Cosmology with Galaxy Clusters

1
Cosmology with Galaxy Clusters
Zoltán Haiman
Columbia University
Collaborators Joe Mohr (Illinois)
Gil Holder (IAS)
Wayne Hu (Chicago)
Licia Verde (U Penn)
David Spergel (Princeton)
Cosmology with SZ Cluster Surveys
Chicago, 17-20 September 2003
2
An overview?
cluster cosmology literature
my contributions
3
Outline of Talk

• Cosmological Sensitivity of Clusters
  why clusters?
  current constraints
  
• Constraints from Future Samples
  abundance
  evolution
  power spectrum
• SZ X-ray synergy

4
Current Cosmology Constraints
SN
(SCP)
??
CMB
(WMAP)
LSS
(2dF)
Verde www (2003)
?M
strong degeneracy in any single experiment
5
Why Galaxy Clusters?

• Theory

Clusters relatively simple objects. Evolution of
massive cluster abundance determined by gravity.
Clusters straddle the epoch of dark energy
domination 0ltzlt3.

• Future observations

Current samples of tens of clusters soon to be
replaced by thousands of clusters with mass
estimates in dedicated large (SZE, X-ray, weak
lensing) surveys

• Why Do We Need Yet Another Cosmological Probe?

(Impressive constraints - but dark energy still
elusive)

• - Degeneracies differ from CMB, SNe, Galaxies
• Systematics are different
• Unique exponential dependence
• Modelability

6
An advantage unique to clusters?

• A cluster sample can deliver many observables

SZE decrement X-ray flux
Angular size
Number of galaxies Spatial distribution (2d,
3d) Lensing signatures

• We can construct several cosmology tests

dN/dz abundance evolution
(including mass function dN/dM) P(k) spatial
power spectrum (including
Alcock-Paczynski) Scaling relations between
SZ/X-rays/sizes (including dA
measurement)
Best?
better
good
Simultaneous determination of cosmological
and cluster structural parameters (with their
evolution)
7
Outline of Talk

• Cosmological Sensitivity of Clusters
  why clusters?
  current constraints
  
• Constraints from Future Samples
  abundance
  evolution
  power spectrum
• SZ X-ray synergy

8
Local Cluster Abundance Constraints
Reiprich Böhringer (2002)
Pierpaoli et al. (2003)
?8
?M

• 63 bright X-ray clusters (REFLEX) - Soft
  X-ray flux limit 2?10-11 erg/s/cm2 - 20,000
  sq. degrees (half sky), z 0

9
Cluster Abundance Evolution Constraints
Patrick Henry (2003)
using dN/dT evolution 24 clusters at zlt0.2 19
clusters at zgt0.3 marginalized over ?8
??
w
?M
10
Cluster Abundance Evolution Constraints
Patrick Henry (2003)
using dN/dT evolution 24 clusters at zlt0.2 19
clusters at zgt0.3 marginalized over ?8
w
?M
11
Cluster Abundance Evolution Constraints
Schuecker et al. (2003)
?M
depth very important!
w

• - 426 X-ray clusters (REFLEX sample)
• - Soft X-ray flux limit 3?10-12 erg/s/cm2
• 10,000 sq. degrees
• redshifts 0ltzlt0.2 ? looses w constraint despite
  larger

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Summary of Current Results
Local Sample of 100 clusters have
constrained matter density and power spectrum
normalization to accuracy comparable to other
methods (CMB, SNe)
Bridle et al. (2003)
Similar results for ?M from cluster baryon
fraction and mass/light arguments
Lin et al. (2003), Ostriker et al. (2003)
Dark energy constraints are not yet
available, we need larger samples extending
to larger distance (z1)
Current systematics are dominated by M-T
relation, and are at the level of statistical
errors
Pierpaoli et al. (2003)
13
Outline of Talk

• Cosmological Sensitivity of Clusters
  why clusters?
  current constraints
  
• Constraints from Future Samples
  abundance
  evolution
  power spectrum
• SZ X-ray synergy

14
Galaxy Cluster Abundance
Dependence on cosmological parameters
of clusters per unit area and z
comoving volume
mass limit
mass function
mass function
Jenkins et al. 2001
Hubble volume N-body simulations in three
cosmologies cf Press-Schechter
growth function
power spectrum (?8, M-r)
overall normalization
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A note on the mass function

• Success

Simulations find a fitting formula that is
accurate (to 10 in dN/dM) and is universal
cosmology scales out when mass is appropriately
defined.

