Some issues in cluster cosmology

1. Some issues in cluster cosmology Tim McKay University of Michigan Department of Physics CFCP Dark Energy Workshop

2. An outline • Cluster counting in theory • Cluster counting in practice • General considerations • Optical cluster selection • Weak lensing cluster surveys • Imagining the future CFCP Dark Energy Workshop

3. Cluster counting constraints on the expansion history • Probing growth of linear perturbations by measuring the space density of the largest peaks Theorist’s cluster = mass peak to R200 • Counts, mass spectrum of halos • Analytic theory and N-body simulations predict dn/dM as a function of z • Cosmology comes from comparison of observed dn/dM vs. z to theory CFCP Dark Energy Workshop

4. Cluster detection methods How do we measure mass peaks in 3D? We don’t CFCP Dark Energy Workshop

5. What’s a ‘cluster’ made of? Large peak in matter density • Dark matter clump (~75% of mass) • Many luminous galaxies (~2.5%: 10% of baryons) • BCG and red sequence • Additional galaxies • Diffuse light • Hot gas (~22.5%: 90% of baryons) • Emits X-rays • Causes SZ decrement in microwave background CFCP Dark Energy Workshop

6. What’s are the cluster observables? Cluster detection measures something other than mass: some observables like SZe, X-ray flux, X-ray temperature, galaxy richness, galaxy v, shear….. To approach dn/dM vs. z we need to know: M(observables,z) Efficiency(observables, z) The mass function is very steep! CFCP Dark Energy Workshop

7. In reality this should be something like: Relating cluster counts to the predicted dn/dM Usually this relation is written: CFCP Dark Energy Workshop

8. Cluster detection methods: observer’s clusters • Clusters of galaxies: 2D, 2.5D, 3D • Clusters of hot gas: X-ray, Sunyaev-Zeldovitch • Clusters of projected mass: 2D, 2.1D? In every case we must learn the astrophysics to constrain M=f(observable) CFCP Dark Energy Workshop

9. Analogy to SNe For SNe, we want to know luminosity: measure spectrum, stretch, rise time, extinction, peak to tail ratio etc…. For clusters, we want to know mass: measure SZe, Fx, Tx, gal, lensing, Ngal, etc. We need to count all clusters: • absolute efficiency required • fundamentally a Poisson limited process (cosmic variance) CFCP Dark Energy Workshop

10. How will we learn what we need to know? • Study clusters through all these methods • Add extensions of structure formation modeling • Couple both through observations of scaling relations • Once we constrain clusters, we still need to understand observational effects • K-corrections, angular resolution effects, projection, sensitivity vs. z, noise correlations CFCP Dark Energy Workshop

11. Finding clusters of galaxies in 2D optical data • In the common wisdom this is plagued by projection • New methods rely on uniform colors of cluster ellipticals (they are all old) • Color <=> redshift: find clusters of objects with tightly clustered colors • Provides good redshifts and projection is not an issue CFCP Dark Energy Workshop

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13. SDSS ‘maxBCG’ cluster catalog Jim Annis (FNAL) An example cluster at z=0.15 E/S0 ridgeline CFCP Dark Energy Workshop

14. SDSS ‘maxBCG’ cluster catalog Jim Annis (FNAL) Redshift estimates tested by > 104 spectra CFCP Dark Energy Workshop

15. How do we compare maxBCG to clusters of mass? • Do all clusters of mass have red sequence ellipticals? => Galaxy evolution vs. environment • The observables are ‘Ngals’, z, and a luminosity. How do these relate to mass? Uncertainties here affect both efficiency and mass estimation CFCP Dark Energy Workshop

16. Mass calibration for maxBCG clusters Calibration of mass (v) from weak lensing vs. Ngals Distribution of Ngals(M)? CFCP Dark Energy Workshop

17. Finding clusters in the projected mass distribution • The weak lensing observable is shear, related to projected mass by a geometric filter • Weak lensing signal is independent of evolution in the baryons CFCP Dark Energy Workshop

