1. Cosmology with Galaxy Clusters Princeton University Zoltán Haiman Dark Energy Workshop, Chicago, 14 December 2001 Collaborators: 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. } II. } III.

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 Constraints using dN/dz of ~18,000 clusters in a wide angle X-ray survey (Don Lamb’s talk) Planck measurements of CMB anisotropies 2,400 Type Ia SNe from SNAP MMMM  -  M to ~1% -   to ~5% Z. Haiman / DUET Power comparable to:

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

6. Observables in Future Surveys SZ decrement: X-ray flux:

7. Predicting the Limiting Masses Overall value of M min : 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 redshift log(M/M ⊙ ) X-ray survey SZE survey w = -0.6 w = -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 H 0 dependency: M ∝ H 0 -1 XR: flux=5x10 -14 erg s -1 cm -2 SZ: 5  detection in mock SZA observations (hydro sim.)

9. Which Effect is Driving Constraints? Fiducial  CDM cosmology: Examine sensitivity of dN/dz to five parameters  M, w,  , H 0,  8 by varying them individually.  M = 0.3   = 0.7 w = -1 (=  ) H 0 = 72 km s -1 Mpc -1  8 = 1 n = 1 Assume that we know local abundance N(z=0)

10. Sensitivity to  M in SZE Survey 12 deg 2 SZE survey  M =0.27  M =0.30  M =0.33 dN/dz shape relatively insensitive to  M Sensitivity driven by  8 change  M effects local abundance: N(z=0) ∝  M →  8 ∝  M -0.5 Haiman, Mohr & Holder 2001

11. Sensitivity to w in SZE Survey 12 deg 2 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) Haiman, Mohr & Holder 2001

12. Sensitivity to  M,w in X-ray Survey w=-1 w=-0.6 w=-0.2 Sensitivity driven by M min  M =0.27  M =0.30  M =0.33 Sensitivity driven by  8 change w MM 10 4 deg 2 X-ray survey Haiman, Mohr & Holder 2001

13. Sensitivities to Sensitivities to  ,  8, H 0 Changes in   and w similar Changes in  8 effect (only the) exponential term H 0 dependence weak, only via curvature in P(k) not degenerate with any other parameter dN/dz(>M/h) independent of H 0 in power law limit P ∝ k n change redshift when dark energy kicks in combination of volume and growth function

14. When is Mass Limit Important? in the sense of driving the cosmology-sensitivity 00 wH0H0  SZno XRnoyesno overwhelmed by  8 -sensitivity if local abundance held fixed

15. (  M vs w) from 12 deg 2 SZE survey 33 1  2  Constraints using ~200 clusters vs 1% measurement of CMB peak location or 1% determination of d l (z=1) from SNe Clusters alone: ~4% accuracy on  0 ; ~40% constraint on w MM w Haiman, Mohr & Holder 2001

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 T x 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 - T x relation)

18. Shape 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]

19. Cluster Power Spectrum Galaxy clusters highly biased: Large amplitude for P C (k) = b 2 P(k) Cluster bias (in principle) calculable Expected statistical errors on P(k) FKP (Feldman, Kaiser &Peacock 1994) “signal-to-noise” increased by b 2 ~25 rivals that of SDSS spectroscopic sample

20. Cluster 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 

21. Effect on the Cluster Power Spectrum Courtesy W. Hu / DUET Neutrino Mass example m =0.2eV  h 2 ≈ 0.002 Pure P(k) “shape test” CMB anisotropies 3D power spectrum

22. (  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 h 2  h 2 DUET+Planck Accuracy  h 2 ~ 0.002

23. Angular Power Spectrum Cooray, Hu & Haiman, in preparation To apply geometric d A (z) test from physical scales of P(k) Cooray et al. 2001 Matter-radiation equality scale k eq ∝  M h 2 “standard rod” when calibrated from CMB Mh2Mh2

24. (  m vs w) from Angular Power Spectrum Cooray, Hu & Haiman, in preparation Projected 2D angular power spectrum in 5 redshift bins between 0<z<0.5. clusters break CMB degeneracies & shrink confidence regions with ~12,000 clusters  M h 2 w Using geometric d A (z) test from physical scales of P(k) Cooray et al. 2001 DUET+Planck: w ~ to 5%

25. Cluster 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:  h 2 ~ 0.002 - shape test w ~ to 5% - d A (z) test Enough “signal-to-noise” to consider 3-4 z- or M-bins: evolution of clustering peak bias theories / non-gaussianity

26. SZE and X-ray Synergy Verde, Haiman & Spergel 2001  S T X  S - T X scaling relation expected to have small scatter: (1) SZ signal robust (2) effect of cluster ages Using scaling relations, we can simultaneously Probe cosmology and test cluster structure SZ decrement vs TemperatureSZ decrement vs Angular size

27. Fundamental Plane: (  S,T X,  ) Verde, Haiman & Spergel 2001 Plane shape sensitive to cosmology and cluster structure  Tests the origin of scatter

28. (  S,T X ) scaling relations + dN/dz test work in preparation Using a sample of ~200 clusters Different M min -  0 degeneracies  can check on systematics systematics

29. 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?