1. Cosmology with Galaxy Clusters Columbia University Zoltán Haiman Cosmology with SZ Cluster Surveys Chicago, 17-20 September 2003 Collaborators: Joe Mohr (Illinois) Gil Holder (IAS) Gil Holder (IAS) Wayne Hu (Chicago) Wayne Hu (Chicago) Licia Verde (U Penn) Licia Verde (U Penn) David Spergel (Princeton) David Spergel (Princeton)

2. cluster cosmology literaturemy contributions An overview?

3. Outline of Talk 1. Cosmological Sensitivity of Clusters – why clusters? – current constraints 2. Constraints from Future Samples – abundance evolution – power spectrum – SZ + X-ray synergy

4. Current Cosmology Constraints MMMM  Verde www (2003) CMB SN LSS (SCP) (WMAP+) (2dF) strong degeneracy in any single experiment

5. Why Galaxy Clusters? Theory: Clusters relatively simple objects. Evolution of massive cluster abundance determined by gravity. Clusters straddle the epoch of dark energy domination 0<z<3. Future observations: Current samples of tens of clusters soon to be replaced by thousands of clusters with mass estimates in dedicated large (SZE, X-ray, weak lensing) surveys Why Do We Need Yet Another Cosmological Probe? - Degeneracies differ from CMB, SNe, Galaxies - Systematics are different - Unique exponential dependence - Modelability (Impressive constraints - but dark energy still elusive)

6. An advantage unique to clusters? A cluster sample can deliver many observables SZE decrement X-ray flux Angular size Number of galaxies Spatial distribution (2d, 3d) Lensing signatures We can construct several cosmology tests dN/dz – abundance evolution (including mass function dN/dM) P(k) – spatial power spectrum (including Alcock-Paczynski) Scaling relations – between SZ/X-rays/sizes (including d A measurement) Simultaneous determination of cosmological and cluster structural parameters (with their evolution) Best? better good

7. Outline of Talk 1. Cosmological Sensitivity of Clusters – why clusters? – current constraints 2. Constraints from Future Samples – abundance evolution – power spectrum – SZ + X-ray synergy

8. Local Cluster Abundance Constraints - 63 bright X-ray clusters (REFLEX+) - Soft X-ray flux limit 2  10 -11 erg/s/cm 2 - 20,000 sq. degrees (half sky), z ~ 0 MMMM 8888 Reiprich & Böhringer (2002) Pierpaoli et al. (2003)

9. Cluster Abundance Evolution Constraints  w using dN/dT evolution 24 clusters at z<0.2 19 clusters at z>0.3 [marginalized over  8 ] Patrick Henry (2003) MMMM

10. Cluster Abundance Evolution Constraints w using dN/dT evolution 24 clusters at z<0.2 19 clusters at z>0.3 [marginalized over  8 ] Patrick Henry (2003) MMMM

11. Cluster Abundance Evolution Constraints MMMM w Schuecker et al. (2003) - 426 X-ray clusters (REFLEX sample) - Soft X-ray flux limit 3  10 -12 erg/s/cm 2 - 10,000 sq. degrees - redshifts 0<z<0.2  looses w constraint despite larger # depth very important!

12. Summary of Current Results Local Sample of ~ 100 clusters have constrained matter density and power spectrum normalization to accuracy comparable to other methods (CMB, SNe) Similar results for  M from cluster baryon fraction and mass/light arguments Dark energy constraints are not yet available, we need larger samples extending to larger distance (z~1) Current systematics are dominated by M-T relation, and are at the level of statistical errors Lin et al. (2003), Ostriker et al. (2003) Bridle et al. (2003) Pierpaoli et al. (2003)

13. Outline of Talk 1. Cosmological Sensitivity of Clusters – why clusters? – current constraints 2. Constraints from Future Samples – abundance evolution – power spectrum – SZ + X-ray synergy

14. 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

15. A note on the mass function Success: Simulations find a fitting formula that is accurate (to ~10 % in dN/dM) and is universal: cosmology scales out when mass is appropriately defined. However: We need to either understand this universality from first principles or have available a very large suite of simulations on a fine grid. Test runs? Encouraging: Original result in three, widely separated cosmologies recently also confirmed for w > -1. Also agrees with Press-Schechter scaling Linder & Jenkins (2003)

16. Observables in Future Surveys SZ decrement: X-ray flux: weak lensing shear….

17. 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 (Holder et al. 2001)

18. Which Effect is Driving Constraints? Pick fiducial  CDM cosmology: Compute dN/dz by varying five parameters  M, w,  , H 0,  8  M = 0.3   = 0.7 w = -1 H 0 = 72 km s -1 Mpc -1  8 = 0.9 n = 1 Evaluate likelihood (Fisher matrix, Monte Carlo) - depends on which parameter and survey - Haiman, Mohr & Holder (2001) Holder, Haiman & Mohr (2001) Weller, Battye & Kneissl (2002) Levine, Schultz & White (2002) Hu & Kravtsov (2003) Majumdar & Mohr (2003a,b) Hu (2003) Battye & Weller (2003)

