Cosmology with Galaxy Clusters
from the SDSS maxBCG Sample
Jochen Weller
Annalisa Mana, Tommaso Giannantonio,
Gert Hütsi
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more low
mass clusters
Theory: Counting Halos in
Simulations
Count halos in Nbody simulations
Measure “universal”
mass function density of cold dark
matter halos of given
mass
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
•#13,823
•7,500 deg2
•z=0.1-0.3
•red
sequence
method
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Catalogue: Koester et. al 2007
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Cosmology:
Rozo et al. 2009
The Counts Data
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Counts vs. Theory
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Cosmology with Number
Counts
•Ωm = 0.282
σ8 = 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
•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
Johnston et al. 2007
Sheldon et al. 2007
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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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The Power Spectrum of
maxBCG Clusters
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Hütsi 2009
Non-linear Corrections and
Photo-z Smoothing
•qNL = 14: non-linear
•σz = 59: photo-z smoothing
•beff = 3.2: bias
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Hütsi 2009
Bias for Clusters
Calculate from mass function via peakbackground 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%
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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 Values
Ωm
no Power
Spectrum
All Data
ln N1
ln N2
0.26± 0.80±
0.068 0.069
2.45±
0.11
4.21±
0.16
0.366± 1.01±
0.064 0.058
0.23±
0.024
2.48±
0.085
4.17±
0.13
0.355± 1.02± 18±
0.060 0.058 5.1
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σ8
0.82±
0.041
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σln M
β
qNL
σz
B
-
-
-
35±
6.1
1.10±
0.11
Summary
Clusters selected with richness and weak
lensing masses give meaningful cosmological
constraints
crucial to understand nuisance parameters
power spectrum tightens constraints; but nonlinear modelling required
more to come … different cosmologies,
additional datasets
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Outlook
maxBCG
eRosita
Euclid
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