cosmology with galaxy clusters
DESCRIPTION
Cosmology with Galaxy Clusters. Zolt á n Haiman. Princeton University. Collaborators: Joe Mohr (Illinois) Gil Holder (IAS) Wayne Hu (Chicago) Asantha Cooray (Caltech) - PowerPoint PPT PresentationTRANSCRIPT
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?