Some issues in cluster cosmology

1
Some issues in cluster cosmology

• Tim McKay
• University of Michigan
• Department of Physics

2
An outline

• Cluster counting in theory
• Cluster counting in practice
• General considerations
• Optical cluster selection
• Weak lensing cluster surveys
• Imagining the future

3
Cluster counting constraints on the expansion
history

• Probing growth of linear perturbations by
  measuring the space density of the largest peaks
• Theorists 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

4
Cluster detection methods

• How do we measure mass peaks in 3D?

We dont
5
Whats 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

6
Whats 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!

7
Relating cluster counts to the predicted dn/dM

• Usually this relation is written

8
Cluster detection methods observers 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 Mf(observable)
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)

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

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 ltgt redshift find clusters of objects with
  tightly clustered colors
• Provides good redshifts and projection is not an
  issue

12
(No Transcript)
13
SDSS maxBCG cluster catalog Jim Annis (FNAL)
An example cluster at z0.15
E/S0 ridgeline
14
SDSS maxBCG cluster catalog Jim Annis (FNAL)
Redshift estimates tested by gt 104 spectra
15
How do we compare maxBCG to clusters of mass?

• Do all clusters of mass have red sequence
  ellipticals? gt 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
16
Mass calibration for maxBCG clusters

• Calibration of mass (?v) from weak lensing vs.
  Ngals
• Distribution of Ngals(M)?

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

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.
19
How to measure shear?

• Intrinsic shapes are elliptical and unknown
  (?mean?0.3)
• gt 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)

20
Size magnitude relation
25th magnitude
Ground gt0.3 half light radius Space gt0.05
half light radius
Gardner Satyapal Sizes from STIS HDF south
images
21
?critical Important geometry dependence
22
Some model lensing data sets

• Ground based R25 (size limited)
• Space based R28
• Space based R30
• Apply these observations to the Virgo
  simulation cluster catalogs from Evrard et al.

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.
24
Survey to 25th magnitude

• Dotted lines
• Detected
• Dashed lines
• Detected with an incorrect source z distribution!

Virgo truth Mgt5x1013Msun Mgt1x1014Msun
25
Survey to 28th magnitude

• Dotted lines
• Detected
• Dashed lines
• Detected with an incorrect source z distribution!

Mgt5x1013Msun Mgt1x1014Msun
26
Survey to 30th magnitude

• Dotted lines
• Detected
• Dashed lines
• Detected with an incorrect source z distribution!

Mgt5x1013Msun Mgt1x1014Msun
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.)

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!
29
Combined Foreground lens Background lens
Example of projection effects from White, van
Waerbeke, and Mackey
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 zlt0.15)

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?
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

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?)