cosmology with galaxy clusters from the sdss maxbcg sample

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Cosmology with Galaxy Clusters from the SDSS

maxBCG SampleJochen Weller

Annalisa Mana, Tommaso Giannantonio,Gert Hütsi

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Theory: Counting Halos in Simulations

Count halos in N-body simulations

Measure “universal” mass function - density of cold dark matter halos of given mass

more lowmass clusters

more low redshift clusters

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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

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The SDSS maxBCG Sample

Catalogue: Koester et. al 2007Cosmology: Rozo et al. 2009

•#13,823•7,500 deg2

•z=0.1-0.3•red sequencemethod

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The Counts Data

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Counts vs. Theory

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Cosmology with Number Counts

•Ωm = 0.282σ8 = 0.85•Ωm = 0.2•σ8 = 0.78

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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

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Mass Data

Johnston et al. 2007Sheldon et al. 2007

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

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Results – Counts and Weak Lensing Mass

Consistentwith Rozo et al.2009

Implemented intoCOSMOMC: Lewis & Bridle

self calibraition:Majumdar & Mohr 2003Lima & Hu 2005

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The Power Spectrum of maxBCG Clusters

Hütsi 2009

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Non-linear Corrections and Photo-z Smoothing

Hütsi 2009

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

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Bias for Clusters

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

average bias

beff = Bb_i

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Bias vs. Mass Selection

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Model and PriorsnS = 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%

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Power Spectrum Included

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Parameter Degeneracies

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Models vs. Data

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Marginalized ValuesΩm σ8 ln N1 ln N2 σln M β qNL σz B

no Power

Spectrum

0.26±0.068

0.80±0.069

2.45±0.1

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4.21±0.1

6

0.366±0.064

1.01±0.058

- - -

All Data 0.23±0.024

0.82±0.041

2.48±0.085

4.17±0.1

3

0.355±0.060

1.02±0.058

18±5.1

35±6.1

1.10±0.1

1

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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

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Outlook maxBCG

eRosita

Euclid