Studying
clusters and
cosmology
with Chandra
Some thoughts…
Licia Verde
Princeton University
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Overview
•The potential of combining:
X-rays + optical + CMB…..
•Clusters scaling relations with X-rays and
the Sunyaev-Zeldovich effect
• constraining dark energy (Quintessence)
•Conclusions
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Coordinated Cluster Measurements
Optical:
Galaxy Cluster
• Redshift velocity dispersion
• Photometry and lensing
mm-Wave:
• SZ – Compton Scattering
HOT Electrons
X-ray Flux:
chandra
• Temperature and luminosity probe
mass
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SZ Signature
Hot electron gas
imposes a unique
spectral signature
145 GHz
decrement
220 GHz
null
270 GHz
increment
NO SZ Contribution in Central Band
Easy to find!
1.4°x 1.4°
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Clusters as Cosmological Probes
Multiple
observables
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Clusters counts (*)
SZ luminosity
Central SZ decrement
X-ray temperature (*)
X-ray luminosity(*)
Angular size(*)
Velocity Dispersion
Redshift
Lensing Mass
Kinetic SZ amplitude
Multiple uses
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Standard candles
Standard rulers
Probes of volume
Probes of velocity field
Probes of initial conditions
Need to know
cluster physics
Linked theoretical/observational
effort essential for using these
observables as cosmological probes.
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Amplitude of
fluctuations
Scaling relations
Gravitational lensing
of CMB gives F
Kinetic SZ gives v2
Cluster counts give
– N(M,z)
– N(FSZ,z)
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Clusters scaling relations
(e.g., size temperature, mass-temperature)
Mohr et al 1997, Mohr et al 2000
(Verde et al. 2000)
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New scaling relations that include the SZ decrement
(Verde, Haiman, Spergel 2002)
chandra
Observables: SZ, angular size, redshift,Temperature
“constraints”: M-T relation

T  (1  z f ) M
1/ 
(  1.5,  1)
THSC
Virial relation
Total SZ decrement
TR  M
S
TM

2
2

dA
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If our understanding of cluster physics is correct
Narrow
Clusters should occupy a fundamental plane
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Modifications in the
Position, orientation
and redshift evolution
of the plane
Different cluster physics
and/or cosmology
Scaling relations with SZ
(THSC prediction)
narrow
broad
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Formation redshift?
Mathiessen 2001 finds no evidence for zf
being relevant to clusters properties
Only formation redshift
Only stochastic
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300 clusters with follow up
Assume cosmology, study cluster physics 
fM Lacey & Cole 94 parameter for the formation redshift distribution
2D KS test
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Back to:

T  (1  z f ) M
1/ 
(  1.5,  1)
Observations e.g., Xu et al. 2001, Mohr, Evrard 1997, Mohr et al 1999
1.6    1.98
 eff  1.6
Effect of formation redshift
Can constrain a fiducial model:
  1.500..05
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Deviations from virialization parameterized by
For a fiducial model

  1 0.03
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Assume cluster physics, study cosmology
Assume formation redshift
distribution is important
Constraints from
Sz, , z
Used KS,
Lokelihood is much
more sensitive
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MAP 2 yr
Cluster
abundance
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ADD information about dN/dz (mass function)
With Z. Haiman
Break the cluster physics/cosmology degeneracy
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 Shown a “taste” of the many possibilites
The fundamental plane/scaling relations approach can be
generalized to include other observables such as
velocity dispersion, X-ray luminosity, shear,
central SZ decrement….
Used KS test, likelihood is much more sensitive
Insensitive to the mass function and independent from it
Can be used in tandem with dN/dz (clusters counts) to
lift degeneracies between cosmology and cluster physics
Important to constrain clusters physics (fixed cosmology)
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Dark energy 
Verde et al 2002
deBernardis et al. 2001
Perlmutter et al. 1998
Nature? Equation of state?
From Verde et al. 2002
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MAP will constrain
s 8 and cosmological parameters
The growth of structure
(i.e. cluster abundance
evolution)
Nature of
dark energy
Haiman et al. 2000
(once we know clusters physics)
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Conclusions
• X-ray
+CMB +optical + theory
• Clusters scaling relations with SZ (Tx)
(study cluster physics and cosmology)
• constrain dark energy exploiting
growth rate of structure
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END
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