CLUSTERS OF GALAXIES

Lecture 1Introduction and

Structure Formation

Clusters of Galaxies:a short overview

Clusters of GalaxiesX-ray Band

K108≈∝RMT Tot

gas

XX--Ray ImagingRay ImagingXX--rays rays and and optical optical light show light show us us a a different picture different picture

XX--Ray ImagingRay ImagingXX--rays rays and and optical optical light show light show us us a a different picture different picture

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

have clearly decoupled from have clearly decoupled from the the Hubble flowHubble flow, , they they

carry important cosmological informationcarry important cosmological information

Physical conditions Physical conditions in in clusters clusters are are unlike anywhere unlike anywhere

else. else. TheyThey are are laboratories where we laboratories where we can can study study the the

lawslaws of of physics physics under under conditions unachiavable conditions unachiavable

elsewhereelsewhere..

The Physics of the ICMThe Physics of the ICM

Cool Cores Cool Cores

Cold Fronts Cold Fronts

Metals Metals & the ICM& the ICM

NonNon--thermal processes thermal processes in in clusters clusters

The The ClusterCluster--CosmologyCosmologyconnectionconnection

XX--ray Luminosity functionray Luminosity function, X, X--ray ray

Temperature Temperature function function and and their evolutiontheir evolution

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

SuperSuper--Clusters Clusters

XX--Ray ImagingRay Imaging

Central regions feature Central regions feature approxapprox. . constant surface constant surface brightness brightness

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

Emission is traced Emission is traced out out to to

11--2 2 Mpc from Mpc from the corethe coreMohr et al. (1999)

Principio Fondamentale dellaCosmologia

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 linearizethe 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 grovesor

= 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 or

The 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