observations. The simulated magnetic field inside the c
lusters is a result of turbulent amplification within them, with the magnetic seed originating from star-burst driven, galactic outflows. We evaluate three models, where we choose different normalizations for the Cosmic Ray proton population within clusters. Similar to our previous analysis of the Coma cluster (Donnert et al. 2010), the radial profile and the morphological properties of observed radio halos can not be reproduced, even with a radially increasing energy fraction within the cosmic ray proton population. Scaling relations between X-ray luminosity and radio power can be reproduced by all models, however all models fail in the prediction of clusters with no radio emission. Also the evolutionary tracks of our largest clusters in all models fail to reproduce the observed bi-modality in radio luminosity. This provides additional evidence that the framework of hadronic, secondary models is disfavored to reproduce the large scale diffuse radio emission of galaxy clusters. We also provide predictions for the unavoidable emission of $gamma$-rays from the hadronic models for the full cluster set. None of such secondary models is yet excluded by the observed limits in $gamma$-ray emission, emphasizing that large scale diffuse radio emission is a powerful tool to constrain the amount of cosmic ray protons in galaxy clusters.