18. How to find masses from lensing: ‘Tangential shear’ is related to density contrast crit is the surface mass density for multiple lensing Measure T and crit and you have the surface mass density contrast. Deriving a mass from this still requires model fitting. CFCP Dark Energy Workshop

19. How to measure shear? Intrinsic shapes are elliptical and unknown (mean0.3) => how to determine distortion? Strong lensing: distortions larger than intrinsic ellipticity Weak lensing: distortions smaller than intrinsic ellipticity Statistical measurement: many source galaxies required Must be able to measure the shape of each galaxy to use it Shear measurement requires correction of instrumental PSF and distortion effects. For stable PSFs new methods will allow this to arbitrary precision (Gary Bernstein later…) CFCP Dark Energy Workshop

20. Size magnitude relation 25th magnitude Ground: >0.3” half light radius Space: >0.05” half light radius Gardner & Satyapal: Sizes from STIS HDF south images CFCP Dark Energy Workshop

21. Ds  ’  Source  Observer Lens  Dds Dd critical:Important geometry dependence CFCP Dark Energy Workshop

22. Some model lensing data sets • Ground based R=25 (size limited) • Space based R=28 • Space based R=30 Apply these ‘observations’ to the Virgo simulation cluster catalogs from Evrard et al. CFCP Dark Energy Workshop

23. Basics for three surveys: why go so faint? Basic geometry is similar for the three surveys. Sensitivity changes due to source density. Lensing S/N is much higher for a deeper space based survey. Sensitivity tilted to low-z. CFCP Dark Energy Workshop

24. Survey to 25th magnitude • Dotted lines: • Detected • Dashed lines: • Detected with an incorrect source z distribution! Virgo ‘truth’ M>5x1013Msun M>1x1014Msun CFCP Dark Energy Workshop

25. Survey to 28th magnitude • Dotted lines: • Detected • Dashed lines: • Detected with an incorrect source z distribution! M>5x1013Msun M>1x1014Msun CFCP Dark Energy Workshop

26. Survey to 30th magnitude • Dotted lines: • Detected • Dashed lines: • Detected with an incorrect source z distribution! M>5x1013Msun M>1x1014Msun CFCP Dark Energy Workshop

27. What goes into formulating mass? • Cluster redshift • Source distribution (variance?) • Other mass projected along line of sight • Random • Associated (filaments etc.) • (X-ray and SZ are better….) CFCP Dark Energy Workshop

28. Cluster detection: peaks in the projected mass Projection effects and ‘dark clusters’: White, van Waerbeke and Mackey astro-ph/0111490 Combined methods: find in optical, measure with lensing, understand projection? Very bad on a steeply falling spectrum! CFCP Dark Energy Workshop

29. Combined Foreground lens Background lens Example of projection effects from White, van Waerbeke, and Mackey CFCP Dark Energy Workshop

30. An additional concern: cosmic variance in cluster normalization Virgo simulations of Evrard et al. astro-ph/011024 Shows dn/dM for 16 independent ‘local’ universes (5000 square degrees to z<0.15) CFCP Dark Energy Workshop

31. Cosmic variance and 8 Interpreting dn/dM for cosmology requires 8 constraints from local universe. Cosmic variance is about 0.06 Local counts to 6x1014M CFCP Dark Energy Workshop

32. Clusters for cosmology • Clusters make great cosmological probes • Very detectable • Evolution is approachable • Sensitive (exponential) dependence on cosmology • Clusters are complex: we must understand them better to use them for cosmology • Observing clusters is complex: measurements are projected CFCP Dark Energy Workshop

33. Clusters for cosmology Imagine having: SZe, z, Fx, Tx, gal, lensing, Ngal, etc. This will allow systematic control analogous to Sne Still need to know absolute number (cosmic variance, dark clusters?) CFCP Dark Energy Workshop