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Article Contents

ABSTRACT

1.INTRODUCTION

2.THE OBSERVED PROPERTIES OF GALAXY CLUSTERS

3.UNDERSTANDING THE FORMATION OF GALAXY CLUSTERS

3.1.Initial density perturbation field and its linear evolution

3.2.Non-linear evolution of spherical perturbations and non-linear mass scale

3.2.1.Spherical collapse model

3.2.2.The nonlinear mass scale M_NL

3.3.Nonlinear collapse of real density peaks

3.4.Equilibrium

3.5.Internal structure of cluster halos

3.5.1.Density Profile

3.5.2.Velocity dispersion profile and velocity anisotropy

3.5.3.Shape

3.6.Mass definitions

3.6.1.The Friends-of-Friends mass

3.6.2.The Spherical Overdensity mass

3.7.Abundance of halos

3.7.1.The mass function and its universality

3.7.2.Calibrations of halo mass function in cosmological simulations

3.8.Clustering of halos

3.9.Self-similar evolution of galaxy clusters

3.9.1.Self-similar model: assumptions and basic expectations

3.9.2.The Kaiser model for cluster scaling relations

3.9.3.Extensions of the Kaiser model

3.9.4.Practical implications for observational calibrations of scaling relations

3.10.Cluster formation and Thermodynamics of the Intra-cluster gas

3.10.1.Gravitational collapse of the intra-cluster gas

3.10.2.Phenomenological pre-heating models

3.10.3.The role of radiative cooling

3.10.4.Thermodynamics of the intracluster medium with stellar and active galactic nuclei feedback

4.REGULARITY OF THE CLUSTER POPULATIONS

4.1.Characterizing regularity

4.2.Scaling relations

5.CLUSTER FORMATION IN ALTERNATIVE COSMOLOGICAL MODELS

5.1.Mass function and bias of clusters in non-Gaussian models

5.2.Formation of clusters in modified gravity models

6.SUMMARY AND OUTLOOK

REFERENCES