Cosmological Constraints from the SDSS maxBCG Cluster Sample

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Cosmological Constraints from the SDSS maxBCG
Cluster Sample
Eduardo Rozo
UC Berkeley, Feb 24, 2009
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People Erin Sheldon David Johnston Risa
Wechsler Eli Rykoff Gus Evrard Tim McKay Ben
Koester Jim Annis Matthew Becker Jiangang-Hao Josh
ua Frieman Hao-Yi Wu.
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Summary

• maxBCG contraints are tight ?8(?M/0.25)0.41
  0.832?0.033.
• maxBCG constraints are comparable to and
  consistent with those derived from X-ray studies.
• maxBCG constraints are consistent with WMAP5.
  Joint constraints are ?8 0.807?0.020, ?M
  0.265?0.016.
• Cluster abundances can help constrain the growth
  of structure. As such, they are an important
  probe of modified gravity scenarios.
• Follow up observations can help, but we must be
  smart about it.

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Constraining Cosmology with Cluster Abundances
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The Broad Brush Background
Our protagonist is ?8, a measure of how clumpy
the matter distribution of the universe is.
High ?8 - Universe is very clumpy. Low ?8 -
Universe is more homogeneous.
Why is this measurement important? - It can help
constrain dark energy.
CMB measures inhomogeneities at z1200. Given the
CMB, general relativity, and a dark energy model,
we can predict how inhomogeneous the local
universe is. By comparing CMB prediction to local
measurements of ?8 we can constrain dark energy
models.
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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
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Why is Measuring ?8 Difficult?
The main difficulty is that mass is not directly
observable. One measures cluster abundances as a
function of a mass tracer ?.
We must understand how ? relates to cluster mass.

• Two approaches
• Understand P(?M) as best as possible a-priori
  (e.g. Mantz et al. 2008, Henry et al. 2008,
  Vikhlinin et al. 2008).
• Parameterize P(?M), and simultaneously fit for
  these parameters in addition to cosmology.

We must supplement cluster abundance data with
other mass-sensitive observables, e.g. ?M??, ?ln
M?, b(?), etc.
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Data
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maxBCG
maxBCG is a red sequence cluster finder - looks
for groups of uniformly red galaxies.
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The Perseus Cluster
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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.
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Other Data - 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).

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Collecting the Data Cluster Stacking
Lensing, X-ray, and velocity dispersion data are
all based on cluster stacking

• Select all clusters of a given richness.
• Stack all fields (SDSS/ROSAT) to measure the mean
  weak lensing/X-ray signal of the clusters.
• Repeat procedure along random points, and
  subtract uncorrelated background.

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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.
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Average Weak Lensing Masses as a Function of
Richness
But what about the scatter?
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Constraining the Scatter in Mass at Fixed Richness
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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!
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The Method

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

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

• Cluster abundance as a function of richness.
• Mean cluster mass as a function of richness
  (weak lensing, Johnston et al. 2008).
• Scatter in mass at fixed richness
  (abundancelensingX-rays, Rozo et al. 2008).

Model (6 parameters)

• Halo abundance n(M,z) from Tinker et al. 2008
  (depends on cosmology).
• Assume P(ln N200M) is Gaussian must specify
  mean and variance.
• Assume ?ln N200M? varies linearly with ln M (2
  parameters).
• Assume Var(ln N200M) is constant (mass
  independent, 1 parameter).
• Assume flat ?CDM cosmology, only vary ?8 and ?M
  (2 parameters).
• Allow for a systematic bias in lensing mass
  estimates (1 parameter).

