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Cosmology with Galaxy Clusters from the SDSS maxBCG Sample

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Cosmology with Galaxy Clusters from the SDSS maxBCG Sample

Jochen Weller

Annalisa Mana, TommasoGiannantonio,

GertHütsi

Recontres de Moriond 2012

redshift clusters

more low

mass clusters

Theory: Counting Halos in Simulations- Count halos in N-body simulations
- Measure “universal” mass function - density of cold dark matter halos of given mass

Recontres de Moriond 2012

Universality of the Mass Function

- Claims of universal parameterization in terms of linear fluctuation σ(M)
- Tinker et al. 2008 find additional redshift dependence (strongest effect in amplitude, but also shape)
- This effect can be included in parameterization

Recontres de Moriond 2012

The SDSS maxBCG Sample

- #13,823
- 7,500 deg2
- z=0.1-0.3
- red sequencemethod

Catalogue: Koester et. al 2007

Cosmology: Rozo et al. 2009

Recontres de Moriond 2012

The Counts Data

Recontres de Moriond 2012

Counts vs. Theory

Recontres de Moriond 2012

Scaling Relation and Scatter

- Assume linear scaling in log mass-richness relations: ln M = a lnNgal +b
- Scatter constrained by x-ray and weak lensing data (Rozo et al. 2009)
- For analysis we require: σNgal|lnM
- Simply related via scaling relation: use as prior in analysis; related via slope

Recontres de Moriond 2012

Mass Data

- stacked weak lensing
- fit by fixing: M1 = 1.3×1014 M and M2 = 1.3×1015 Mand ln N1 and ln N2 as free parameters
- allow for bias in mass measurement by a factor β

Johnston et al. 2007

Sheldon et al. 2007

Recontres de Moriond 2012

Results – Counts and Weak Lensing Mass

Implemented into

COSMOMC:

Lewis & Bridle

Consistent

with Rozo et al.

2009

self calibraition:

Majumdar & Mohr 2003

Lima & Hu 2005

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Non-linear Corrections and Photo-z Smoothing

- qNL= 14: non-linear
- σz= 59: photo-z smoothing
- beff= 3.2: bias

Hütsi 2009

Recontres de Moriond 2012

Bias for Clusters

- Calculate from mass function via peak-background split (Tinker et al. 2010)
- average bias

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beff = Bb_i

Bias vs. Mass Selection

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Model and Priors

- nS =0.96
- h = 0.7
- Ωb = 0.045
- flat, ΛCDM
- photo-z errors: σzphot|z= 0.008
- β=1.0±0.06
- σlnM see previous slide
- B=1.0±0.15
- σz=30±10
- purity/completeness: Error added in quadrature: 5%

Recontres de Moriond 2012

Power Spectrum Included

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Parameter Degeneracies

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Models vs. Data

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Marginalized Values

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Summary

- Clusters selected with richness and weak lensing masses give meaningful cosmological constraints
- crucial to understand nuisance parameters
- power spectrum tightens constraints; but non-linear modelling required
- more to come … different cosmologies, additional datasets

Recontres de Moriond 2012

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