Cosmological Constraints from the SDSS maxBCG Cluster Sample

1
Cosmological Constraints from the SDSS maxBCG
Cluster Sample
Eduardo Rozo
Einstein Fellows Symposium Oct 28, 2009
2
People Risa Wechsler Erin Sheldon David
Johnston Eli Rykoff Gus Evrard Tim McKay Ben
Koester Jim Annis Matthew Becker Jiangang-Hao Josh
ua Frieman David Weinberg
3
Summary

• Principal maxBCG constraint S8
  ?8(?M/0.25)0.41 0.832?0.033.
• maxBCG constraint on S8 is of higher precision
  than and consistent with WMAP5 constraint on the
  same quantity.
• maxBCG constraint is comparable to and
  consistent with those derived from X-ray studies
  
• clusters are a robust cosmological probe
• cluster systematics are well understood!
• Cluster abundances constrain the growth of
  structure. As such, clusters are fundamentally
  different from geometric dark energy probes such
  as SN or BAO.
• Everything we have done with SDSS we can repeat
  with DES the best is yet to come!

4
Constraining Cosmology with Cluster Abundances
5
The Star of the Show ?8
?8 parameterizes the amplitude of the matter
power spectrum at z0.
Large ?8 - The z0 universe is very clumpy. Small
?8 - The z0 universe is fairly homogeneous.
Why is this measurement important? - It can help
constrain dark energy.
CMB measures inhomogeneities at z1200. CMB GR
Dark Energy model unique prediction for
?8 Comparing the CMB prediction to local ?8
measurements allows one to test dark
energy/modified gravity models.
6
How to Measure ?8 with Clusters
The number of clusters at low redshift depends
sensitively on ?8.
?81.1
Number Density (Mpc-3)
?80.9
?80.7
Mass
7
How to Measure ?8 with Clusters
The number of clusters at low redshift depends
sensitively on ?8.
?81.1
Number Density (Mpc-3)
Simple! To measure ?8, just count the number of
galaxy clusters as a function of mass.
?80.9
?80.7
Mass
8
Problem is, we dont see mass
Must rely instead on mass tracers (e.g. galaxy
counts).
9
Data
10
maxBCG
maxBCG is a red sequence cluster finder - looks
for groups of uniformly red galaxies.
11
The Perseus Cluster
12
The maxBCG Catalog
maxBCG is a red sequence cluster finder - looks
for groups of uniformly red galaxies.

• Catalog covers 8,000 deg2 of SDSS imaging with
  0.1 lt z lt 0.3.
• Richness N200 number of red galaxies brighter
  than 0.4L (mass tracer).
• 13,000 clusters with ? 10 (roughly
  M200c31013 M?).
• ?90 pure.
• ?90 complete.

Main observable n(N200)- no. of clusters as a
function of N200.
13
Understanding the Richness-Mass Relation The
maxBCG Arsenal

• Lensing measures the mean mass of clusters as a
  function of richness (Sheldon, Johnston).
• X-ray measurements of the mean X-ray luminosity
  of maxBCG clusters as a function of richness
  (Rykoff, Evrard).
• Velocity dispersions measurements of the mean
  velocity dispersion of galaxies as a function of
  richness (Becker, McKay).

These measurements are all based on cluster
stacks. Only possible thanks to the large number
of clusters in the sample.
14
The X-ray Luminosity of maxBCG Clusters
Stack RASS fields along cluster centers to
measure the mean X-ray luminosity as a function
of richness.
15
Cosmology
16
Summary of Analysis
Observables

• n(N200) - cluster counts as a function of
  richness
• Weak lensing cluster masses
• Scatter in mass at fixed richness (ask me later
  if interested).

Model (6 parameters)

• n(M,z) - cluster counts as a function of mass
  (Tinker et al., 2008).
• Mean richness-mass relation is a power-law (2
  parameters).
• Scatter of the richness-mass relation is mass
  independent (1 parameter).
• Flat ?CDM cosmology (2 relevant parameters, ?8
  and ?M).
• Allow for a systematic bias in lensing mass
  estimates (1 parameter).

