CLUSTERS OF GALAXIES

Lecture 1Introduction and

Structure Formation

Clusters of Galaxies:a short overview

Clusters of GalaxiesX-ray Band

K108RMT Tot

gas

X-Ray ImagingX-Ray ImagingX-rays and optical light show us a different picture X-rays and optical light show us a different picture

X-Ray ImagingX-Ray ImagingX-rays and optical light show us a different picture X-rays and optical light show us a different picture

Why study ClustersWhy study Clusters Clusters are the largest structures in the Universe Clusters are the largest structures in the Universe

to have clearly decoupled from the Hubble flow, to have clearly decoupled from the Hubble flow, they carry important cosmological informationthey carry important cosmological information

Physical conditions in clusters are unlike Physical conditions in clusters are unlike anywhere else. They are laboratories where we anywhere else. They are laboratories where we can study the laws of physics under conditions can study the laws of physics under conditions unachiavable elsewhere.unachiavable elsewhere.

The Physics of the ICMThe Physics of the ICM

Cool Cores Cool Cores Cold Fronts Cold Fronts Metals & the ICMMetals & the ICM Non-thermal processes in clusters Non-thermal processes in clusters

The Cluster-Cosmology The Cluster-Cosmology connectionconnection

X-ray Luminosity function, X-ray X-ray Luminosity function, X-ray Temperature function and their evolutionTemperature function and their evolution

Scaling relations, entropy and baryonic Scaling relations, entropy and baryonic fraction fraction

Super-Clusters Super-Clusters

X-Ray ImagingX-Ray Imaging Central regions feature Central regions feature

approx. constant surface approx. constant surface brightness brightness

In outer regions the In outer regions the surface brightness falls surface brightness falls off as a power-law with off as a power-law with index approx. 3 index approx. 3

Emission is traced out to Emission is traced out to 1-2 Mpc from the core1-2 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 gravitazionaledi piccole perturbazioni di densita’.

Structure Formation

Structure Formation

Structure Formation

1000 galaxies within 1Mpc

Structure FormationLinear Theory

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:

Pressure termGravitational term

Structure FormationLinear Theory

Jeans Length

Pressure dominates; perturbation oscillatesor

Gravity dominates; perturbation groves

or= o

Structure Formationspherical collapse (1)

Let us consider a perturbation with

It acts as a closed universe (follows the cycloid equations)

The density of the perturbation is

When the perturbation reaches the maximum expansion at We have

t

A

Structure Formationspherical collapse (2)

Energy Virial theorem

Radius and density of the perturbation at the virial

Density contrast at the virial

Linear theory density contrast

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

It is based on the linear theory and uses only and

Density of objects per unit of mass

Mass FunctionPress & Schechter formalism

We consider a density field smoothed on the scale orThe probability that the fluctuation Is collapsed is given by

where

The number density is then

Or equivalently

Mass FunctionPress & Schechter formalism

Intracluster Medium

Hydrostatic equilibrium (spherical symmetry)

We can measure the Cluster mass

Dynamical Properties of the Galaxies

Isothermal Cluster King profile Beta Profile