Ebook: Astrophysics of Galaxy Clusters

This is the second Fermi School devoted to the astrophysics of galaxy clusters, held 4 years after the School “Background Microwave Radiation and Intracluster Cosmology”, directed by Professor Francesco Melchiorri and one of us (YR). The motivation for this School was provided by significant expansion in research on these largest gravitationally bound systems, and great interest in multi-faceted observational, theoretical, and numerical simulations of clusters.

Key topics in the astrophysics of clusters were covered in a series of ten pedagogical (multi-lecture) reviews; the program included also some eight seminar talks. Written versions of most of the reviews and seminar talks are included in this volume. Even though the preparation of this volume was delayed by late submission of some of the reviews, we believe that the papers included here still provide a very useful and updated account of key aspects of a wide range of topics in cluster research.

The School was attended by a substantial group of research students and senior scientists. Participants benefited from ample opportunities for informal interaction in the very enjoyable and aesthetically pleasing Villa Monastero and other locations in Varenna.

We dedicate this volume to the memory of our esteemed colleague Professor Francesco Melchiorri, a leader in experimental CMB research and a mentor to many.

Y. Rephaeli and A. Cavaliere

Clusters of galaxies are the largest relaxed structures in the Universe, and have proven to be among the most important cosmological probes. They are composed of roughly 85% dark matter, 12% hot gas, and 3% stars and galaxies. In this paper, the basic properties of clusters are reviewed. The physics of the intracluster gas is described in some detail. Gases at these temperatures (10⁷–10⁸ K) mainly emit X-rays. Many clusters of galaxies have central regions of dense, cooler intracluster gas called “cool cores.” The properties and physics of cool cores are reviewed. Clusters are formed hierarchically by mergers of smaller systems. The basic physics of cluster mergers is discussed. Finally, I describe the phenomena which occur when clusters with cool cores merge. Mergers may disrupt cool cores. Cool cores in merging clusters lead to sharp density discontinuities called “cold fronts” which have proven to be one of the most common features of high-resolution Chandra images of clusters.

We review numerical simulations of galaxy clusters with an emphasis on cosmological basics, numerical methodologies, and recent results. The following topics are covered: the standard cosmological framework, growth of perturbations in the linear regime, analytic models for nonlinear perturbation growth, statistics of galaxy cluster populations, virial scaling relations, overview of numerical methods, simulating gas in galaxy clusters, basic results on adiabatic clusters (Santa Barbara cluster comparison project), effect of additional physics, recent progress in galaxy clustering modeling (Galcons, turbulence, AGN jets, cluster-wide B-fields), simulating statistical samples and lightcones, and simulated SZE surveys.

I review the properties of galaxy systems as determined from optical and infrared measurements. Covered topics are: cluster identification, global cluster properties and their scaling relations, cluster internal structure and dynamics, and properties of cluster galaxy populations.

We review some of the recent work on the use of S-Z measurements to probe galaxy clusters and the global properties of the universe. While the full potential of using the effect to map the gas and total mass profiles of clusters has yet to be realized, analyses of BIMA and OVRO measurements have already yielded statistically meaningful results for the mean gas mass fraction of clusters and for the Hubble parameter. We briefly summarize some of the extensive theoretical studies of the S-Z induced CMB anisotropy and its diagnostic value (also to test alternative cosmological models), and recent work to determine the redshift evolution of the CMB temperature.

The study of the metal enrichment of the intra-cluster and inter-galactic media (ICM and IGM) represents a direct means to reconstruct the past history of star formation, the role of feedback processes and the gas-dynamical processes which determine the evolution of the cosmic baryons. In these lectures, I review the approaches that have been followed so far to model the enrichment of the ICM in a cosmological context. While the presentation will be focused on the role played by hydrodynamical simulations, I will also discuss other approaches based on semi-analytical models of galaxy formation, also critically discussing pros and cons of the different methods. I will first review the concept of the model of chemical evolution to be implemented in any chemo-dynamical description. I will emphasise how the predictions of this model critically depends on the choice of the stellar initial mass function, on the stellar lifetimes and on the stellar yields. I will then overview the comparisons presented so far between X-ray observations of the ICM enrichment and model predictions. I will show how the most recent chemo-dynamical models are able to capture the basic features of the observed metal content of the ICM and its evolution. I will conclude by highlighting the open questions in this study and the direction of improvements for cosmological chemo-dynamical models of the next generation.