• Encouraging

Original result in three, widely separated
cosmologies recently also confirmed for w gt -1.
Also agrees with Press-Schechter scaling
Linder Jenkins (2003)

• However

We need to either understand this
universality from first principles or have
available a very large suite of simulations on a
fine grid. Test runs?
16
Observables in Future Surveys
SZ decrement
X-ray flux
weak lensing shear.
17
Mass Limits and Dependence on w
XR flux5x10-14 erg s-1 cm-2
SZ 5? detection in mock SZA observations
(Holder et al. 2001)
X-ray survey
X-ray surveys more sensitive to mass
limit sensitivity amplified in the
exponential tail of dN/dM
w -0.9
w -0.6
log(M/M?)
w, ?M non-negligible
sensitivity
SZE survey
?? dependence weak
H0 dependency M ? H0-1
redshift
18
Which Effect is Driving Constraints?
- depends on which parameter and survey -
Pick fiducial ?CDM cosmology
?M 0.3
?? 0.7
w -1
H0 72 km s-1 Mpc-1
?8 0.9
n 1
Compute dN/dz by varying five parameters
?M, w, ??, H0 , ?8
Evaluate likelihood (Fisher matrix, Monte
Carlo)
Haiman, Mohr Holder (2001)
Hu Kravtsov (2003)
Holder, Haiman Mohr (2001)
Majumdar Mohr (2003a,b)
Weller, Battye Kneissl (2002)
Hu (2003)
Levine, Schultz White (2002)
Battye Weller (2003)
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Sensitivity to ?M ,w in SZE Survey
Haiman, Mohr Holder 2001
w-1
w-0.6
w-0.2
dN/dz/12 deg2
0
1
2
3
0
1
2
3
redshift
redshift
overall scaling and ?8 change
volume (low-z) growth (high-z)
20
Power Complementarity
Z. Haiman / DUET
Constraints using dN/dz of 18,000 clusters in
a wide angle X-ray survey (SPT gives similar
results)
Power comparable to
??
Planck measurements of CMB anisotropies
2,400 Type Ia SNe from SNAP

• ?M to 1
• ?? to 5

?M
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Dark Energy Constraints
DUET proposal J.Mohr/Z.Haiman
Using 104 deg2 X-ray 20,000 clusters between 0
lt z ? 1 (marginalized over H0 and ?8)
??
Planck measurement of CMB anisotropies and
polarization

• ?M to 1
• w to 5

w
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Time-dependence of w(z)
with J. Khoury, cf Weller et al 2001

• w(z)w0 w1z
• Fixed mass limit of 21014 h-1 M?
• 4000 square degrees (25,000 clusters)
• Errors from 4x4 Fisher matrix
• WMAP w0 -0.8
• ?CDM w1 0.3
• ?? 0.01 ?? 0.01
• ??8 0.006 ??8 0.005
• ?w0 0.12 ?w0 0.10
• ?w1 0.25 ?w1 0.19
• (0.04)
  (0.03)
• Combine with P(k)

23
Outline of Talk

• Cosmological Sensitivity of Clusters
  why clusters?
  current constraints
  
• Constraints from Future Samples
  abundance
  evolution
  power spectrum
• SZ X-ray synergy

24
Cluster Power Spectrum
Dependence on cosmological parameters
Observable
cluster bias
growth function
redshift distortion
transfer function
inverse volume
initial spectrum
Radial modes
Hubble constant

