Cosmological Constraints from the SDSS maxBCG Cluster Sample

1. Cosmological Constraints from the SDSS maxBCG Cluster Sample Eduardo Rozo Einstein Fellows Symposium Oct 28, 2009

2. People: Risa Wechsler Erin Sheldon David Johnston Eli Rykoff Gus Evrard Tim McKay Ben Koester Jim Annis Matthew Becker Jiangang-Hao Joshua Frieman David Weinberg

3. Summary • Principal maxBCG constraint: S8 = 8(M/0.25)0.41= 0.8320.033. • maxBCG constraint on S8 is of higher precision than and consistent with WMAP5 constraint on the same quantity. • maxBCG constraint is comparable to and consistent with those derived from X-ray studies: • clusters are a robust cosmological probe • cluster systematics are well understood! • Cluster abundances constrain the growth of structure. As such, clusters are fundamentally different from geometric dark energy probes such as SN or BAO. • Everything we have done with SDSS we can repeat with DES: the best is yet to come!

4. Constraining Cosmology with Cluster Abundances

5. The Star of the Show: 8 8 parameterizes the amplitude of the matter power spectrum at z=0. Large 8 - The z=0 universe is very clumpy. Small 8 - The z=0 universe is fairly homogeneous. Why is this measurement important? - It can help constrain dark energy. CMB measures inhomogeneities at z~1200. CMB + GR + Dark Energy model = unique prediction for 8 Comparing the CMB prediction to local 8 measurements allows one to test dark energy/modified gravity models.

6. How to Measure 8 with Clusters The number of clusters at low redshift depends sensitively on 8. 8=1.1 Number Density (Mpc-3) 8=0.9 8=0.7 Mass

7. How to Measure 8 with Clusters The number of clusters at low redshift depends sensitively on 8. 8=1.1 Number Density (Mpc-3) Simple! To measure 8, just count the number of galaxy clusters as a function of mass. 8=0.9 8=0.7 Mass

8. Problem is, we don’t see mass… Must rely instead on mass tracers (e.g. galaxy counts).

9. Data

10. maxBCG maxBCG is a red sequence cluster finder - looks for groups of uniformly red galaxies.

11. The Perseus Cluster

12. The maxBCG Catalog maxBCG is a red sequence cluster finder - looks for groups of uniformly red galaxies. • Catalog covers ~8,000 deg2 of SDSS imaging with 0.1 < z < 0.3. • Richness N200 = number of red galaxies brighter than 0.4L* (mass tracer). • ~13,000 clusters with ≥ 10 (roughly M200c~3•1013 M). • 90% pure. • 90% complete. Main observable: n(N200)- no. of clusters as a function of N200.

13. Understanding the Richness-Mass Relation: The maxBCG Arsenal • Lensing: measures the mean mass of clusters as a function of richness (Sheldon, Johnston). • X-ray: measurements of the mean X-ray luminosity of maxBCG clusters as a function of richness (Rykoff, Evrard). • Velocity dispersions: measurements of the mean velocity dispersion of galaxies as a function of richness (Becker, McKay). These measurements are all based on cluster stacks. Only possible thanks to the large number of clusters in the sample.

14. LX Richness The X-ray Luminosity of maxBCG Clusters Stack RASS fields along cluster centers to measure the mean X-ray luminosity as a function of richness.

15. Cosmology

16. Summary of Analysis Observables: • n(N200) - cluster counts as a function of richness • Weak lensing cluster masses • Scatter in mass at fixed richness (ask me later if interested). Model (6 parameters): • n(M,z) - cluster counts as a function of mass (Tinker et al., 2008). • Mean richness-mass relation is a power-law (2 parameters). • Scatter of the richness-mass relation is mass independent (1 parameter). • Flat CDM cosmology (2 relevant parameters, 8 andM). • Allow for a systematic bias in lensing mass estimates (1 parameter).

