# Presentation: 313806

## Self-calibration in Cluster Studies of Dark Energy

- Joe Mohr
**Department of Astronomy**
**Department of Physics**
**University of Illinois**

## Cluster Survey Studies of the Dark Energy: Complementary and Competitive

- Cluster constraints on dark energy:
- The cluster redshift distribution, the cluster power spectrum and 30% accurate mass measurements for 100 clusters between z of 0.3 and 1.2
- WMAP cosmology (8=0.84, m=0.27 k=0); 29000 clusters in the 4000 deg2 SPT survey.
- The joint constraints on w and m:
- Curvature free (dashed); fixed (solid)
- Marginalized w 68% uncertainty is 0.046 (flat) or 0.071 (curvature varying)
- Parameter degeneracies complementary

- SPT: Majumdar & Mohr
- SNAP: Perlmutter & Schmidt
- WMAP: Spergel et al

## Cluster Redshift Distribution is Sensitive to the Dark Energy Equation of State

- Raising **w** at fixed ******E**:
- decreases volume surveyed

- decreases growth rate of density perturbations

**w** constraints:

## What Are the Primary Challenges?

- Primary challenges are:
- Sensitive cluster finding over large solid angle
*A special purpose X-ray survey mission like DUO *
*Special purpose SZE surveys like the South Pole Telescope*
*Large optical/near-IR (OIR) survey projects like SDSS, PAN-STARRS, RCS2, CTIO Dark Energy Survey or LSST*
- Obtaining redshift estimates for all of these clusters
*Requires photometric redshift estimates from multiband OIR surveys*
*Extensive effort, but natural by-product of other projects*
- Connecting observables (X-ray/SZE/OIR flux or weak lensing shear) to the cluster halo mass

## Cluster Mass-Temperature Scaling Relations

- Emission weighted mean temperature is a good predictor of galaxy cluster mass (~20% scatter)

**Finoguenov, Reiprich & **
**Boehringer 2001**

**X-ray Flux Limited Sample**

**Mohr, Mathiesen & Evrard 1999**

*Implication:  *Structure of cluster ICM and dark matter comparable for clusters of the same mass.  Similar scaling relations are also seen in hydrodynamical simulations of galaxy clusters and in the observed K-band properties of the galaxies!

## Systematic Errors in Cluster Mass Estimates

- Systematic errors in mass estimates could potentially bias determinations of the density and nature of the dark energy
- In fact, this problem lies at the root of problems some have encountered in interpreting the rather small cluster samples available today
- High yield surveys over contiguous portions of the sky-- like the DUO X-ray survey-- will enable us to overcome this limitation through a process we call *self-calibration*

## Self-calibration in Galaxy Cluster Studies of the Dark Energy

- High yield cluster surveys can in principle deliver percent level constraints on the equation of state of the dark energy and many other cosmological parameters of interest
- Haiman, Mohr & Holder 2000
- Holder, Haiman & Mohr 2001
- Weller et al 2001
- Levine et al 2002
- Hu & Kravtsov 2003
**Majumdar & Mohr 2003**
**Hu 2003**
**Majumdar & Mohr 2003b**

- Working Requirements:
- Hierarchical structure formation theory is correct
- A mass-observable relation exists that can be used to estimate cluster halo masses from observables like X-ray luminosity, galaxy light, weak lensing shear, SZE luminosity
- Crude redshift estimates are available for each cluster detected in the survey

- The last three papers have shown that high yield cluster surveys can constrain cosmology while solving for the nature and evolution of the mass-observable relation.

## 	Imagine that you are presented with a dataset including ~104 clusters with redshift estimates and X-ray or SZE flux measurements.  What can you learn about the fundamental parameters of cosmology?
Assume you know nothing about clusters except that
Mass-observable scaling relations exist and evolve with redshift
(30% accurate (1 sigma) mass estimates of 100 clusters distributed evenly in mass and redshift from 0.3 to 1.2 that come from detailed observational studies from X-ray or other methods)

Parametrize your lack of knowledge: 
7 cosmological parameters (h, M, E, B, w, 8, and n )
3 scaling relation parameters: power law slope, normalization and redshift evolution

Use the survey data to measure the cluster redshift distribution and cluster power spectrum

Use Fisher matrix approach to examine parameter constraints and degeneracies

- Assume you know nothing about clusters except that
*Mass-observable scaling relations exist and evolve with redshift*
*(30% accurate (1 sigma) mass estimates of 100 clusters distributed evenly in mass and redshift from 0.3 to 1.2 that come from detailed observational studies from X-ray or other methods)*
- Parametrize your lack of knowledge:
*7 cosmological parameters (h, ****M**, ****E**, ****B**, w, ****8**, and n )*
*3 scaling relation parameters: power law slope, normalization and redshift evolution*
- Use the survey data to measure the cluster redshift distribution and cluster power spectrum
- Use Fisher matrix approach to examine parameter constraints and degeneracies

- A Thought Experiment

## Constraints on the Dark Energy Equation of State

- Joint constraints on M and w for DUET (assuming zero curvature)
- List of constraints:
- Green- uses dN/dz and assumes perfect knowledge of mass-observable relation
- Red- self cal with dN/dz
- Blue- self cal with dN/dz & Pcl(k)
- Magenta- self cal with dN/dz & 100 mass estimates
- Black- self calibrating with dN/dz, Pcl(k) and 100 mass estimates

**Majumdar & Mohr, ApJ submitted (astro-ph/0305341)**

- Self-calibration using cluster power spectrum, redshift distribution and detailed studies of 100 clusters provides 6.2% 1 constraint on w for DUET
- Pcl(k) is providing indirect cluster mass information through its amplitude, which depends on the cluster bias, which is mass dependent.  Moreover, Pcl(k) constrains the transfer function of density perturbations, which is very sensitive to the matter density m

## Survey Self-calibration and Cosmology

*Implication:*  The most robust cluster mass estimates will be statistical estimates derived from the properties of tens of thousands of clusters.  Large samples required.  Direct mass estimates advantageous, if they are unbiased at the few % level.
*Implication:*  Simulated cluster mass-observable relations will be an important guide for tuning the survey analysis, but they will not be used to calibrate the surveys.
*Implication:* Self-calibration reduces the need for high-accuracy flux calibration of the survey and high-accuracy flux corrections in each cluster.  It reduces sensitivity to cluster redshift errors, too.
*Improvements:*  There is additional dark energy information to be had by including (a) the mass function as a function of redshift together with (b) the cluster power spectrum with CMB calibration.  Many levels of redundancy in this approach.

## Why X-ray Cluster Surveys?

- The mass-observable relations in the optical are not as clean
*On the left:* adopt X-ray emission peak as cluster center, choose cluster radius using the emission weighted mean X-ray temperature (calibrated by cluster studies with temperature profiles- Finoguenov, Reiprich & Boehringer)
*On the right:* finding clusters and boot-strapping to the halo mass using only the K band galaxy data