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?