The equilibria of the intracluster plasma (ICP) and of the gravitationally dominant dark matter (DM) are governed by the hydrostatic and the Jeans equation, respectively. Jeans, with the DM “entropy” set to K∝r^α and α~1.25–1.3 applying from groups to rich clusters, yields our radial α-profiles for DM density and gravitational potential. In the ICP the entropy run k(r) is mainly shaped by shocks, as steadily set by supersonic accretion of gas at the cluster boundary, and intermittently driven from the center by merging events or by AGNs; the resulting equilibrium is described by the exact yet simple formalism constituting the ICP “Supermodel”. With a few parameters, this accurately represents the runs of density n(r) and temperature T(r) as required by recent X-ray data on surface brightness and spectroscopy for both cool core (CC) and non cool core (NCC) clusters; the former are marked by a middle temperature peak, whose location is predicted from rich clusters to groups. The Supermodel inversely links the inner runs of n(r) and T(r), and highlights their central scaling with entropy n_c∝k_c⁻¹ and T_c∝k_c^0.35, to yield radiative cooling times t_c≈0.3 (k_c/15keV cm²)^1.2Gy. We discuss the stability of the central values so focused both in CC and NCC clusters. From the Supermodel we derive as limiting cases the classic polytropic β-models, and the “mirror” model with T(r)∝σ²(r) suitable for NCC and CC clusters, respectively; these highlight how the ICP temperature T(r) tends to mirror the DM velocity dispersion σ²(r) away from entropy injections. Finally, we discuss how the Supermodel connects information derived from X-ray and gravitational lensing observations.

Modern hydrodynamical simulations offer nowadays a powerful means to trace the evolution of the X-ray properties of the intra-cluster medium (ICM) during the cosmological history of the hierarchical build up of galaxy clusters. In these lectures I review the current status of these simulations and how their predictions fare in reproducing the most recent X-ray observations of clusters. After briefly discussing the shortcomings of the self-similar model, based on assuming that gravity only drives the evolution of the ICM, I discuss how the processes of gas cooling and non-gravitational heating are expected to bring model predictions into better agreement with observational data. I then present results from the hydrodynamical simulations, performed by different groups, and how they compare with observational data. As terms of comparison, I use X-ray scaling relations between mass, luminosity, temperature and pressure, as well as the profiles of temperature and entropy. The results of this comparison can be summarised as follows: a) simulations, which include gas cooling, star formation and supernova feedback, are generally successful in reproducing the X-ray properties of the ICM outside the core regions; b) simulations generally fail in reproducing the observed “cool core” structure, in that they have serious difficulties in regulating overcooling, thereby producing steep negative central temperature profiles. This discrepancy calls for the need of introducing other physical processes, such as energy feedback from active galactic nuclei, which should compensate the radiative losses of the gas with high density, low entropy and short cooling time, which is observed to reside in the innermost cluster regions.

Traditional estimators of the mass of galaxy clusters assume that the cluster components (galaxies, intracluster medium, and dark matter) are in dynamical equilibrium. Two additional estimators, that do not require this assumption, were proposed in the 1990s: gravitational lensing and the caustic technique. With these methods, we can measure the cluster mass within radii much larger than the virial radius. In the caustic technique, the mass measurement is only based on the celestial coordinates and redshifts of the galaxies in the cluster field of view; therefore, unlike lensing, it can be, in principle, applied to clusters at any redshift. Here, we review the origin, the basics and the performance of the caustic method.