17. Cosmological Constraints 8(M/0.25)0.41 = 0.832  0.033 Joint constraints: 8 = 0.8070.020 M = 0.2650.016

18. Systematics • We have explicitly checked our result is robust to: • Moder changes in the purity and completeness of the maxBCG sample. • Allowing other comsological parameters to vary (h, n, m). • Curvature in the mean richness-mass relation ln |M. • Mass dependence in the scatter of the richness-mass relation. • Removing the lowest and highest richness bins. • The cluster abundance normalization condition does depend on: • Prior on the bias of weak lensing mass estimates. • Prior on the scatter of the richness-mass relation. Current constrains are properly marginalized over our best estimates of the relevant systematics.

19. Comparison to X-rays

20. Cosmological Constraints from maxBCG are Consistent with and Comparable to those from X-rays includes WMAP5 priors

21. Cosmological Constraints from maxBCG are Consistent with and Comparable to those from X-rays This agreement is a testament to the robustness of galaxy clusters as cosmological probes, and demonstrates that cluster abundance systematics are well understood. includes WMAP5 priors

22. Cluster Abundances and Dark Energy

23. Cluster Abundances and Dark Energy WMAP+BAO+SN: WMAP+BAO+SN+maxBCG: w=-0.9950.067 w=-0.9910.053 (20% improvement)

24. A More Interesting Way to Read this Plot wCDM+WMAP5+SN+GR predict 8m0.4 to ~10% accuracy Cluster abundances test this prediction with a 5% precision level WMAP+BAO+SN: WMAP+BAO+SN+maxBCG: w=-0.9950.067 w=-0.9910.053 (20% improvement)

25. The Future

26. Prospects for Improvement Many prospects for improvement: • Cross check maxBCG results using velocity dispersions as a completely independent mass calibration data set. • Improve the quality of richness measures as a mass tracer. • Improved understanding of the scatter of the richness-mass relation. • Improved cluster centering. • Improved weak lensing calibration. • Add more cluster observables (e.g. 2pt function). • Improved mass calibration from Chandra and SZA follow up of clusters.

27. Prospects for Improvement Most important prospect for improvement: the Dark Energy Survey (DES) The analysis that we have carried out with the maxBCG cluster catalog can be replicated for cluster catalogs derived from the DES. Furthermore, these analysis can be cross-calibrated with other surveys (e.g. SPT, eRosita), which can further improve dark energy constraints (see e.g. Cunha 2008). The future of precision cluster cosmology look very bright indeed!

28. Summary • Principal maxBCG constraint: S8 = 8(M/0.25)0.41= 0.8320.033. • maxBCG constraint on S8 is of higher precision than and consistent with WMAP5 constraint on the same quantity. • maxBCG constraint is comparable to and consistent with those derived from X-ray studies: • clusters are a robust cosmological probe • cluster systematics are well understood! • Cluster abundances constrain the growth of structure. As such, clusters are fundamentally different from geometric dark energy probes such as SN or BAO. • Everything we have done with SDSS we can repeat with DES: the best is yet to come!

29. Constraining the Scatter in Mass at Fixed Richness

30. Constraining the Scatter Between Richness and Mass Using X-ray Data Consider P(M,LX|Nobs). Assuming gaussianity, P(M,LX|Nobs) is given by 5 parameters: M|Nobs LX|Nobs (M|Nobs) (LX|Nobs) r [correlation coefficient] Known (measured in stacking). Individual ROSAT pointings give the scatter in the M - LX relation. We can use our knowledge of the M - LX relation to constrain the scatter in mass!

31. The Method Assumea value for (M|Nobs) and r. Note this fully specifies P(M,LX|Nobs). For each cluster in the maxBCG catalog, assign M and LX using P(M,LX|Nobs). Select a mass limited subsample of clusters, and fit for LX-M relation. If assumed values for (M|Nobs) and r are wrong, then the “measured” X-ray scaling with mass will not agree with known values. Explore parameter space to determine regions consistent with our knowledge of the LX - M relation.

32. ln M|N ≈ 0.45 Scatter in the Mass - Richness Relation Using X-ray Data r (Correlation Coef.) ln M|N

33. Final Result ln M|N ≈ 0.45 +/- 0.1 r > 0.85 (95% CL) Probability Density Scatter in mass at fixed richness