Review to be published in 2012 Annual Reviews of
Astronomy & Astrophysics

astro-ph/1205.5556

For a PDF version of the article, click here.

INAF Osservatorio Astronomico di Trieste, Italy;

and INFN Istituto Nazionale di Fisica Nucleare, Trieste, Italy;

**Abstract:**
Formation of galaxy clusters corresponds to the collapse of the
largest gravitationally bound overdensities in the initial density
field and is accompanied by the most energetic phenomena since the
Big Bang and by the complex interplay between gravity-induced
dynamics of collapse and baryonic processes associated with galaxy
formation. Galaxy clusters are, thus, at the cross-roads of cosmology
and astrophysics and are unique laboratories for testing models of
gravitational structure formation, galaxy evolution, thermodynamics
of the intergalactic medium, and plasma physics. At the same time,
their large masses make them a useful probe of growth of structure
over cosmological time, thus providing cosmological constraints that
are complementary to other probes. In this review, we describe our
current understanding of cluster formation: from the general picture
of collapse from initial density fluctuations in an expanding
Universe to detailed simulations of cluster formation including the
effects of galaxy formation. We outline both the areas in which
highly accurate predictions of theoretical models can be obtained
and areas where predictions are uncertain due to uncertain physics
of galaxy formation and feedback. The former includes the
description of the structural properties of the dark matter halos
hosting cluster, their mass function and clustering
properties. Their study provides a foundation for cosmological
applications of clusters and for testing the fundamental assumptions
of the standard model of structure formation. The latter includes
the description of the total gas and stellar fractions, the
thermodynamical and non-thermal processes in the intracluster
plasma. Their study serves as a testing ground for galaxy formation
models and plasma physics. In this context, we identify a
suitable radial range where the observed thermal properties of the
intra-cluster plasma exhibit the most regular behavior and thus can
be used to define robust observational proxies for the total cluster
mass. Finally, we discuss the formation of clusters in
non-standard cosmological models, such as non-Gaussian models for
the initial density field and models with modified gravity, along
with prospects for testing these alternative scenarios with large
cluster surveys in the near future.

**Keywords:** Cosmology, galaxy clusters, intra-cluster medium

**Table of Contents**

- INTRODUCTION
- THE OBSERVED PROPERTIES OF GALAXY CLUSTERS
- UNDERSTANDING THE FORMATION OF GALAXY CLUSTERS
- Initial density perturbation field and its linear evolution
- Non-linear evolution of spherical perturbations
and non-linear mass scale
- Spherical collapse model.
- The nonlinear mass scale
*M*_{NL}

- Nonlinear collapse of real density peaks
- Equilibrium
- Internal structure of cluster halos
- Density Profile
- Velocity dispersion profile and velocity anisotropy
- Shape

- Mass definitions
- The Friends-of-Friends mass
- The Spherical Overdensity mass

- Abundance of halos
- The mass function and its universality
- Calibrations of halo mass function in cosmological simulations

- Clustering of halos
- Self-similar evolution of galaxy clusters
- Self-similar model: assumptions and basic expectations
- The Kaiser model for cluster scaling relations
- Extensions of the Kaiser model
- Practical implications for observational calibrations of scaling relations

- Cluster formation and Thermodynamics of the
Intra-cluster gas
- Gravitational collapse of the intra-cluster gas
- Phenomenological pre-heating models
- The role of radiative cooling
- Thermodynamics of the intracluster medium with stellar and active galactic nuclei feedback

- REGULARITY OF THE CLUSTER POPULATIONS
- Characterizing regularity
- Scaling relations

- CLUSTER FORMATION IN ALTERNATIVE COSMOLOGICAL
MODELS
- Mass function and bias of clusters in non-Gaussian models
- Formation of clusters in modified gravity models

- SUMMARY AND OUTLOOK
- REFERENCES