Cosmological Constraints from the maxBCG Cluster Sample

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Cosmological Constraints from the maxBCG Cluster
Sample
Eduardo Rozo October 12, 2006
In collaboration with Risa Wechsler, Benjamin
Koester, Timothy McKay, August Evrard, Erin
Sheldon, David Johnston, James Annis, and Joshua
Frieman.
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What Should You Get Out of This Talk

• Dark energy affects growth of inhomogeneities.
• Measuring the magnitude of inhomogeneities in
  early universe (from CMB) and at the present
  epoch can place constraints on dark energy.
• The number of galaxy clusters is a sensitive
  probe of the degree of inhomogeneity of the
  universe.
• Using clusters of galaxies to place cosmological
  constraints requires a good understanding of the
  cluster selection function.
• We introduce a formalism to properly account
  these difficulties, and find that the maxBCG
  cluster sample from the SDSS can provide some
  cosmological constraints even after marginalizing
  over uncertainties in the selection function.
• A better understanding of the selection function
  is still needed. Additional data, e.g. weak
  lensing measurements of maxBCG clusters, will
  help tighten our constraints.

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The Preposterous Universe
Dark energy (75)
Ordinary matter (5)
Dark matter (20)
We know next to nothing about dark matter. We
know nothing about dark energy other than how
much of it there is.
Figure taken from Sean Carrolls webpage
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How Can Dark Energy be Constrained?
Dark energy affects the distance to a given
redshift.
SNIa measures distances in an interval z0-1.
CMB constrains distance to last scattering.
Dark energy also affects the growth of structure.
Can we draw a similar picture in this case?
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Structure Formation
The number density of halos is a powerful probe
of dark matter clustering.
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Structure Formation
The rate at which structure grows depends on dark
energy.
CDM LCDM
z 3 z 1
z 0
Measuring the amplitude of fluctuations at two
vastly different epochs can set constraints on
dark energy.
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A Key Question Just How Clumpy is the Universe
Today?
The growth of structure is a powerful probe of
dark energy. We know how clumpy the early
universe was thanks to the CMB. We dont know
how clumpy the universe is today.
Main difficulty we see galaxies, but we are
interested in how the matter is distributed. We
need ways for measuring the clumpiness (i.e.
clustering amplitude) of matter at the present
epoch ?8.
We can use halo counting to measure ?8.
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Halo Counting to Measure ?8
More clumpiness (higher ?8) More massive
halos.
?81.1
?80.9
?80.7
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Halo Counting to Measure Clumpiness
Recipe for measuring ?8
1- Identify large halos as galaxy clusters
(maxBCG). 2- Count the number of galaxies in each
cluster (richness), a proxy for halo
mass. 3- Plot No. of clusters vs. richness and
compare to predictions.
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Finding Galaxy Clusters The maxBCG Algorithm
Clusters have a population of early type galaxies
that define a very narrow ridgeline in
color-magnitude space.
A broad brush description

1. Label bright galaxies in ridgeline relation as
   candidate Brightest Cluster Galaxies (BCGs).
2. Use model for radial and color distribution of
   galaxies in clusters to compute likelihood of
   candidate BCGs.
3. Rank order candidate BCGs by likelihood. Top
   most candidate is included in the catalog along
   with its member galaxies. All members are
   dropped from the candidate BCG list. Iterate.

Galaxy membership criteria must have ridgeline
colors, be brighter than some cutoff, and be
within a specified scaled aperture.
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Perseus as Imaged by the SDSS
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A Sample Cluster
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A Quick Comparison to X-ray Clusters
We match maxBCG clusters to X-ray clusters from
the NORAS and REFLEX surveys.

• Of 97 X-ray clusters in, we find
• 79 (80) are well matched (centers agree within
  250 h-1 kpc)
• 18 are not well matched.

• Of the 18 poor matches,we find
• 6 clusters with likely X-ray contamination.
• 6 clusters with blue BCGs.
• 2 merging systems.
• 4 systems with ambiguous BCGs.

