1. Cosmological Constraints from the maxBCG Cluster Sample Eduardo Rozo October 12, 2006 In collaboration with: Risa Wechsler, Benjamin Koester, Timothy McKay, August Evrard, Erin Sheldon, David Johnston, James Annis, and Joshua Frieman.

2. What Should You Get Out of This Talk Dark energy affects growth of inhomogeneities. Measuring the magnitude of inhomogeneities in early universe (from CMB) and at the present epoch can place constraints on dark energy. The number of galaxy clusters is a sensitive probe of the degree of inhomogeneity of the universe. Using clusters of galaxies to place cosmological constraints requires a good understanding of the cluster selection function. We introduce a formalism to properly account these difficulties, and find that the maxBCG cluster sample from the SDSS can provide some cosmological constraints even after marginalizing over uncertainties in the selection function. A better understanding of the selection function is still needed. Additional data, e.g. weak lensing measurements of maxBCG clusters, will help tighten our constraints.

3. The Preposterous Universe Dark energy (75%) Dark matter (20%) Ordinary matter (5%) We know next to nothing about dark matter. We know nothing about dark energy other than how much of it there is. Figure taken from Sean Carroll’s webpage

4. How Can Dark Energy be Constrained? Dark energy affects the distance to a given redshift. SNIa measures distances in an interval z~0-1. CMB constrains distance to last scattering. Dark energy also affects the growth of structure. Can we draw a similar picture in this case?

5. Structure Formation The number density of halos is a powerful probe of dark matter clustering.

6. Structure Formation The rate at which structure grows depends on dark energy. CDM LCDM z = 3 z = 1 z = 0 Measuring the amplitude of fluctuations at two vastly different epochs can set constraints on dark energy.

7. A Key Question: Just How Clumpy is the Universe Today? The growth of structure is a powerful probe of dark energy. We know how clumpy the early universe was thanks to the CMB. We don’t know how clumpy the universe is today. Main difficulty: we see galaxies, but we are interested in how the matter is distributed. We need ways for measuring the clumpiness (i.e. clustering amplitude) of matter at the present epoch:  8. We can use halo counting to measure  8.

8. Halo Counting to Measure  8 More clumpiness (higher  8 ) More massive halos.  8 =1.1  8 =0.7  8 =0.9

9. Halo Counting to Measure Clumpiness 1- Identify large halos as galaxy clusters (maxBCG). 2- Count the number of galaxies in each cluster (richness), a proxy for halo mass. 3- Plot No. of clusters vs. richness and compare to predictions. Recipe for measuring  8 :

10. Finding Galaxy Clusters: The maxBCG Algorithm Clusters have a population of early type galaxies that define a very narrow ridgeline in color-magnitude space. 1.Label bright galaxies in ridgeline relation as candidate Brightest Cluster Galaxies (BCGs). 2.Use model for radial and color distribution of galaxies in clusters to compute likelihood of candidate BCGs. 3.Rank order candidate BCGs by likelihood. Top most candidate is included in the catalog along with its member galaxies. All members are dropped from the candidate BCG list. Iterate. A broad brush description: Galaxy membership criteria: must have ridgeline colors, be brighter than some cutoff, and be within a specified scaled aperture.

11. Perseus as Imaged by the SDSS

12. A Sample Cluster

13. A Quick Comparison to X-ray Clusters We match maxBCG clusters to X-ray clusters from the NORAS and REFLEX surveys. Of 97 X-ray clusters in, we find: 79 (~80%) are well matched (centers agree within 250 h -1 kpc) 18 are not well matched. Of the 18 poor matches,we find: 6 clusters with likely X-ray contamination. 6 clusters with blue BCGs. 2 merging systems. 4 systems with ambiguous BCGs.

14. Halo Counting to Measure Clumpiness 1- Identify large halos as galaxy clusters (maxBCG). 2- Count the number of galaxies in each cluster (richness), a proxy for halo mass. 3- Plot No. of clusters vs. richness and compare to predictions. Recipe for measuring  8 : Can we actually do this?

15. Selection Function: Letting the Genie out of the Bottle

16. Selection Function Want to count halos of a given mass to measure  8. However… Can we find all halos? (completeness) Are all detections real? (purity) We predict number of halos of a given mass. We observe number of clusters of a given richness. How are these two related?

17. Selection Function P(R obs |m) = probability a halo of mass m is detected as a cluster of richness R obs. What we mean by selection function: If we knew the selection function, we could predict the no. of clusters we will observe in various cosmologies. N(R obs ) =  n(m)*P(R obs |m) Number of clusters (what we observe) Number of halos (what we predict) Selection function We need to properly model the selection function.

18. Modeling the Selection Function We assume detecting a cluster is a two step process: 1- The halo has some probability P(R true |m) of having R true galaxies (HOD). 2- We have a probability P(R obs |R true ) of finding the halo as a cluster with R obs galaxies. Assume this is a property of the cluster finding algorithm! (Selection Function). Measure P(R obs |R true ) directly from simulations. (Will depend on how clusters are matched to halos)

19. Calibration of the Selection Function signal noise Completeness Purity

20. Signal and Noise c(R true ) = fraction of halos in signal band - completeness. P(R obs |R true ) = c(R true )P S (R obs |R true ) + P N (R obs |R true ) We can calibrate these.Hard to calibrate. We do not need to know this! Only need to know fraction of clusters that are “noise” - purity.

21. Completeness

22. Purity

23. The maxBCG cluster sample is highly pure and complete.

24. Does the Model Work?

25. The Model Works

26. Agreement is not trivial. Our model accurately describes the halo selection function.

27. Can We Recover Physical Parameters ?

28. Knowledge of selection function Percent lever accuracy in parameter estimation. Includes “traditional” systematics - e.g. projection effects. maxBCG can in principle be a useful tool for precision cosmology.

29. Uncertainties in the Selection Function Result in Larger Error Bars Percent Level Priors on Selection Function Parameters

30. Applying the Method to Data Different simulations had different selection functions. Use generous priors on selection function. Use priors on cosmological parameters from other data sets (  m h 2 from CMB, h from SN). Use theoretical prior on slope of HOD (how galaxies populate halos). Can still provide meaningful constraints on the power spectrum amplitude  8.

31. Applying the Method to Data

32. End Result  8 = 1.05 +/- 0.12  = 0.76 +/- 0.05 (selection function prior)  8 = 0.92 +/- 0.11 (HOD prior:  =1.00 +/- 0.05) HOD + selection function prior.

33. Trouble? Selection function priors and theoretical HOD priors are inconsistent.

34. End Result  8 = 1.05 +/- 0.12  = 0.76 +/- 0.05 (selection function prior)  8 = 0.92 +/- 0.11 (HOD prior:  =1.00 +/- 0.05) HOD + selection function prior.

35. Caveats and Future Work Can we robustly characterize the selection function from simulations? Need more and better simulations. Is the selection function cosmology dependent? Need simulations for various cosmologies. Is there evolution in the selection function and/or richness-mass relation? Include evolution as a nuissance parameter. Is there curvature in the richness-mass relation? Use weak lensing date to relax richness-mass relation parameterization.

36. Summary and Conclusions Developed a new way for characterizing cluster selection function. Method allows for marginalization over uncertainties in selection function. Used simulations to prove method recovers simulation parameters with percent level accuracy when selection function is known. Demonstrated maxBCG can be a powerful tool of precision cosmology; traditional systematics are not a difficulty. Application of method to data shows tension between selection function calibration and theoretical prior. More work is needed to fully realize the promise of cluster abundance methods for constraining cosmological parameters.