Weak gravitational lensing of background galaxies is a unique, direct probe of the distribution of matter in clusters of galaxies. We review several important aspects of cluster weak gravitational lensing together with recent advances in weak-lensing techniques for measuring cluster lensing profiles and constraining cluster structure parameters.

We investigate the structure and history of Dark Matter (DM) halos in galaxies and galaxy systems. Our theoretical framework is provided by the two-stage cosmogonical development of DM halos, and by the related “α-profiles”. The latter solve the Jeans equation for the self-gravitating DM equilibria, and yield the radial runs of the density ρ(r) and the velocity dispersion σ_r²(r) in terms of the DM “entropy” K≡σ_r²/ρ^2/3∝r^α highlighted by recent N-body simulations to have a uniform slope α within the halo “body”. The former constrains the entropy slope α to a value within the narrow range 1.25–1.3; such a value applies in the halo body since the transition time that, both in our semianalytic description and in state-of-the-art numerical simulations, is found to separate two stages in the development of a DM halo: an early fast collapse including a few violent major mergers building up the halo body by dynamical relaxation; and a later, quasi-equilibrium stage during which the body is almost unaffected while the outskirts develop from the inside-out by minor mergers and smooth accretion. These physically based α-profiles meet the overall requirements from gravitational lensing observations, being intrinsically flatter at the center and steeper in the outskirts relative to the empirical NFW formula. In quantitative detail, we test them with the recent extensive dataset from weak and strong lensing observations in and around the cluster A1689. We find an optimal fit at both small and large scales in terms of a halo constituted by an early body with α≈1.25 and by recent extended outskirts making up a concentration parameter c≈10; we consistently interpret the latter value in terms of the variance expected in the two-stage halo development under the standard ΛCDM cosmology.

In this lecture I present our recent results of characterizing cosmological shocks within adaptive mesh refinement N-body/hydrodynamic simulations that are used to predict non-thermal components of large-scale structure. We propose a modified algorithm for finding shocks from those used on unigrid simulations that reduces the shock frequency of low Mach number shocks by a factor of ~3. We then apply our new technique to a large, (512 h⁻¹ Mpc)³, cosmological volume and study the shock Mach number ([Mscr ]) distribution as a function of pre-shock temperature, density, and redshift. We find that the Mach number evolution can be interpreted as a method to visualize large-scale structure formation. By applying results from nonlinear diffusive shock acceleration models using the first-order Fermi process, we calculate the amount of kinetic energy that is converted into cosmic ray protons.

We describe a method to detect galaxy clusters and groups in photometric redshift surveys that is suitable for the analysis of the variation of galaxy properties with environment in deep fields, as well as a follow-up technique for future cosmological studies based on the analysis of large scale structures. As an application of our method we describe the discovery of a localized overdensity at z~1.6 in the GOODS-South Field, presumably a poor cluster in the process of formation. The cluster has been detected as a 4σ peak in the three-dimensional galaxy density field estimated from the state-of-the-art photometric redshifts of the GOODS-MUSIC catalog. It is embedded in the larger scale overdensity of galaxies known to exist at z=1.61 in the area. The properties of the member galaxies are compared to those of the surrounding field: we found that the two populations have significantly different luminosity, stellar mass and colour distributions. The reddest galaxies have colors consistent with a forming “red sequence”: the colors of the reddest cluster galaxies, evolved according to their best fit models, are consistent with the red sequence of lower redshift massive clusters. The estimated total mass of the cluster is in the range 1.2×10¹⁴–3.5×10¹⁴.

We describe the results of a deep survey for Lyα emission line galaxies at z~3.1, carried out with the multislit imaging spectroscopy (MSIS) technique, with the FORS2 spectrograph on VLT-UT1. We discuss the criteria used to select the emission line galaxies and present the main physical characteristics of the sample: redshift, observed flux and equivalent width distributions.