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CLUSTERS OF GALAXIES. Lecture 1 Introduction and Structure Formation. Clusters of Galaxies: a short overview. Clusters of Galaxies X-ray Band. X-Ray Imaging. X-rays and optical light show us a different picture . X-Ray Imaging. X-rays and optical light show us a different picture .
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CLUSTERS OF GALAXIES Lecture 1 Introduction and Structure Formation
X-Ray Imaging X-rays and optical light show us a different picture
X-Ray Imaging X-rays and optical light show us a different picture
Why study Clusters • Clusters are the largest structures in the Universe to have clearly decoupled from the Hubble flow, they carry important cosmological information • Physical conditions in clusters are unlike anywhere else. They are laboratories where we can study the laws of physics under conditions unachiavable elsewhere.
The Physics of the ICM • Cool Cores • Cold Fronts • Metals & the ICM • Non-thermal processes in clusters
The Cluster-Cosmology connection • X-ray Luminosity function, X-ray Temperature function and their evolution • Scaling relations, entropy and baryonic fraction • Super-Clusters
X-Ray Imaging • Central regions feature approx. constant surface brightness • In outer regions the surface brightness falls off as a power-law with index approx. 3 • Emission is traced out to 1-2 Mpc from the core Mohr et al. (1999)
Principio Fondamentale della Cosmologia L’Universo e’ Omogeneo ed Isotropo Perche’ osserviamo le stelle, le galassie, gli ammassi di galassie? La struttura su larga scala si e’ formata per la crescita gravitazionale di piccole perturbazioni di densita’.
Structure Formation 1000 galaxies within 1Mpc
Let us consider the density field with density fluctuations: This is subject to the continuity equations of Eulero and Poisson: Entropy conservation The system does not have a generic analytic solution. However we can linearize the Fourier transform of the previous system. In this case we have: Structure FormationLinear Theory
Gravitational term Pressure term Jeans Length or Pressure dominates; perturbation oscillates or Gravity dominates; perturbation groves = o Structure FormationLinear Theory
Let us consider a perturbation with A It acts as a closed universe (follows the cycloid equations) The density of the perturbation is We have When the perturbation reaches the maximum expansion at t Structure Formationspherical collapse (1)
Energy Virial theorem Radius and density of the perturbation at the virial Linear theory density contrast Density contrast at the virial Structure Formationspherical collapse (2)
Density of objects per unit of mass It is based on the linear theory and uses only and Mass FunctionPress & Schechter formalism The press & Schechter formalism is WRONG It is simple and help to identify the main “topics” It gives also a simple analytic formula for the mass function
The probability that the fluctuation Is collapsed is given by where The number density is then Or equivalently Mass FunctionPress & Schechter formalism We consider a density field smoothed on the scale or
Hydrostatic equilibrium (spherical symmetry) We can measure the Cluster mass Dynamical Properties of the Galaxies King profile Beta Profile Isothermal Cluster Intracluster Medium
