SDSS Cluster Abundances

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SDSS Cluster Abundances
Cluster Collaborators Steve Kent Rita Kim Tim
Mcay Erin Sheldon Bob Nichol Chris Miller Tomo
Goto Neta Bahcall Daniel Eisenstein Marc
Postman Cosmology Collaborators Martin
Makler Steve Kent Scott Dodelson Josh
Friemann Tim Mckay Erin Sheldon

• Constraints on Cosmology
• James Annis
• Experimental Astrophysics/ Fermilab

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The MaxBCG Cluster Finder
The Signal
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z 0.13
z 0.06
z 0.20
Likelihood 1.9
Likelihood -7.8
Likelihood -8.4
N0
N19
N0
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Cluster Photometric Redshifts
Photo-z
rms 0.019
Spectroscopic z
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The Cluster Galaxy Number Function
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Completeness
True N

Measured N
z
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Scaling Mass with N
Velocity Dispersion Weak Lensing
s (km/s)
N
log s 0.53 log N 2.06 log s
0.70 log N 1.75
log M 1.5 log N log M
2.1 log N
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Hubble Volume Simulations
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Number Function Prediction Halo Occupation
Models

• An intuitive framework with predictive power
  (Seljak 2000)
• All matter is in the form of isolated haloes with
  mass M
• Bright galaxy at halo center
• Density profile given by NFW
• Halo mass function given by Press-Schecter or
  variants.
• The observed slope 1.8 power law galaxy
  correlation function is a generic prediction of
  these models, as long as
• Observations suggest 0.5 lt b lt 0.8 (Sheth et al
  2000, Scoccimarro et al 2001, Berlind and
  Weinberg 2002)
• Jenkins 2001 mass function

cosmology
power spectra
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Parameters of Interest
Black line is a fiducial model. Red, orange,
green, blue vary the parameter of
interest. Dotted lines are a different redshift.
Om
s8
n
f?
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Systematics

• Possible systematic errors
• Cosmological covariance
• Incorporate in fisher matrix. Smaller than
  statistical errors
• Selection function of cluster finding algorithm
• Determine E/S0 k-correction. Effect small at z lt
  0.3.
• Scatter in N(M)
• Reverse Malmquist bias due to scatter in N(M)
• Weak lensing bias
• 20-30 in mass calibration
• Jenkins mass function uncertainty
• 20 in abundance
• Details of conversion of weak lensing shear to
  M200
• Cosmology dependence of cluster finding algorithm

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Systematics

• Serious systematic errors
• Calibration of N(M)
• Largest systematic uncertainty.
• Changing scaling to higher mass increases Om,
  lower fv
• Coalescence of potential clusters centers
• Changes abundance and tilt
• Preference for n0.93 in this data the result of
  differing coalescence methods between simulation
  and observations
• Performing a simulation-like coalescence on the
  data causes a preference for n1.0. The best fit
  values there are then little changed, except for
  a lower fv
• Changing either tilt or coalescence individually
  leads to relatively large changes in parameters.
• Systematics Om ? .1, s8 ? .1, f? ? 0.1-0.2

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s8
Om
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fv
Om
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Conclusions

• The SDSS data allows constructions of cluster
  catalogs
• Very complete to low masses
• With redshifts
• 0 lt z lt 0.5
• Halo models provide framework for interpreting
  and predicting number functions
• Weak lensing provides calibration of N(M)
• Number Function M/L
• Om 0.27 ? .07 ? .1 Om 0.18 ?
  0.08-0.07
• s8 1.04 ? .11 ? .1 s8 1.04 ?
  0.3-0.2
• f? 0.30 ? .08 ? 0.1-0.2

Conclusions
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Using ¼ of the SDSS

• 2000 sq-degrees of SDSS data now available (The
  DR1)
• More clusters
• Better weak lensing calibration
• Consistency checks
• Velocity dispersion calibration of N(M)
• Direct power spectrum measurements
• Systematic errors will dominate
• Program to estimate each systematic
• Analyze Hubble Volume simuations to check physics

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Clusters as Cosmological Probes
Why would you want to?

• In terms of being able to model objects ab initio
  clusters rank just below the CMB.
• The formation of high mass halos is likely
  independent of the complex gas dynamics, star
  formation and feedback effects of galaxy
  formation instead only gravitational physics.
• Analytical techniques
• Press-Schecter follow the hierarchical structure
  formation of a gaussian density field in the
  linear perturbation limit. Unreasonably
  effective.
• Gott-Gunn follow the hierarchical structure
  formation of a single cluster under spherical
  tophat collapse.
• N-body techniques
• The Virgo Consortium Hubble volume simulation
• The Santa Barbra Cluster Comparison Project
• Sensitive to Dark Matter and Dark Energy
• Dark Energy
• Supernova sensitivity through r(z)
• Cluster sensitivity through r(z) and D(z), the
  growth function
• Dark Matter
• Cluster sensitivity again through r(z) and D(z),
  and P(k)

Application
Haimen, Mohr, and Holder (2001)
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Parameter Estimation
Application
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Cosmology

• Constraints from 1/20th of the SDSS
• Ellipse from abundances
• Flattening from evolution

s8
Application
Om
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Spatial Position
Signal Calibration
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Cosmology
Application
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Number Function Prediction

• Elements
• A mass function useful for any reasonable
  cosmology
• The Jenkins mass function, derived from
  simulations
• A halo model to predict N given M
• Seljak 2000, Sheth et al 2000, Scoccimarro et al
  2001, Berlind and Weinberg 2002
• Predict
• weak lensing calibration of mass gives