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In a growing number of galaxy clusters diffuse extended radio sources have been found. These sources are not directly associated with individual cluster galaxies. The radio emission reveal the presence of cosmic rays and magnetic fields in the intracluster medium (ICM). We classify diffuse cluster radio sources into radio halos, cluster radio shocks (relics), and revived AGN fossil plasma sources. Radio halo sources can be further divided into giant halos, mini-halos, and possible “intermediate” sources. Halos are generally positioned at cluster center and their brightness approximately follows the distribution of the thermal ICM. Cluster radio shocks (relics) are polarized sources mostly found in the cluster’s periphery. They trace merger induced shock waves. Revived fossil plasma sources are characterized by their radio steep-spectra and often irregular morphologies. In this review we give an overview of the properties of diffuse cluster radio sources, with an emphasis on recent observational results. We discuss the resulting implications for the underlying physical acceleration processes that operate in the ICM, the role of relativistic fossil plasma, and the properties of ICM shocks and magnetic fields. We also compile an updated list of diffuse cluster radio sources which will be available on-line ( http://galaxyclusters.com ). We end this review with a discussion on the detection of diffuse radio emission from the cosmic web.

The total mass of a galaxy cluster is one of its most fundamental properties. Together with the redshift, the mass links observation and theory, allowing us to use the cluster population to test models of structure formation and to constrain cosmological parameters. Building on the rich heritage from X-ray surveys, new results from Sunyaev-Zeldovich and optical surveys have stimulated a resurgence of interest in cluster cosmology. These studies have generally found fewer clusters than predicted by the baseline Planck Λ CDM model, prompting a renewed effort on the part of the community to obtain a definitive measure of the true cluster mass scale. Here we review recent progress on this front. Our theoretical understanding continues to advance, with numerical simulations being the cornerstone of this effort. On the observational side, new, sophisticated techniques are being deployed in individual mass measurements and to account for selection biases in cluster surveys. We summarise the state of the art in cluster mass estimation methods and the systematic uncertainties and biases inherent in each approach, which are now well identified and understood, and explore how current uncertainties propagate into the cosmological parameter analysis. We discuss the prospects for improvements to the measurement of the mass scale using upcoming multi-wavelength data, and the future use of the cluster population as a cosmological probe.

In recent years, observations of the Sunyaev-Zeldovich (SZ) effect have had significant cosmological implications and have begun to serve as a powerful and independent probe of the warm and hot gas that pervades the Universe. As a few pioneering studies have already shown, SZ observations both complement X-ray observations—the traditional tool for studying the intra-cluster medium—and bring unique capabilities for probing astrophysical processes at high redshifts and out to the low-density regions in the outskirts of galaxy clusters. Advances in SZ observations have largely been driven by developments in centimetre-, millimetre-, and submillimetre-wave instrumentation on ground-based facilities, with notable exceptions including results from the Planck satellite. Here we review the utility of the thermal, kinematic, relativistic, non-thermal, and polarised SZ effects for studies of galaxy clusters and other large scale structures, incorporating the many advances over the past two decades that have impacted SZ theory, simulations, and observations. We also discuss observational results, techniques, and challenges, and aim to give an overview and perspective on emerging opportunities, with the goal of highlighting some of the exciting new directions in this field.

As the largest virialized structures in the universe, galaxy clusters continue to grow and accrete matter from the cosmic web. Due to the low gas density in the outskirts of clusters, measurements are very challenging, requiring extremely sensitive telescopes across the entire electromagnetic spectrum. Observations using X-rays, the Sunyaev–Zeldovich effect, and weak lensing and galaxy distributions from the optical band, have over the last decade helped to unravel this exciting new frontier of cluster astrophysics, where the infall and virialization of matter takes place. Here, we review the current state of the art in our observational and theoretical understanding of cluster outskirts, and discuss future prospects for exploration using newly planned and proposed observatories.

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.

Four decades ago, the firm detection of an Fe-K emission feature in the X-ray spectrum of the Perseus cluster revealed the presence of iron in its hot intracluster medium (ICM). With more advanced missions successfully launched over the last 20 years, this discovery has been extended to many other metals and to the hot atmospheres of many other galaxy clusters, groups, and giant elliptical galaxies, as evidence that the elemental bricks of life—synthesized by stars and supernovae—are also found at the largest scales of the Universe. Because the ICM, emitting in X-rays, is in collisional ionisation equilibrium, its elemental abundances can in principle be accurately measured. These abundance measurements, in turn, are valuable to constrain the physics and environmental conditions of the Type Ia and core-collapse supernovae that exploded and enriched the ICM over the entire cluster volume. On the other hand, the spatial distribution of metals across the ICM constitutes a remarkable signature of the chemical history and evolution of clusters, groups, and ellipticals. Here, we summarise the most significant achievements in measuring elemental abundances in the ICM, from the very first attempts up to the era of XMM-Newton , Chandra , and Suzaku and the unprecedented results obtained by Hitomi . We also discuss the current systematic limitations of these measurements and how the future missions XRISM and Athena will further improve our current knowledge of the ICM enrichment.

