1. Some issues in cluster cosmology
Tim McKay
University of Michigan
Department of Physics
12/7/2018
CFCP Dark Energy Workshop

2. CFCP Dark Energy Workshop
An outline
Cluster counting in theory
Cluster counting in practice
General considerations
Optical cluster selection
Weak lensing cluster surveys
Imagining the future
12/7/2018
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
12/7/2018
CFCP Dark Energy Workshop

4. Cluster detection methods
How do we measure mass peaks in 3D?
We don’t
12/7/2018
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
12/7/2018
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!
12/7/2018
CFCP Dark Energy Workshop

7. Relating cluster counts to the predicted dn/dM
Usually this relation is written:
In reality this should be something like:
12/7/2018
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)
12/7/2018
CFCP Dark Energy Workshop

9. CFCP Dark Energy Workshop
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)
12/7/2018
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
12/7/2018
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
12/7/2018
CFCP Dark Energy Workshop

12. CFCP Dark Energy Workshop
12/7/2018
CFCP Dark Energy Workshop

13. SDSS ‘maxBCG’ cluster catalog Jim Annis (FNAL)
An example cluster at z=0.15
E/S0 ridgeline
12/7/2018
CFCP Dark Energy Workshop

14. SDSS ‘maxBCG’ cluster catalog Jim Annis (FNAL)
Redshift estimates tested by > 104 spectra
12/7/2018
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
12/7/2018
CFCP Dark Energy Workshop

16. Mass calibration for maxBCG clusters
Calibration of mass (v) from weak lensing vs. Ngals
Distribution of Ngals(M)?
12/7/2018
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
12/7/2018
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.
12/7/2018
CFCP Dark Energy Workshop

19. CFCP Dark Energy Workshop
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…)
12/7/2018
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
12/7/2018
CFCP Dark Energy Workshop

21. critical: Important geometry dependence   ’ 
Observer
Source
Lens Ds
Dds Dd
12/7/2018
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.
12/7/2018
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.
12/7/2018
CFCP Dark Energy Workshop

24. CFCP Dark Energy Workshop
Survey to 25th magnitude
Dotted lines:
Detected
Dashed lines:
Detected with an incorrect source z distribution!
Virgo ‘truth’
M>5x1013Msun
M>1x1014Msun
12/7/2018
CFCP Dark Energy Workshop

25. CFCP Dark Energy Workshop
Survey to 28th magnitude
Dotted lines:
Detected
Dashed lines:
Detected with an incorrect source z distribution!
M>5x1013Msun
M>1x1014Msun
12/7/2018
CFCP Dark Energy Workshop

26. CFCP Dark Energy Workshop
Survey to 30th magnitude
Dotted lines:
Detected
Dashed lines:
Detected with an incorrect source z distribution!
M>5x1013Msun
M>1x1014Msun
12/7/2018
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….)
12/7/2018
CFCP Dark Energy Workshop

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!
12/7/2018
CFCP Dark Energy Workshop

29. Combined Foreground lens Background lens
Example of projection effects from White, van Waerbeke, and Mackey
12/7/2018
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)
12/7/2018
CFCP Dark Energy Workshop

31. CFCP Dark Energy Workshop
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
12/7/2018
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
12/7/2018
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?)
12/7/2018
CFCP Dark Energy Workshop