# Presentation: 847589

## SDSS Cluster Abundances

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

**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**

## The MaxBCG Cluster Finder

- The Signal

**The MaxBCG Cluster Finder**

## z = 0.06

**z = 0.06**

**z = 0.13**

**z = 0.20**

**Likelihood= -7.8**

**N=0**

**N=19**

**N=0**

**Likelihood= 1.9**

**Likelihood= -8.4**

##  Cluster Photometric Redshifts

- Photo-z

- Spectroscopic z

- rms = 0.019

## The Cluster Galaxy Number Function

##  Completeness

- Measured N

- True N

- %

- z

## Scaling Mass with N

-  σ (km/s)

-  N

-  log σ = 0.53 log N + 2.06             log σ = 0.70 log  N + 1.75

-  Velocity Dispersion       Weak Lensing

-  log M ~ 1.5 log N                      log M ~ 2.1 log N

## Hubble Volume Simulations

## 

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 <= b <= 0.8 (Sheth et al 2000, Scoccimarro et al 2001, Berlind and Weinberg 2002)
Jenkins 2001 mass function:

- 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 <= b <= 0.8 (Sheth et al 2000, Scoccimarro et al 2001, Berlind and Weinberg 2002)
- Jenkins 2001 mass function:

- Number Function Prediction:   Halo Occupation Models

**power spectra**

**cosmology**

## Parameters of Interest

- Black line is a fiducial model.
- Red, orange, green, blue vary the parameter of interest.
- Dotted lines are a different redshift.

-  Ωm

-  σ8

-  fν

-  n

## 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 < 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

## Systematics

- Serious systematic errors:
- Calibration of N(M)
- Largest systematic uncertainty.
- Changing scaling to higher mass increases Ωm, lower fv
- Coalescence of potential clusters centers
- Changes abundance and tilt
- Preference for n=0.93 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 n=1.0. 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: Ωm=  .1, σ8 =  .1, fν =  +0.1-0.2

##  σ8 

-  σ8

-  Ωm

## Slide 17

## Slide 18

## Slide 19

##  Ωm

-  Ωm

-  fv

## The SDSS data allows constructions of cluster catalogs
Very complete to low masses
With redshifts
0 <= z <= 0.5
Halo models provide framework for interpreting and predicting number functions
Weak lensing provides calibration of N(M)

       Number Function                       M/L
Ωm= 0.27  .07  .1                  Ωm= 0.18  +0.08-0.07
σ8 = 1.04  .11  .1              σ8 = 1.04  +0.3-0.2
fν = 0.30  .08  +0.1-0.2

- Very complete to low masses
- With redshifts
- 0 <= z <= 0.5
- Halo models provide framework for interpreting and predicting number functions
- Weak lensing provides calibration of N(M)
-        Number Function                       M/L
- Ωm= 0.27  .07  .1                  Ωm= 0.18  +0.08-0.07
- σ8 = 1.04  .11  .1              σ8 = 1.04  +0.3-0.2
- fν = 0.30  .08  +0.1-0.2

- Conclusions

- Conclusions

**Notes:**
omega_m = 0.18 (+0.08, -0.07), sigma_8 = 1 (+0.3, -0.2), and a best-fit normalization relation of Sigma_8 * Omega_m0.6 = 0.35 +- 0.03. All best, 

## 
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

- 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

- Using 1⁄4 of the SDSS

## 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)

- 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

- Clusters as Cosmological Probes

- Haimen, Mohr, and Holder (2001)

**Why would you want to?**

## Parameter Estimation

## Cosmology

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

-  Ωm

-  σ8

##  Spatial Position

- Signal Calibration

## Cosmology

## 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