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Clusters, Cosmology and Mergers 253 August E. Evrard and Isabella M. Gioia

1 Gravitational Instability: Theory and Computation 256

1.1 The late universe 256

1.2 Isolated, spherical clusters 257

1.3 3-D hierarchical clustering 259

2 The Discrete Cluster Population 267

2.1 From cluster surveys to cosmology 267

2.2 The mass function 268 2.2.1 Frequency of Mergers 272

2.3 Cluster internal structure 274

2.3.1 Dark matter density profiles 274

2.3.2 The dark matter virial theorem 276

2.3.3 The ICM virial relation 278

2.4 Cluster observables 282

3 Constraints on Cosmological parameters 283

3.1 Cluster surveys 284

3.2 from the cluster baryon fraction 286

3.3 from the local temperature function 288

3.4 from distant cluster counts 290

3.4.1 SZ survey yields 293

3.4.2 X-ray flux limited samples from ROSAT 295

4 Summary 296

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