Galaxy Clusters

1
Galaxy Clusters
Dark Matter Neutralinos
September 9
August 28
2005
Houches
Les

• What they tell us about dark matter
• (and dark energy)
• James G. Bartlett
• APC - Université Paris 7

2
Why Clusters?

• Diverse astrophysical observations point to the
  existence of dark matter and constrain its
  properties

Galaxy clusters are a central example
(and also dark energy)
3
How So?

• Cluster composition
• Existence of DM
• Quantity of DM inside clusters and out
• Quantity of DE
• Evolution of cluster population
• Quantity of DM DE
• Cluster DM halo profile
• collisionless matter
• Indirect detection of dark matter
• e.g., annihilation products

4
Galaxy Clusters - our program

• Introduction
• Discovery of dark matter
• The making of a galaxy cluster
• Cluster composition (M/L ratio, fgas(z))
• Galactic stellar mass
• Hot gas mass- Intracluster medium (ICM)
• Total mass
• Virial theorem
• X-ray gas in hydrostatic equilibrium
• Gravitational lensing
• Intracluster stellar mass?
• Cosmological constraints
• Cluster evolution (dn/dMdz) - proposed cluster
  surveys
• Cluster dark matter halo profile (NFW profile)
• Dark matter annihilation in clusters?

5
Discovery
Zwicky 1933 Smith 1936
Galaxy motions within the Coma (Zwicky)
and Virgo (Smith) clusters
Clusters are bound objects
Escape velocity must be greater than galaxy
velocities
From internal galactic dynamics
Coma
Virgo
http//www.robgendlerastropics.com
6
Virgo cluster
Des ensembles dun millier de galaxies liées par
la gravité
Virgo Cluster
http//www.robgendlerastropics.com
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The Making of a Galaxy Cluster
Coma
8
Galaxy Clusters
(J. Schomberts http//zebu.uoregon.edu/js/)
morphology-density relation
Galaxies

• Mostly red ellipticals
• Mgal 0.02 Mtot

10 - 1000
poor groups - rich clusters
Gas
heated by infall

• Mgas 0.1Mtot
• T 1 15 keV (poor ? rich)

Dark Matter
?

• Mtot 1014 - 1015 Msol
• Rvir Mpc

9
Galactic Stellar Mass (1)
Galaxy luminosity function
Schechter 1976, ApJ 203, 297
Normalization for field galaxies
Numbers depend on the band and type of galaxy
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Field Luminosity Function
gals/volume
Field galaxies
Schechter function (Schechter 1976, ApJ 203, 297)
2dF
? ? 1.2 (1.21?0.03) ?
? 0.015 h2 Mpc-3 (1.61?0.08 x 10-2) Mbj ?
-19.6 -5logh (-19.66?0.07)
(L ? 1010 Lsun)
Norberg et al. 2002, MNRAS 336, 907
11
SDSS Composite Cluster LFs
Popesso et al 2005, 433, 415
RASS-SDSS
130 clusters

• Two components
• Universal bright end
• Variable steep
• faint end

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Hertzsprung-Russell Diagram
13
Galactic Stellar Mass (2)
Total cluster luminosity
Depends on stellar population
Total cluster luminosity
Luminous (stellar) mass
14
Hot Gas Mass (1)
Intracluster medium
X-ray emission
Roughly isothermal
Beta-model
Mohr et al. 1999, ApJ 517, 627
15
Hot Gas Mass (2)
Mohr et al. 1999, ApJ 517, 627
45 clusters ROSAT PSPC z0
16
Total Mass virial theorem
Virial equilibrium
16 CNOC clusters
Carlberg et al. 1996, ApJ 462, 32
Carlberg et al. 1997, ApJ 478, 462
17
Total Mass X-rays
Hydrostatic equilibrium
Arnaud et al. 2005, 0502210
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Total Mass - lensing
Weak lensing small distortion of
background galaxies
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Lensing
S
?
?
?
L
O
DOL
DLS
DOS
Distances angulaires
Lens equation
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Weak lensing
Convergence
Image distortions
Complex shear
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Lensing preserves surface brightness
Change of image ellipticities
lensing
Weak lensing
(reduced shear)
(prefactor accounts for z distribution of sources)
Relation to mass
with
mass here!!
22
Lensing Results
Cypriano et al. 2003, ApJ 613, 95 24 X-ray
Abell clusters
For an isothermal sphere
Generally good agreement
23
Mass-to-Light Ratio
(e.g., Carlberg et al. 1996, ApJ 462, 32)
Much bigger than stellar value!!
From field LF
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Intracluster Stellar Mass
Could there be stars outside the galaxies?
Zibetti et al. 0501194
683 SDSS clusters
of total light
More concentrated than the galaxies
25
Gas-Mass Fraction fgas
from BBN/CMB
measure
Mohr et al. 1999, ApJ 517, 627
45 clusters ROSAT PSPC z0
26
Gas-Mass fraction fgas(z)
Assume fgas(z)const.
Observed values
SCDM
Allen et al. 2004, MNRAS 353, 457
26 clusters Chandra z0.07-0.9
?CDM
27
Allen et al. 2004, MNRAS 353, 457
?K free
flat
fgas CMB combined
28
More Careful Look (1)
Mass-to-Light not constant!!
Yang et al. 2005, MNRAS 358, 217
2dF groups
29
More Careful Look (2)
Vikhlinin et al. 0507092
13 low-z clusters observed with Chandra
A133
Total mass
gas mass
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More Careful Look (3)
Sadat et al. 0503426
Vikhlinin et al. 0507092

