Cosmology with Galaxy Clusters Princeton University Zoltán Haiman Dark Energy Workshop, Chicago, 14...
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Transcript of Cosmology with Galaxy Clusters Princeton University Zoltán Haiman Dark Energy Workshop, Chicago, 14...
Cosmology with Galaxy ClustersCosmology with Galaxy Clusters
Princeton University
Zoltán Haiman
Dark Energy Workshop, Chicago, 14 December 2001
Collaborators: Collaborators: Joe Mohr (Illinois)Joe Mohr (Illinois) Gil Holder (IAS)Gil Holder (IAS) Wayne Hu (Chicago)Wayne Hu (Chicago) Asantha Cooray (Caltech)Asantha Cooray (Caltech) Licia Verde (Princeton)Licia Verde (Princeton) David Spergel (Princeton)David Spergel (Princeton)
} } I.I.
} } II.II.
} } III.III.
Outline of Talk 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
IntroductionIntroductionEra of “Precision Cosmology”:
Parameters of standard cosmological modelto be determined to high accuracy by CMB,Type Ia SNe, and structure formation (weaklensing, Ly forest) studies.
Future Galaxy Cluster Surveys:
Current samples of tens of clusters can be replacedby 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
Power & Complementarity Power & Complementarity
Constraints using dN/dzof ~18,000 clusters in awide angle X-ray survey (Don Lamb’s talk)
Planck measurementsof CMB anisotropies
2,400 Type Ia SNefrom SNAP
MM
M to ~1%
to ~5%
Z. Haiman / DUET
Power comparable to:
Galaxy Cluster AbundanceGalaxy Cluster AbundanceDependence on cosmological parameters
8.30 )]log(61.0[exp1
315.0 MzM
M
gdM
d
MdM
dn
growthfunction
powerspectrum (8, M-r)
JenkinsJenkinset al. 2001et al. 2001
minM dM
dndM
dzd
dV
dzd
dN
comoving volume
masslimit
massfunction
# of clusters per unit area and z:
mass function:
overallnormalization
Hubble volumeN-body simulationsin three cosmologiescf: Press-Schechter
)( 2hM )( 32rhM M
Observables in Future SurveysObservables in Future Surveys
2A
virvirICM2
CMB
2d
TMfTkndl
cm
σ
T
ΔTΔS eBe
e
T
2L
22L4
1
d
L)Λ(TndV
πdF X
eeX
SZ decrement:SZ decrement:
X-ray flux:X-ray flux:
Predicting the Limiting MassesPredicting 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)
Mass Limits and Dependence on wMass Limits and Dependence on w
redshift
log(
M/M
⊙)
X-ray surveyX-ray survey
SZE surveySZE survey
ww = -0.6= -0.6
ww = -0.9= -0.9
• X-ray surveys more sensitive to mass limit sensitivity amplified in the exponential tail of dN/dM
• w, M non-negligible sensitivity
• dependence weak
• H0 dependency: M ∝ H0
-1
XR: flux=5x10-14 erg s-1 cm-2
SZ: 5 detection in mock SZA observations (hydro sim.)
Which Effect is Driving Constraints?Which Effect is Driving Constraints?
• Fiducial CDM cosmology:
• Examine sensitivity of dN/dz to five parameters
M, w, , H0 , 8
by varying them individually.