Most galaxies comparable to or larger than the mass of the Milky Way host hot, X-ray emitting atmospheres, and many such galaxies are radio sources. Hot atmospheres and radio jets and lobes are the ingredients of radio-mechanical active galactic nucleus (AGN) feedback. While a consensus has emerged that such feedback suppresses cooling of hot cluster atmospheres, less attention has been paid to massive galaxies where similar mechanisms are at play. Observation indicates that the atmospheres of elliptical and S0 galaxies were accreted externally during the process of galaxy assembly and augmented significantly by stellar mass loss. Their atmospheres have entropy and cooling time profiles that are remarkably similar to those of central cluster galaxies. About half display filamentary or disky nebulae of cool and cold gas, much of which has likely cooled from the hot atmospheres. We review the observational and theoretical perspectives on thermal instabilities in galactic atmospheres and the evidence that AGN heating is able to roughly balance the atmospheric cooling. Such heating and cooling may be regulating star formation in all massive spheroids at late times.

The detailed velocity structure of the diffuse X-ray emitting intra-cluster medium (ICM) remains one of the last missing key ingredients in understanding the microphysical properties of these hot baryons and constraining our models of the growth and evolution of structure on the largest scales in the Universe. Direct measurements of the gas velocities from the widths and shifts of X-ray emission lines were recently provided for the central region of the Perseus Cluster of galaxies by Hitomi , and upcoming high-resolution X-ray microcalorimeters onboard XRISM and Athena are expected to extend these studies to many more systems. In the mean time, several other direct and indirect methods have been proposed for estimating the velocity structure in the ICM, ranging from resonant scattering to X-ray surface brightness fluctuation analysis, the kinematic Sunyaev-Zeldovich effect, or using optical line emitting nebulae in the brightest cluster galaxies as tracers of the motions of the ambient plasma. Here, we review and compare the existing estimates of the velocities of the hot baryons, as well as the various overlapping physical processes that drive motions in the ICM, and discuss the implications of these measurements for constraining the viscosity and identifying the source of turbulence in clusters of galaxies.

Galaxy clusters grow by gas accretion, mostly from mergers of substructures, which release powerful shock waves into cosmic plasmas and convert a fraction of kinetic energy into thermal energy, amplification of magnetic fields and into the acceleration of energetic particles. The modeling of the radio signature of cosmic shocks, combined with the lack of detected γ -rays from cosmic ray (CR) protons, poses challenges to our understanding of how cosmic rays get accelerated and stored in the intracluster medium. Here we review the injection of CRs by cosmic shocks of different strengths, combining the detailed “microscopic” view of collisionless processes governing the creation of non-thermal distributions of electrons and protons in cluster shocks (based on analytic theory and particle-in-cell simulations), with the “macroscopic” view of the large-scale distribution of cosmic rays, suggested by modern cosmological simulations. Time dependent non-linear kinetic models of particle acceleration by multiple internal shocks with large scale compressible motions of plasma with soft CR spectra containing a noticeable energy density in the super-thermal protons of energies below a few GeV which is difficult to constrain by Fermi observations are discussed. We consider the effect of plasma composition on CR injection and super-thermal particle population in the hot intracluster matter which can be constrained by fine high resolution X-ray spectroscopy of Fe ions.

The distribution of chemical elements in the hot intracluster medium (ICM) retains valuable information about the enrichment and star formation histories of galaxy clusters, and on the feedback and dynamical processes driving the evolution of the cosmic baryons. In the present study we review the progresses made so far in the modelling of the ICM chemical enrichment in a cosmological context, focusing in particular on cosmological hydrodynamical simulations. We will review the key aspects of embedding chemical evolution models into hydrodynamical simulations, with special attention to the crucial assumptions on the initial stellar mass function, stellar lifetimes and metal yields, and to the numerical limitations of the modelling. At a second stage, we will overview the main simulation results obtained in the last decades and compare them to X-ray observations of the ICM enrichment patterns. In particular, we will discuss how state-of-the-art simulations are able to reproduce the observed radial distribution of metals in the ICM, from the core to the outskirts, the chemical diversity depending on cluster thermo-dynamical properties, the evolution of ICM metallicity and its dependency on the system mass from group to cluster scales. Finally, we will discuss the limitations still present in modern cosmological, chemical, hydrodynamical simulations and the perspectives for improving the theoretical modelling of the ICM enrichment in galaxy clusters in the future.