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Cosmology with Galaxy Clusters from the SDSS maxBCG Sample. Jochen Weller Annalisa Mana , Tommaso Giannantonio , Gert Hütsi. more low redshift clusters. more low mass clusters. Theory: Counting Halos in Simulations . Count halos in N-body simulations - PowerPoint PPT Presentation
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Cosmology with Galaxy Clusters from the SDSS
maxBCG SampleJochen Weller
Annalisa Mana, Tommaso Giannantonio,Gert Hütsi
Recontres de Moriond 2012
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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
Recontres de Moriond 2012
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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
Recontres de Moriond 2012
Recontres de Moriond 2012 4
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
Recontres de Moriond 2012 8
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 9
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