• Dependence on T
• Not converging

31
More Careful Look (4)
Kravtsov et al. 0501227
Numerical simulations
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Summary

• Cluster composition
• Total mass
• Gas mass
• Galactic stellar mass
• Intracluster stellar mass small
• Cosmology constraints
• Getting more complex?

33
Cluster Evolution

• Overview of structure formation
• The mass function
• Observables the mass
• Some results
• SZ effect future surveys

34
Overview of Structure Formation(1)
Idea uniform (Cosmo Princ.) distribution with
deviations
random field
The deviations are taken to be the result of a
stochastic physical process
Is a random variable (RV) at each point in
space it is a random field (RF)
Description statistics of the field
35
Overview of Structure Formation (2)
galaxy fluctuations
mass density fluctuations
A Gaussian, random field
Density contrast
Power spectrum
36
Overview of Structure Formation (3)
Overdensity inside sphere of radius R
Gaussian random field
Shape in k given by model (?Mh2, ?Bh2)
Evolution with z
Normalization parameter
37
The Mass Function(1)
Jenkins et al. 2001, MNRAS 321, 372
Varying cosmo and z
38
The Mass Function (2)
Cluster abundance Its evolution sensitive
to cosmology
Rosati et al. 2002, ARAA 40, 539
39
Surveying for Clusters

• Want them out to high redshift
• Need a way to estimate mass
• Velocity dispersion difficult
• Lensing SOON
• X-rays
• Luminosity hard to model
• Temperature GOOD!
• SZ effect SOON

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Temperature-Mass Relation
Pointecouteau et al. 0502210
10 local clusters (zXMM-Newton
41
Results (1)
Blanchard et al. 2000, AA 362, 809
At z0 50 clusters
At z0.3 15 clusters
42
Results (2)
Blanchard et al. 2000, AA 362, 809
(see also Viana Liddle 1999)
Henry 2000, ApJ 534, 565
Borgani et al. 2001, ApJ 561, 13
Luminosity function
43
Summary

• Cluster evolution is very sensitive to cosmology
• Current results are discrepant?
• Need more clusters out to higher redshifts with
  mass estimates
• thats hard!

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Cosmological ConstraintsMass-limited Catalog

• 12 sq. deg. survey
• M1014h-1 solar mass

?8 marginalized
45
Sunyaev-Zeldovich Effect
T5 keV
(CL0016 Carlstrom et al.)
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Thermal SZ Effect
x 6.51
For y x- 2.26
2.28 ?104 mJy/arcmin2
xo 3.83
Compton y-parameter
d?
10-4
For Tcmb 2.726K
?- 128 GHz
?- 2.34 mm
?o 218 GHz
?o 1.38 mm
? 370 GHz
? 0.80 mm
?-
?
?o
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Cluster Surveys
Selection is a KEY issue (Bartlett 2000, Melin et
al. 2005)
(Korolov et al, 1986)

• Efficient at high z
• ?i const, Ssz?Dang-2
• Spectral signature
• unique, no k-correction
• Ssz ? gas thermal energy
• robust, independent of spatial/
• thermal structure

An SZ flux-limited survey
Mass selected catalog, Uniform in redshift
Detection mass
Important for evolutionary studies - same kind
of object observed at different epochs
48
12 sq. degs.
100 sq. degs.
Mei Bartlett
49
Planck
Planck
30000 sq. deg.
50,000 clusters with 2 at z1
Largest, deepest full-sky catalog to date
50
Conclusions

• Clusters studies are a cornerstone of cosmology
• They constrain DM DE
• By their composition
• By their evolution
• Current results may be fortuitously too good
• Evolution via SZ surveys potentially powerful
  tool over next few years.

Nourish your critical spirit with reflection!