Some issues in cluster cosmology

Transcription

1 Some issues in cluster cosmology Tim McKay University of Michigan Department of Physics 1/30/2002 CFCP Dark Energy Workshop 1

2 An outline Cluster counting in theory Cluster counting in practice General considerations Optical cluster selection Weak lensing cluster surveys Imagining the future 1/30/2002 CFCP Dark Energy Workshop 2

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 R 200 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 1/30/2002 CFCP Dark Energy Workshop 3

4 Cluster detection methods How do we measure mass peaks in 3D? We don t 1/30/2002 CFCP Dark Energy Workshop 4

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 1/30/2002 CFCP Dark Energy Workshop 5

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 σ v, shear.. To approach dn/dm vs. z we need to know: M(observables,z) Efficiency(observables, z) The mass function is very steep! 1/30/2002 CFCP Dark Energy Workshop 6

7 Relating cluster counts to the predicted dn/dm Usually this relation is written: dn dωdz = dv dωdz M zlim dn dvdm dm In reality this should be something like: dn dωdz = dv dωdz z b ( ) ( ),, 0 dn dvdm z dm do zemozdo g 1/30/2002 CFCP Dark Energy Workshop 7

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) 1/30/2002 CFCP Dark Energy Workshop 8

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, F x, T x, σ gal, lensing, N gal, etc. We need to count all clusters: absolute efficiency required fundamentally a Poisson limited process (cosmic variance) 1/30/2002 CFCP Dark Energy Workshop 9

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 1/30/2002 CFCP Dark Energy Workshop 10

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 1/30/2002 CFCP Dark Energy Workshop 11

12 1/30/2002 CFCP Dark Energy Workshop 12

13 SDSS maxbcg cluster catalog Jim Annis (FNAL) An example cluster at z=0.15 E/S0 ridgeline 1/30/2002 CFCP Dark Energy Workshop 13

14 SDSS maxbcg cluster catalog Jim Annis (FNAL) Redshift estimates tested by > 10 4 spectra 1/30/2002 CFCP Dark Energy Workshop 14

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 N gals, z, and a luminosity. How do these relate to mass? Uncertainties here affect both efficiency and mass estimation 1/30/2002 CFCP Dark Energy Workshop 15

16 Mass calibration for maxbcg clusters Calibration of mass (σ v ) from weak lensing vs. N gals Distribution of N gals (M)? 1/30/2002 CFCP Dark Energy Workshop 16

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 1/30/2002 CFCP Dark Energy Workshop 17

18 How to find masses from lensing: Tangential shear is related to density contrast γ θ Σ = Σ < θ Σ θ T af crit a f af Σ crit is the surface mass density for multiple lensing Measure γ T and Σ crit and you have the surface mass density contrast. Deriving a mass from this still requires model fitting. 1/30/2002 CFCP Dark Energy Workshop 18

19 How to measure shear? Intrinsic shapes are elliptical and unknown (ε 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 ) 1/30/2002 CFCP Dark Energy Workshop 19

20 Size magnitude relation 25 th magnitude Ground: >0.3 half light radius Space: >0.05 half light radius Gardner & Satyapal: Sizes from STIS HDF south images 1/30/2002 CFCP Dark Energy Workshop 20

21 Σ critical : Important geometry dependence D s Source α θ ξ α Observer Lens β Σ critical c D ds D d D F 2 s = = 035. G DD d ds cm H G 2 4π g D 1Gpc I KJ 1 1/30/2002 CFCP Dark Energy Workshop 21

22 Some model lensing data sets 1. Ground based R=25 (size limited) 2. Space based R=28 3. Space based R=30 Apply these observations to the Virgo simulation cluster catalogs from Evrard et al. 1/30/2002 CFCP Dark Energy Workshop 22

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. 1/30/2002 CFCP Dark Energy Workshop 23

24 Survey to 25 th magnitude Dotted lines: Detected Dashed lines: Detected with an incorrect source z distribution! Virgo truth M>5x10 13 M sun M>1x10 14 M sun 1/30/2002 CFCP Dark Energy Workshop 24

25 Survey to 28 th magnitude Dotted lines: Detected Dashed lines: Detected with an incorrect source z distribution! M>5x10 13 M sun M>1x10 14 M sun 1/30/2002 CFCP Dark Energy Workshop 25

26 Survey to 30 th magnitude Dotted lines: Detected Dashed lines: Detected with an incorrect source z distribution! M>5x10 13 M sun M>1x10 14 M sun 1/30/2002 CFCP Dark Energy Workshop 26

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.) 1/30/2002 CFCP Dark Energy Workshop 27

28 Cluster detection: peaks in the projected mass Projection effects and dark clusters : White, van Waerbeke and Mackey astro-ph/ Combined methods: find in optical, measure with lensing, understand projection? Very bad on a steeply falling spectrum! 1/30/2002 CFCP Dark Energy Workshop 28

29 Combined Foreground lens Background lens Example of projection effects from White, van Waerbeke, and Mackey 1/30/2002 CFCP Dark Energy Workshop 29

30 Virgo simulations of Evrard et al. astroph/ Shows dn/dm for 16 independent local universes (5000 square degrees to z<0.15) An additional concern: cosmic variance in cluster normalization 1/30/2002 CFCP Dark Energy Workshop 30

31 Cosmic variance and σ 8 Interpreting dn/dm for cosmology requires σ 8 constraints from local universe. Cosmic variance is about 0.06 Local counts to 6x10 14 M 1/30/2002 CFCP Dark Energy Workshop 31

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 1/30/2002 CFCP Dark Energy Workshop 32

33 Clusters for cosmology Imagine having: SZe, z, F x, T x, σ gal, lensing, N gal, etc. This will allow systematic control analogous to Sne Still need to know absolute number (cosmic variance, dark clusters?) 1/30/2002 CFCP Dark Energy Workshop 33