Cosmology with Galaxy Clusters

1
Cosmology with Galaxy Clusters
Zoltán Haiman
Princeton University
Collaborators Joe Mohr (Illinois)
Gil Holder (IAS)
Wayne Hu (Chicago)
Asantha Cooray (Caltech)
Licia Verde
(Princeton) David
Spergel (Princeton)
I.
II.
III.
Dark Energy Workshop, Chicago, 14 December 2001
2
Outline of Talk

1. Cosmological Sensitivity of Cluster Surveys
   what
   is driving the constraints?
2. Beyond Number Counts
   what can we learn from dN/dM,
   P(k), and scaling laws

3
Introduction
Era of Precision Cosmology
Parameters of standard cosmological model to be
determined to high accuracy by CMB, Type Ia SNe,
and structure formation (weak lensing, Ly?
forest) studies.
Future Galaxy Cluster Surveys
Current samples of tens of clusters can be
replaced by thousands of clusters with mass
estimates in planned SZE and X-ray surveys
Why Do We Need Yet Another Cosmological Probe?
- Systematics are different (and possible to
model!) - Degeneracies are independent of CMB,
SNe, Galaxies - Unique exponential dependence
4
Power Complementarity
Z. Haiman / DUET
Constraints using dN/dz of 18,000 clusters in
a wide angle X-ray survey (Don Lambs talk)
Power comparable to
??
Planck measurements of CMB anisotropies
2,400 Type Ia SNe from SNAP

• ?M to 1
• ?? to 5

?M
5
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
6
Observables in Future Surveys
SZ decrement
X-ray flux
7
Predicting the Limiting Masses
Overall value of Mmin determines
expected yield and hence statistical power
of the survey
Scaling with cosmology effects sensitivity
of the survey to variations in cosmic
parameters
To make predictions, must assume SZE
M-T relation (Bryan Norman 1998)
?c (z) (top-hat collapse)
?(r) (NFW
halo) X-ray L-T relation (Arnaud
Evrard 1999
assuming it holds at all z)
8
Mass Limits and Dependence on w
XR flux5x10-14 erg s-1 cm-2
SZ 5? detection in mock SZA observations
(hydro sim.)
X-ray survey
X-ray surveys more sensitive to mass
limit sensitivity amplified in the
exponential tail of dN/dM
w -0.9
log(M/M?)
w -0.6
w, ?M non-negligible
sensitivity
SZE survey
?? dependence weak
H0 dependency M ? H0-1
redshift
9
Which Effect is Driving Constraints?
Fiducial ?CDM cosmology
?M 0.3
?? 0.7
w -1 ( ?)
H0 72 km s-1 Mpc-1
?8 1
n 1
Examine sensitivity of dN/dz to five
parameters ?M, w,
??, H0 , ?8 by varying them individually.
Assume that we know local abundance N(z0)
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Sensitivity to ?M in SZE Survey
?M effects local abundance N(z0) ? ?M ? ?8
? ?M-0.5
12 deg2 SZE survey
dN/dz shape relatively insensitive to ?M
Sensitivity driven by ?8 change
Haiman, Mohr Holder 2001
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Sensitivity to w in SZE Survey
Haiman, Mohr Holder 2001
12 deg2 SZE survey
w-1
w-0.6
w-0.2
dN/dz shape flattens with w
Sensitivity driven by volume (low-z) growth
(high-z)
12
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
13
Sensitivities to ?? , ?8 , H0
Changes in ?? and w similar
change redshift when dark energy kicks
in combination of volume and growth function
Changes in ?8 effect (only the) exponential
term
not degenerate with any other parameter
H0 dependence weak, only via curvature in
P(k)
dN/dz(gtM/h) independent of H0 in power law limit
P?kn
14
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
15
(?M vs w) from 12 deg2 SZE survey
Haiman, Mohr Holder 2001
?M
w
Clusters alone 4 accuracy on ?0 40
constraint on w
16
Outline of Talk

1. Cosmological Sensitivity of Cluster Surveys
   what is
   driving the constraints?
2. Beyond Number Counts
   what can we learn from dN/dM,
   P(k), and scaling laws

17
Beyond Number Counts
Large surveys contain information in
addition to total number and redshift
distribution of clusters
Shape of dN/dM Power
Spectrum
Scaling relations
Advantages of combining ?S? and Tx

Goal complementary information provides an
internal cross-check on systematic errors
Degeneracies between cosmology
and cluster physics
different for each probe
(e.g. for dN/dz and for ?S? - Tx relation)
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Shape of dN/dM
work in progress
Change in dN/dM under 10 change in ?M (0.3
?0.33) Consider seven z-bins, readjust ?8 2 ?
significance for DUET sample of 20,000
clusters
encouraging, but must explore full degeneracy
space
19
Cluster Power Spectrum
Galaxy clusters highly biased
Large amplitude for PC(k) b2
P(k) Cluster bias (in
principle) calculable
Expected statistical errors on P(k)
FKP (Feldman, Kaiser Peacock
1994) signal-to-noise
increased by b2 25 rivals
that of SDSS spectroscopic sample
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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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Effect on the Cluster Power Spectrum
Neutrino Mass example m?0.2eV ??h2
0.002
Pure P(k) shape test
Courtesy W. Hu / DUET
CMB anisotropies
3D power spectrum
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(?M vs ?? ) from Cluster Power Spectrum
Cooray, Hu Haiman, in preparation
Use 3D power spectrum DUET improves CMB neutrino
limits factor of 10 over MAP factor of 2
over Planck (because of degeneracy breaking)
?M h2
DUETPlanck Accuracy ??h2 0.002
?? h2
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Angular Power Spectrum
Cooray, Hu Haiman, in preparation
To apply geometric dA(z) test from physical
scales of P(k) Cooray et al. 2001 Matter-radiatio
n equality scale keq ? ?Mh2 standard rod when
calibrated from CMB
?Mh2
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(?m vs w) from Angular Power Spectrum
Cooray, Hu Haiman, in preparation
Using geometric dA(z) test from physical
scales of P(k) Cooray et al. 2001
with 12,000 clusters
Projected 2D angular power spectrum in 5 redshift
bins between 0ltzlt0.5. clusters break
CMB degeneracies shrink confidence regions
?M h2
w
DUETPlanck w to 5
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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 (rivals
SDSS spectroscopic sample)
Expected statistical errors from
DUETPlanck ??h2 0.002
- shape test w to 5
- dA(z) test
Enough signal-to-noise to consider 3-4 z-
or M-bins evolution of
clustering peak bias theories /
non-gaussianity
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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 2001
27
Fundamental Plane (?S? ,TX, ?)
Verde, Haiman Spergel 2001
Plane shape sensitive to cosmology and
cluster structure ? Tests the origin
of scatter
28
(?S? ,TX) scaling relations dN/dz test
work in preparation
Using a sample of 200 clusters Different Mmin -
?0 degeneracies
? can check on systematics
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Conclusions

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