M = 0.3 = 0.7w = -1 (= )
H0 = 72 km s-1 Mpc-1
8 = 1 n = 1
• Assume that we know local abundance N(z=0)
Sensitivity to Sensitivity to M M in SZE Surveyin SZE Survey
12 deg2 SZE survey
M=0.27M=0.30M=0.33
dN/dz shape relativelyinsensitive to M
Sensitivity drivenby 8 change
M M effects local abundance: effects local abundance: N(z=0) N(z=0) ∝∝ M M → → 88 ∝∝ MM-0.5-0.5
Haiman, Mohr & Holder 2001
Sensitivity to w in SZE SurveySensitivity to w in SZE Survey
12 deg2 SZE survey
w=-1w=-0.6w=-0.2
dN/dz shape flattens with w
Sensitivity driven by: volume (low-z) growth (high-z)
Haiman, Mohr & Holder 2001
Sensitivity to Sensitivity to MM,w in X-ray Survey,w in X-ray Survey
w=-1w=-0.6w=-0.2
Sensitivity driven by Mmin
M=0.27M=0.30M=0.33
Sensitivity driven by 8 change
w
M
104 deg2 X-ray surveyHaiman, Mohr & Holder 2001
Sensitivities to Sensitivities to , 8 , H0
• Changes in and w similar
• Changes in 8 effect (only the) exponential term
• H0 dependence weak, only via curvature in P(k)
not degenerate with any other parameter
dN/dz(>M/h) independent of H0 in power law limit P k∝ n
change redshift when dark energy kicks incombination of volume and growth function
When is Mass Limit Important?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-sensitivityif local abundance held fixed
((M M vs w) from 12 degvs w) from 12 deg22 SZE survey SZE survey
3
1 2
Constraints using~200 clusters
vs
1% measurement ofCMB peak location
or
1% determinationof dl(z=1) from SNe
Clusters alone: ~4% accuracy on 0; ~40% constraint on w
M
w
Haiman, Mohr & Holder 2001
Outline of Talk 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
Beyond Number CountsBeyond 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)
Shape of dN/dMShape of dN/dM
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
work in progress
[encouraging, but must explore full degeneracy space]
Cluster Power SpectrumCluster 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
kk
k
k
Pbnn
P
P2
2/1 11
Cluster Power Spectrum - AccuraciesCluster Power Spectrum - Accuracies
Z. Haiman / DUET~6,000 clusters in each of three redshift bins
P(k) determined to roughly the same accuracy in each z-bin
Accuracies: k/k=0.1 → 7% k<0.2 → 2%
NB: baryon “wiggles” are detectable at ~2
Effect on the Cluster Power SpectrumEffect on the Cluster Power Spectrum
Courtesy W. Hu / DUET
Neutrino MassNeutrino Mass example m=0.2eV h2≈ 0.002
Pure P(k) “shape test”
CMB anisotropiesCMB anisotropies
3D power spectrum3D power spectrum
((M M vs vs ) from Cluster Power Spectrum) from Cluster Power Spectrum
Cooray, Hu & Haiman, in preparation
Use 3D power spectrum
DUET improves CMBneutrino limits:
factor of ~10 over MAP factor of ~2 over Planck
(because of degeneracy breaking)
M
M
hh22
hh22
DUET+Planck Accuracy
h2 ~ 0.002
Angular Power SpectrumAngular Power Spectrum
Cooray, Hu & Haiman, in preparation
To apply geometric dA(z)
test from physical scales
of P(k) Cooray et al. 2001
Matter-radiation equality scale keq ∝ Mh2
“standard rod” when calibrated from CMB
Mh2
((m m vs w) from Angular Power Spectrumvs w) from Angular Power Spectrum
Cooray, Hu & Haiman, in preparation
Projected 2D angularpower spectrum in 5redshift bins between0<z<0.5.
clusters break CMBdegeneracies & shrinkconfidence regions
with ~12,000 clusters
M
M
hh22
ww
Using geometric dA(z)test from physical scalesof P(k) Cooray et al. 2001
DUET+Planck: w ~ to 5%
Cluster Power Spectrum - SummaryCluster Power Spectrum - Summary
• High bias of galaxy clusters enables accurate measurement of cluster P(k): k/k=0.1 → P(k) to 7% at k=0.1 k<0.2 → P(<k) to 2% (rivals SDSS spectroscopic sample)
• Expected statistical errors from DUET+Planck: 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
SZE and X-ray SynergySZE and X-ray Synergy
Verde, Haiman & Spergel 2001
SS - TTXX scaling relation expected to have small scatter: (1) SZ signal robust (2) effect of cluster ages
Using scaling relations, we can simultaneouslyProbe cosmology and test cluster structure
SZ decrement vs Temperature SZ decrement vs Angular size
Fundamental Plane: Fundamental Plane: ((SS ,T,TXX, , ))
Verde, Haiman & Spergel 2001
Plane shapePlane shapesensitive to sensitive to cosmologycosmologyand clusterand clusterstructurestructure
Tests theTests theorigin oforigin ofscatter scatter
((SS ,T,TXX) scaling relations + dN/dz test) scaling relations + dN/dz test
work in preparation
Using a sampleUsing a sampleof ~200 clustersof ~200 clusters
Different MDifferent Mminmin - - 00 degeneraciesdegeneracies
can check on can check on
systematicssystematics
Conclusions 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?