17
Cosmological Constraints
?8(?M/0.25)0.41 0.832 ? 0.033
Joint constraints ?8 0.807?0.020 ?M
0.265?0.016
18
Systematics

• We have explicitly checked our result is robust
  to
• Moder changes in the purity and completeness of
  the maxBCG sample.
• Allowing other comsological parameters to vary
  (h, n, m?).
• Curvature in the mean richness-mass relation ?ln
  ?M?.
• Mass dependence in the scatter of the
  richness-mass relation.
• Removing the lowest and highest richness bins.
• The cluster abundance normalization condition
  does depend on
• Prior on the bias of weak lensing mass
  estimates.
• Prior on the scatter of the richness-mass
  relation.

Current constrains are properly marginalized over
our best estimates of the relevant systematics.
19
Comparison to X-rays
20
Cosmological Constraints from maxBCG are
Consistent with and Comparable to those from
X-rays
includes WMAP5 priors
21
Cosmological Constraints from maxBCG are
Consistent with and Comparable to those from
X-rays
This agreement is a testament to the robustness
of galaxy clusters as cosmological probes, and
demonstrates that cluster abundance systematics
are well understood.
includes WMAP5 priors
22
Cluster Abundances and Dark Energy
23
Cluster Abundances and Dark Energy
WMAPBAOSN WMAPBAOSNmaxBCG

w-0.995?0.067 w-0.991?0.053 (20 improvement)
24
A More Interesting Way to Read this Plot
wCDMWMAP5SNGR predict ?8?m0.4 to 10 accuracy
Cluster abundances test this prediction with a 5
precision level
WMAPBAOSN WMAPBAOSNmaxBCG

w-0.995?0.067 w-0.991?0.053 (20 improvement)
25
The Future
26
Prospects for Improvement
Many prospects for improvement

• Cross check maxBCG results using velocity
  dispersions as a completely independent mass
  calibration data set.
• Improve the quality of richness measures as a
  mass tracer.
• Improved understanding of the scatter of the
  richness-mass relation.
• Improved cluster centering.
• Improved weak lensing calibration.
• Add more cluster observables (e.g. 2pt
  function).
• Improved mass calibration from Chandra and SZA
  follow up of clusters.

27
Prospects for Improvement
Most important prospect for improvement the
Dark Energy Survey (DES)
The analysis that we have carried out with the
maxBCG cluster catalog can be replicated for
cluster catalogs derived from the
DES. Furthermore, these analysis can be
cross-calibrated with other surveys (e.g. SPT,
eRosita), which can further improve dark energy
constraints (see e.g. Cunha 2008).
The future of precision cluster cosmology look
very bright indeed!
28
Summary

• Principal maxBCG constraint S8
  ?8(?M/0.25)0.41 0.832?0.033.
• maxBCG constraint on S8 is of higher precision
  than and consistent with WMAP5 constraint on the
  same quantity.
• maxBCG constraint is comparable to and
  consistent with those derived from X-ray studies
  
• clusters are a robust cosmological probe
• cluster systematics are well understood!
• Cluster abundances constrain the growth of
  structure. As such, clusters are fundamentally
  different from geometric dark energy probes such
  as SN or BAO.
• Everything we have done with SDSS we can repeat
  with DES the best is yet to come!

29
Constraining the Scatter in Mass at Fixed Richness
30
Constraining the Scatter Between Richness and
Mass Using X-ray Data
Consider P(M,LXNobs). Assuming gaussianity,
P(M,LXNobs) is given by 5 parameters ?MNobs?
?LXNobs? ?(MNobs) ?(LXNobs) r
correlation coefficient
Known (measured in stacking).
Individual ROSAT pointings give the scatter in
the M - LX relation. We can use our knowledge of
the M - LX relation to constrain the scatter in
mass!
31
The Method

1. Assume a value for ?(MNobs) and r. Note this
   fully specifies P(M,LXNobs).
2. For each cluster in the maxBCG catalog, assign M
   and LX using P(M,LXNobs).
3. Select a mass limited subsample of clusters, and
   fit for LX-M relation.
4. If assumed values for ?(MNobs) and r are wrong,
   then the measured X-ray scaling with mass will
   not agree with known values.
5. Explore parameter space to determine regions
   consistent with our knowledge of the LX - M
   relation.

32
Scatter in the Mass - Richness Relation Using
X-ray Data
r (Correlation Coef.)
?ln MN
33
Final Result
?ln MN 0.45 /- 0.1 r gt 0.85 (95 CL)
Probability Density
Scatter in mass at fixed richness