Geometry! (w/ physical scale info)
Transverse modes
Angular diameter distance
Redshift distortion
Scales with growth function
25
Cluster Power Spectrum
Galaxy clusters highly biased
Large amplitude for PC(k) b2 P(k)
Cluster bias as calculable as
mass function
Expected statistical errors on P(k)
FKP (Feldman, Kaiser Peacock
1994) signal-to-noise
increased by b2 25 c.f. SDSS
spectroscopic sample b2 1
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Ideal Tracers of Mass
Hu Haiman 2003
low-mass clusters and groups are not far from
being ideal tracers out to z1
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Cluster Power Spectrum - Accuracies
6,000 clusters in each of three redshift
bins P(k) determined to roughly the same
accuracy in each z-bin Accuracies
?k/k0.1 ? 7 klt0.2 ? 2 NB baryon
wiggles are detectable at 2?
Z. Haiman / DUET
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Acoustic Rings in 2D
Power spectrum is measured at fixed angular scale
and redshift. Inferred spatial scales depend on
the assumed cosmology Forms purely
geometrical test, if CMB priors are
used Insensitive to z-distortion (c.f.
Alcock-Paczynski test)
Hu Haiman (2003)
29
Errors on DA (z) and H(z)
Hu Haiman 2003
CMB priors
Theorists surveys Galaxies 10,000 sq.deg
M1012.1 h-1 M? at 0ltzlt0.1
(SDSS main) M1013.5 h-1 M?
at 0ltzlt0.4 (SDSS LRG) Clusters 4,000
sq.deg M1014.2 h-1 M? at
0ltzlt1.3 (SPT) - 25,000 clusters
30
Errors on w and ?DE
Hu Haiman 2003
Filled ellipses b marginalized to an
overall scaling Empty ellipses ?, b
marginalized (b separately in each ?z0.1 bin)
galaxies ?(w)0.024 ?(?)0.007
clusters ?(w)0.040 ?(?)0.013
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Cluster Power Spectrum - Summary
High bias of galaxy clusters enables
accurate measurement of cluster P(k)
?k/k0.1 ? P(k) to 7 at k0.1
klt0.2 ? P(ltk) to 2
Expected statistical errors from 25,000
clusters ?M to 0.013
- geometrical test w
to 0.04 - geometrical test
??h2 to 0.002 - usual shape test
? Combine with dN/dM (Majumdar Mohr 2003)
Noteworthy for survey planning -
baryon rings are useful contain half the
information
make test robust (CMB, ?)
- photometric redshift (0.01) sufficient to
recover most of the info - including
knowledge of bias would much improve constraints
- z lt 1 clusters are best complement to
CMB
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Outline of Talk

• Cosmological Sensitivity of Clusters
  why clusters?
  current constraints
  
• Constraints from Future Samples
  abundance
  evolution
  power spectrum
• SZ X-ray synergy

33
SZE and X-ray Synergy
Using scaling relations, we can
simultaneously Probe cosmology and test cluster
structure
?S? - TX scaling relation expected to have small
scatter (1) SZ signal robust
(2) effect of cluster ages
SZ decrement vs Temperature
SZ decrement vs Angular size
Verde, Haiman Spergel 2002
34
Fundamental Plane (?S? ,TX, ?)
Verde, Haiman Spergel 2002
Plane shape sensitive to cosmology and
cluster structure ? Tests the origin
of scatter
35
(?S? ,TX) scaling relations dN/dz test
work in preparation
Using a sample of 200 clusters Different Mmin -
?0 degeneracies
? can check on systematics
36
SZE and X-ray Synergy

• Assuming angular diameter (DA) measurements of
• 100 clusters at 0ltzlt1.5 (0.5ltzlt1 has most
  power)
• combined with 12 deg2 SZA sample

Molnar, Haiman, Birkinshaw Mushotzky 2003,
ApJ, submitted
??
w
?M
?M
37
Conclusions

1. Clusters are a tool of precision cosmology
   a unique blend of cosmological
   tests, combining volume, growth function, and
   mass-observable
2. Using dN/dz, P(k) complementary to other probes
   e.g. (?M,w) , (?M, ?? ), (?M, ??
   ) planes vs CMB and SNe
3. Combining tests and SZ and XR can tackle
   systematics solving for cosmology
   AND cluster parameters?

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The End
39
Constraining w
40
Mass vs. Number of Galaxies
Kravtsov et al. 2003
41
Where Does Information Come From?
Hu Haiman 2003
42
Sensitivity to ?M in SZE Survey
?M affects local abundance N(z0) ? ?M ? ?8
? ?M-0.5
Haiman, Mohr Holder 2001
12 deg2 SZE survey
dN/dz/12 deg2
dN/dz shape relatively insensitive to ?M
Sensitivity driven by ?8 change
0
1
2
3
redshift
43
Sensitivity to w in SZE Survey
Haiman, Mohr Holder 2001
12 deg2 SZE survey
w-1
w-0.6
w-0.2
dN/dz/12 deg2
dN/dz shape flattens with w
Sensitivity driven by volume (low-z) growth
(high-z)
0
1
2
3
redshift
44
Sensitivity to ?M,w in X-ray Survey
104 deg2 X-ray survey
Haiman, Mohr Holder 2001
w
Sensitivity driven by Mmin
?M
Sensitivity driven by ?8 change
45
When is Mass Limit Important?
in the sense of driving the
cosmology-sensitivity
?0 w H0 ?
SZ no no no no
XR no yes no no
overwhelmed by ?8-sensitivity if local abundance
held fixed
46
Time-dependence of w(z)
w(z)w0 w1z
Weller et al. 2001
fiducial model w0 -0.8, w1 0.3
Weak limits but can be combined with the other
tests
SNAP
Planck
SPT
SZA