Cosmological Constraints from the SDSS maxBCG Cluster Sample
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Transcript of Cosmological Constraints from the SDSS maxBCG Cluster Sample
Cosmological Constraints from the SDSS maxBCG Cluster Sample
Eduardo Rozo
Einstein Fellows Symposium Oct 28, 2009
People:
Risa Wechsler
Erin Sheldon
David Johnston
Eli Rykoff
Gus Evrard
Tim McKay
Ben Koester
Jim Annis
Matthew Becker
Jiangang-Hao
Joshua Frieman
David Weinberg
Summary
• Principal maxBCG constraint: S8 = 8(M/0.25)0.41 = 0.8320.033.
• 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!
Constraining Cosmology with Cluster Abundances
The Star of the Show: 8
8 parameterizes the amplitude of the matter power spectrum at z=0.
Large 8 - The z=0 universe is very clumpy.
Small 8 - The z=0 universe is fairly homogeneous.
Why is this measurement important? - It can help constrain dark energy.
CMB measures inhomogeneities at z~1200.
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.
How to Measure 8 with Clusters
The number of clusters at low redshift depends sensitively on 8.
8=1.1
8=0.7
8=0.9
Mass
Nu
mb
er
De
nsity
(M
pc-3
)
How to Measure 8 with Clusters
The number of clusters at low redshift depends sensitively on 8.
8=1.1
8=0.7
8=0.9
Mass
Nu
mb
er
De
nsity
(M
pc-3
)
Simple! To measure 8, just count the number of galaxy clusters as a function of mass.
Problem is, we don’t see mass…
Must rely instead on mass tracers (e.g. galaxy counts).
Data
maxBCG
maxBCG is a red sequence cluster finder - looks for groups of uniformly red galaxies.
The Perseus Cluster
The maxBCG Catalog
• Catalog covers ~8,000 deg2 of SDSS imaging with 0.1 < z < 0.3.
• Richness N200 = number of red galaxies brighter than 0.4L* (mass
tracer).
• ~13,000 clusters with ≥ 10 (roughly M200c~3•1013 M).
• 90% pure.
• 90% complete.
maxBCG is a red sequence cluster finder - looks for groups of uniformly red galaxies.
Main observable: n(N200)- no. of clusters as a function of N200.
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.
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.
Richness
L X
Cosmology
Summary of Analysis
• n(N200) - cluster counts as a function of richness
• Weak lensing cluster masses
• Scatter in mass at fixed richness (ask me later if interested).
Observables:
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).
Cosmological Constraints
8(M/0.25)0.41 = 0.832 0.033
Joint constraints: 8 = 0.8070.020 M = 0.2650.016
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.
Comparison to X-rays
Cosmological Constraints from maxBCG are Consistent with and Comparable to those from X-rays
includes WMAP5 priors
Cosmological Constraints from maxBCG are Consistent with and Comparable to those from X-rays
includes WMAP5 priorsThis agreement is a testament to the robustness of galaxy clusters as cosmological probes, and demonstrates that
cluster abundance systematics are well understood.
Cluster Abundances and Dark Energy
Cluster Abundances and Dark Energy
WMAP+BAO+SN:
WMAP+BAO+SN+maxBCG:
w=-0.9950.067
w=-0.9910.053 (20% improvement)
A More Interesting Way to Read this Plot
WMAP+BAO+SN:
WMAP+BAO+SN+maxBCG:
w=-0.9950.067
w=-0.9910.053 (20% improvement)
wCDM+WMAP5+SN+GR predict 8m
0.4 to ~10% accuracy
Cluster abundances test this prediction with a 5% precision level
The Future
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.
Many prospects for improvement:
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).
Prospects for Improvement
Most important prospect for improvement:
the Dark Energy Survey (DES)
The future of precision cluster cosmology look very bright indeed!
Summary
• Principal maxBCG constraint: S8 = 8(M/0.25)0.41 = 0.8320.033.
• 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!
Constraining the Scatter in Mass at Fixed Richness
Constraining the Scatter Between Richness and Mass Using X-ray Data
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!
Consider P(M,LX|Nobs).
Assuming gaussianity, P(M,LX|Nobs) is given by 5 parameters:
M|Nobs LX|Nobs (M|Nobs) (LX|Nobs) r [correlation coefficient]Known (measured in stacking).
The Method
1. Assume a value for (M|Nobs) and r. Note this fully specifies P(M,LX|Nobs).
2. For each cluster in the maxBCG catalog, assign M and LX using P(M,LX|Nobs).
3. Select a mass limited subsample of clusters, and fit for LX-M relation.
4. If assumed values for (M|Nobs) 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.
Scatter in the Mass - Richness Relation Using X-ray Data
ln M|N
r (
Cor
rela
tion
Co
ef.)
ln M|N ≈ 0.45
Scatter in mass at fixed richness
Pro
bab
ility
De
nsity
Final Result
ln M|N ≈ 0.45 +/- 0.1 r > 0.85 (95% CL)