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Biases in Weak Lensing Masses
Consider a source that is in front of a cluster
lens. Due to scatter in the photo-zs, one might
think the source is behind the lens. In that
case, one includes the source when estimating the
lensing signal, even though the source is not
lensed. Scatter in photo-zs dilutes the lensing
signal, and can result in mass estimates that are
biased low. Allow for this possibility by
including a weak lensing mass bias parameter.
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The Model Fits
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The Model Fits
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Cosmological Constraints
?8(?M/0.25)0.41 0.832 ? 0.033
Joint constraints ?8 0.807?0.020 ?M
0.265?0.016
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Systematics

• We have explicitly checked that our main result,
  ?8(?M/0.25)0.41 0.832 ? 0.033, is robust to
• Purity and completeness of the maxBCG sample.
• Cosmological parameters that are allowed vary
  (h, n, m?).
• Curvature in the mean richness-mass relation ?ln
  ?M?.
• Mass dependence in the scatter of the
  richness-mass relation.
• Lowest and highest richness bins.
• The cluster abundance normalization condition
  does depend on
• Width of the prior on the bias of weak lensing
  mass estimates.
• Width of the prior on the scatter of the
  richness-mass relation.

Current constrains are properly marginalized over
our best estimates for the relevant systematics.
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Cosmological Constraints from maxBCG are
Consistent with and Comparable to those from
X-rays
includes WMAP5 priors
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Moral of the Story
The fact that X-ray and optical cosmological
constraints are both tight and consistent with
each other are a testament to the robustness of
cluster abundances as a tool of precision
cosmology.
i.e. current cluster abundance constraints are
robust to selection function effects.
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Cluster Abundances and Dark Energy
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Dark Energy and Cluster Abundances
The simplest parameterization of the evolution of
dark energy is done via the dark energy equation
of state w Pw?. For a cosmological constant,
w-1.
Expect WMAP5low redshift cluster abundance to
tightly constrain w.
NOT TRUE (see e.g. Vikhlinin et al. 2008).
Why? Can cluster abundances really help?
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The Problem ?m and w are Degenerate with WMAP
Data Only
Degeneracy makes ?8 prediction very uncertain,
removing the constraining power from clusters.
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Additional Observables Restore Complementarity
with Cluster Abundances
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Cluster Abundances and Dark Energy
WMAPBAOSN WMAPBAOSNmaxBCG

w-0.995?0.067 w-0.991?0.053 (20 improvement)
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Moral of the Story
Cluster abundances constrain dark energy through
growth of structure (gravity). CMBSNBAO
constrain cosmology through distance-redshift
relations (geometry).
Assuming general relativity, geometry and gravity
are connected in a determinist way. i.e.
CMBSNBAO predict cluster abundances with high
accuracy.
Clusters allow one to search for deviations from
General Relativity.
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The Future
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Prospects for Improvement

• Current cosmological constraints are sensitive
  to
• prior on the weak lensing mass bias.
• prior on the scatter in mass at fixed richness.

• The prior on both of these quantities can be
  improved through follow up observations
• spectroscopic follow up of source galaxies to
  constrain ??c-1?.
• X-ray follow up of clusters to constrain scatter
  in mass.

• However, large numbers of X-ray follow ups are
  needed ( 400).
• X-ray follow will become feasible only through
  improvements in the fidelity of optical mass
  tracers (e.g. Rozo et al. 2008).

Bottom line improvements will only reach the
factor of two level.
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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).
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Follow Up Observations Can Help
Basic idea given a cluster catalog such as DES,
one can follow up a small subset of clusters to
measure P(NM).
Hao-Yi Wu
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Being Smart About Follow Ups
Hao-Yi Wu
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The Challenge
For follow ups to be effective, the follow up
mass estimators should be unbiased at the 5
level or better.
Hao-Yi Wu
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Summary

• maxBCG contraints are tight ?8(?M/0.25)0.41
  0.832?0.033.
• maxBCG constraints are comparable to and
  consistent with those derived from X-ray studies.
• maxBCG constraints are consistent with WMAP5.
  Joint constraints are ?8 0.807?0.020, ?M
  0.265?0.016.
• Cluster abundances can help constrain the growth
  of structure. As such, they are an important
  probe of modified gravity scenarios.
• Follow up observations can help, but we must be
  smart about it.
• Everything we have done with SDSS we can repeat
  with DES the best is yet to come!