# Presentation: 004627

## Studying Dark Energy with Clusters of Galaxies

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

- Outline
-  Observational leverage on dark energy
-  Cluster structure and its evolution
-  Cluster surveys- present and future
-  Remaining challenges

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## How Can One Study the Dark Energy?

- Measuring (relative) distances or volumes out to z~2
- Measuring the growth rate of cosmic structures
- Detecting dark energy clustering in the power spectrum of density fluctuations
- Measure evolution of gravitational potential wells using the Integrated Sachs-Wolfe effect
- Laboratory experiments and Theoretical progress

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## The Dark Energy and Its Equation of State Parameter

- Expansion history of the universe depends on the **amount** and **nature** of dark energy

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## Key Methods to Measure the Expansion History and/or Growth Function

- Type Ia Supernovae as standard candles
- Weak lensing measurements
- Power spectrum measurements
- Galaxy cluster surveys
- (Cosmic Microwave Background anisotropy)

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## Cluster Survey Studies of the Dark Energy are 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 0.3-1.2
- Fiducial cosmology (WMAP: 8=0.84, m=0.27); 29000 clusters in the 4000 deg2 SPT survey.
- The joint constraints on w and m:
- Curvature free to vary (dashed); fixed (solid)
- Marginalized constant w 68% uncertainty is 0.046 (flat) or 0.071 (curvature varying)
- Parameter degeneracies complementary

- SPT: Majumdar & Mohr 2003
- SNAP: Perlmutter & Schmidt 2003
- WMAP: Spergel et al 2003

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

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

- decreases growth rate of density perturbations

**w** constraints:

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## The Cluster Power Spectrum

- A second observable in a large solid angle (contiguous area) cluster survey is the clustering of the clusters
- Clusters are biased tracers of the dark matter, and the bias is a function of cluster mass (rarer, more massive clusters are also more highly biased)
- The cluster power spectrum gives us information about the transfer function of dark matter perturbations, and the transfer function is sensitive to the matter density m
- The amplitude of the cluster power spectrum gives us indirect information about the masses of the clusters

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## What About the Cluster Abundance n(z)?

- The cluster abundance is an integral over the detectable portion of the cluster mass function
- Cluster mass function dn(M,z)/dM depends on mean matter density ****** and amplitude of density fluctuations ******on mass scale **M**

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## Cluster Formation

- As density perturbations grow, clusters appear and the cluster mass function (dn/dM) evolves. We observe the “luminosity” or “shear” function.

- Mass Function

- Luminosity or Flux Function

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## The Press-Schechter Mass Function

- Consider the cosmic density field filtered on a mass scale M
- Assume that density perturbations have collapsed by the time their linearly evolved overdensity exceeds some critical value c
- Abundance (number density) of collapsed objects with mass M is then proportional to an integral over a Gaussian distribution

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## Jenkins Mass Function

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## Abundance Evolution

- Mass function evolution requires only that we know how ******(M)** changes with redshift
- Linear growth of perturbations is sensitive to the expansion history of the universe and to the dark matter density
- Universal expansion is a factor in the drag term
- Clustered dark matter density is a factor in the source term

- Density perturbations evolve more slowly in a low density universe.

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## Cluster redshift distribution dN(z)/dz/d

- Mass Selection Function

**Mass selection function**

- Detection efficiency **f(M)**
- In simplest case, selection is just a step function
*Survey selects all clusters more massive than ****M******lim***
- But we don’t observe *virial mass* directly
- Connecting cluster *virial mass* to *observables* is critically important
*X-ray luminosity or emission weighted temperature*
*SZE luminosity*
*Weak lensing shear amplitude*
*Galaxy light/dynamical estimators*

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## Are Clusters Suitable?

- So far the discussion is really about the emergence and evolution of dark matter halos in an expanding universe
- Will any dark matter halo do?
- Requirements:
- Must be observable over a significant fraction of cosmic history
- Must exhibit regularity
*Observables can be tied to halo mass in a reasonably clean manner*
*Simple redshift evolution is a plus*
- Clusters meet these requirements

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## Galaxy clusters are the most massive, collapsed structures in the universe.  They contain galaxies, hot, ionized gas (107-8K) and dark matter.

