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)