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Halo Counting to Measure Clumpiness
Recipe for measuring ?8
1- Identify large halos as galaxy clusters
(maxBCG). 2- Count the number of galaxies in each
cluster (richness), a proxy for halo
mass. 3- Plot No. of clusters vs. richness and
compare to predictions.
Can we actually do this?
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Selection Function Letting the Genie out of the
Bottle
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Selection Function
Want to count halos of a given mass to measure
?8. However Can we find all halos?
(completeness) Are all detections real? (purity)
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Selection Function
What we mean by selection function
P(Robsm) probability a halo of mass m is
detected as a cluster of
richness Robs.
If we knew the selection function, we could
predict the no. of clusters we will observe in
various cosmologies.
N(Robs) ? n(m)P(Robsm)
Number of clusters (what we observe)
Number of halos (what we predict)
Selection function
We need to properly model the selection function.
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Modeling the Selection Function
We assume detecting a cluster is a two step
process 1- The halo has some probability
P(Rtruem) of having Rtrue galaxies (HOD). 2-
We have a probability P(RobsRtrue) of finding
the halo as a cluster with Robs galaxies.
Measure P(RobsRtrue) directly from
simulations. (Will depend on how clusters are
matched to halos)
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Calibration of the Selection Function
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Signal and Noise
c(Rtrue) fraction of halos in signal band -
completeness.
P(RobsRtrue) c(Rtrue)PS(RobsRtrue)
PN(RobsRtrue)
We can calibrate these.
Hard to calibrate.
We do not need to know this!
Only need to know fraction of clusters that are
noise - purity.
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Completeness
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Purity
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The maxBCG cluster sample is highly pure and
complete.
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Does the Model Work?
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The Model Works
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Agreement is not trivial. Our model accurately
describes the halo selection function.
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Can We Recover Physical Parameters ?
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Knowledge of selection function Percent lever
accuracy in parameter estimation.
Includes traditional systematics - e.g.
projection effects.
maxBCG can in principle be a useful tool for
precision cosmology.
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Uncertainties in the Selection Function Result in
Larger Error Bars
Percent Level Priors on Selection Function
Parameters
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Applying the Method to Data
Different simulations had different selection
functions. Use generous priors on selection
function. Use priors on cosmological
parameters from other data sets (?mh2 from CMB,
h from SN). Use theoretical prior on slope of
HOD (how galaxies populate halos).
Can still provide meaningful constraints on the
power spectrum amplitude ?8.
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Applying the Method to Data
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End Result
HOD selection function prior.
?8 0.92 /- 0.11 (HOD prior
?1.00 /- 0.05)
?8 1.05 /- 0.12 ? 0.76 /- 0.05
(selection function prior)
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Trouble?
Selection function priors and theoretical HOD
priors are inconsistent.
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End Result
HOD selection function prior.
?8 0.92 /- 0.11 (HOD prior
?1.00 /- 0.05)
?8 1.05 /- 0.12 ? 0.76 /- 0.05
(selection function prior)
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Caveats and Future Work
Can we robustly characterize the selection
function from simulations? Need more and
better simulations. Is the selection function
cosmology dependent? Need simulations for
various cosmologies. Is there evolution in the
selection function and/or richness-mass
relation? Include evolution as a nuissance
parameter. Is there curvature in the
richness-mass relation? Use weak lensing
date to relax richness-mass relation
parameterization.
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Summary and Conclusions

• Developed a new way for characterizing cluster
  selection function.
• Method allows for marginalization over
  uncertainties in selection function.
• Used simulations to prove method recovers
  simulation parameters with percent level accuracy
  when selection function is known.
• Demonstrated maxBCG can be a powerful tool of
  precision cosmology traditional systematics are
  not a difficulty.
• Application of method to data shows tension
  between selection function calibration and
  theoretical prior.
• More work is needed to fully realize the promise
  of cluster abundance methods for constraining
  cosmological parameters.