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