19. Sensitivity to  M,w in SZE Survey overall scaling and  8 change Haiman, Mohr & Holder 2001 redshift 0123 dN/dz/12 deg 2  M =0.27  M =0.30  M =0.33 redshift 0123 volume (low-z) + growth (high-z) w=-1 w=-0.6 w=-0.2

20. Power & Complementarity Constraints using dN/dz of ~18,000 clusters in a wide angle X-ray survey (SPT gives similar results) 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:

21. Dark Energy Constraints Using 10 4 deg 2 X-ray ~20,000 clusters between 0 < z ≲ 1 (marginalized over H 0 and  8 ) Planck measurement of CMB anisotropies and polarization w  -  M to ~1% -w to ~5% DUET proposal J.Mohr/Z.Haiman

22. Time-dependence of w(z) w(z)=w 0 + w 1 z Fixed mass limit of 2×10 14 h -1 M ⊙ 4000 square degrees (=25,000 clusters) Errors from 4x4 Fisher matrix WMAP w 0 = -0.8  CDM w 1 = 0.3  = 0.01  = 0.01  8 = 0.006  8 = 0.005  w 0 = 0.12  w 0 = 0.10  w 1 = 0.25  w 1 = 0.19 (0.04) (0.03) Combine with P(k) with J. Khoury, cf Weller et al 2001

23. Outline of Talk 1. Cosmological Sensitivity of Clusters – why clusters? – current constraints 2. Constraints from Future Samples – abundance evolution – power spectrum – SZ + X-ray synergy

24. Cluster Power Spectrum Dependence on cosmological parameters cluster bias growth function redshift distortion transfer function Observable: inverse volume Radial modes: Transverse modes: Angular diameter distance Hubble constant Redshift distortion: Scales with growth function Geometry! (w/ physical scale info) } initial spectrum

25. Cluster Power Spectrum Galaxy clusters highly biased: Large amplitude for P C (k) = b 2 P(k) Cluster bias as calculable as mass function Expected statistical errors on P(k): FKP (Feldman, Kaiser & Peacock 1994) “signal-to-noise” increased by b 2 ~25 c.f. SDSS spectroscopic sample b 2 ~1

26. Ideal Tracers of Mass Hu & Haiman 2003 low-mass clusters and groups are not far from being ideal tracers out to z~1

27. 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 

28. Acoustic Rings in 2D Hu & Haiman (2003) Power spectrum is measured at fixed angular scale and redshift. Inferred spatial scales depend on the assumed cosmology Forms purely geometrical test, if CMB priors are used Insensitive to z-distortion (c.f. Alcock-Paczynski test)

29. Errors on D A (z) and H(z) Theorist’s surveys: Galaxies: 10,000 sq.deg M=10 12.1 h -1 M ⊙ at 0<z<0.1 (SDSS main) M=10 13.5 h -1 M ⊙ at 0<z<0.4 (SDSS LRG) Clusters: 4,000 sq.deg M=10 14.2 h -1 M ⊙ at 0<z<1.3 (SPT) - 25,000 clusters CMB priors Hu & Haiman 2003

30. Errors on w and  DE Hu & Haiman 2003 Filled ellipses: b marginalized to an overall scaling Empty ellipses: , b marginalized (b separately in each  z=0.1 bin) galaxies:  (w)=0.024  (  )=0.007 clusters:  (w)=0.040  (  )=0.013

31. 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% Expected statistical errors from 25,000 clusters:  M ~ to 0.013 - geometrical test w ~ to 0.04 - geometrical test  h 2 ~ to 0.002 - usual shape test  Combine with dN/dM (Majumdar & Mohr 2003) Noteworthy for survey planning - baryon rings are useful: contain ~ half the information make test robust (CMB,  ) - photometric redshift (0.01) sufficient to recover most of the info - including knowledge of bias would much improve constraints - z < 1 clusters are best complement to CMB

32. Outline of Talk 1. Cosmological Sensitivity of Clusters – why clusters? – current constraints 2. Constraints from Future Samples – abundance evolution – power spectrum – SZ + X-ray synergy

33. SZE and X-ray Synergy Verde, Haiman & Spergel 2002  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 Temperature SZ decrement vs Angular size

34. Fundamental Plane: (  S,T X,  ) Verde, Haiman & Spergel 2002 Plane shape sensitive to cosmology and cluster structure  Tests the origin of scatter

35. (  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

36. SZE and X-ray Synergy Molnar, Haiman, Birkinshaw & Mushotzky 2003, ApJ, submitted Assuming angular diameter (D A ) measurements of 100 clusters at 0<z<1.5 (0.5<z<1 has most power) combined with 12 deg 2 SZA sample MMMM MMMM  w

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

38. The End

39. Constraining w

40. Mass vs. Number of Galaxies Kravtsov et al. 2003

41. Where Does Information Come From? Hu & Haiman 2003

42. 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 affects local abundance: N(z=0) ∝  M →  8 ∝  M -0.5 Haiman, Mohr & Holder 2001 redshift 0123 dN/dz/12 deg 2

43. 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 redshift 0123 dN/dz/12 deg 2

44. 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

45. 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

46. Time-dependence of w(z) Weller et al. 2001 w(z)=w 0 + w 1 z SNAPPlanckSPTSZA [fiducial model: w 0 = -0.8, w 1 = 0.3] Weak limits but can be combined with the other tests