In typical structure formation scenarios, low mass clusters emerge in significant numbers at z~2-3

Clusters are good probes, because they are massive and “easy” to detect through their: 

- Galaxy clusters are the most massive, collapsed structures in the universe.  They contain galaxies, hot, ionized gas (107-8K) and dark matter.
- In typical structure formation scenarios, low mass clusters emerge in significant numbers at z~2-3
- Clusters are good probes, because they are massive and “easy” to detect through their:

- Galaxy Clusters Observables

-  X-ray emission

-  Sunyaev-Zel’dovich Effect

-  Light from galaxies

-  Gravitational lensing

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## Clusters Have No Outer Surface

- Dark matter, ICM, and galaxy distributions all fall off with distance from the cluster center, but there’s no clear signature of the edge of the cluster
- Thus, the mass of a galaxy cluster is an ambiguous quantity
- There are preferred definitions of cluster mass- we tend to choose a region which is a few hundred times denser than the background or critical density
- With this definitions, the cluster mass function evolution is simple

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## Dual Nature of Galaxy Clusters

- Clusters are young objects and, yet, as a population they exhibit striking regularity
- Evidence for cluster-subcluster merging abounds:
- 1980’s: *Einstein* images of double clusters, Messy galaxy distributions
- 1990’s: Statistical studies of (X-ray flux limited samples of) galaxy clusters reveal that more than half exhibit merger signatures
- Now: *Chandra* observations reveal merger signatures on even smaller physical scales
- Statistical studies of galaxy clusters reveal regularity
- Implications:
*Cluster population on the whole is regular*
*While mergers are common, recent major mergers that grossly perturb the cluster structure must be relatively rare*

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## The Local Size-Temperature Relation

- Analysis of 45 clusters (an X-ray flux limited sample) observed with the ROSAT PSPC.  Emission weighted mean temperatures taken from the literature
- Characteristics:
*RMS* scatter is ~15% in size
- Slope suggests some source of entropy for the intracluster medium in addition to that provided by shocks during infall and cluster formation

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## 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!

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## Regularity in Galaxy Population, too

- The Halo Occupation Number on group and cluster mass scales varies as the cluster binding mass to the 0.85+/-0.04 power
- Scatter about this bulk behavior is about 30% (similar to scatter in total light)
- Thus, the number of galaxies per unit mass is lower in massive clusters than in low mass clusters and groups
- Galaxies must be lost or must be growing less massive through stripping as their cluster/group halos merge to form higher mass structures

**Lin, Mohr & Stanford 2004 **
**(astro-ph/0402308)**

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## Scaling Relations Persist at Intermediate Redshift 

- Scaling Relations Persist at Intermediate Redshift

- Local ST

- Best Fit ST

**HRI Observations of 11 CNOC Clusters**

** ****Mohr, Reese, Ellingson, Lewis & Evrard, ApJ, 2000**

**Chandra Observations of 35 Clusters**
**(Sanderson et al. in preparation)**

- See also Chandra and XMM studies of Vikhlinin et al 2002, Ettori et al. 2003

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## Scaling Relations and Precision Cosmology

- The good news:
- Existence of these scaling relations demonstrates that simple observables are correlated with mass
- The bad news:
- Not all cluster finding approaches lead to similarly clean mass estimators
*ICM properties are rather clean, because the ICM “lights up” when a cluster collapses and begins to relax*
- X-ray luminosity and temperature are relatively clean
- SZE is promising, but observational issues must be overcome
*Galaxy and dark matter properties are much more challenging*
- Galaxies and dark matter were around long before the cluster collapsed.
- Lensing kernel is very broad in redshift space, so when you find a cluster you have also found the large scale structures surrounding it
- Shape information (projected galaxy and dark matter distributions) will be key in estimating cluster halo mass, but these methods are likely to deliver much less accurate mass estimates
- Need to understand evolution of the mass-observable relations

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## 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
- Cluster selection is also very clean in the X-ray compared to optical methods- projection issues are not as severe

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## 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

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## DUO:  The Dark Universe Observatory

- DUO (PI is Richard Griffiths- CMU) is a NASA Small-Explorer mission currently in Phase A study with 3 other missions.  Two will be selected for flight.
- Goal is to study dark energy, inflation and other cosmological issues with a deep, extragalactic X-ray survey that measures the cluster redshift distribution and power spectrum out to z~0.7
- PI is Richard Griffiths (CMU) with collaborators at Goddard Space Flight Center, Max Planck Institute (Germany), Ball Aerospace, U Illinois, Columbia and U Hawaii.
- Launch in 2007 followed by a two year X-ray survey for galaxy clusters (10,000+) and active galactic nuclei (100,000+)
- 6000 deg2 to 7x10-14 cgs [0.5-10keV] in the north (overlapping SDSS) and deeper, 150 deg2 to 9x10-15 cgs [0.5-10keV] southern survey

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## SZE cluster finding:  10m South Pole Telescope

- Figure courtesy  Tony Stark and John Ruhl

- 	PI John Carlstrom (U Chicago)
- 	Collaborators at Chicago, CWRU, Berkeley, Illinois and Harvard-Smithsonian CfA
- 	Goal:  Study dark energy with cluster redshift distribution and power spectrum out to z~1.5 and study CMB (polarization) on scales of 1 arcmin and above
- 	Survey of 4000 deg2 in three bands begins Feb 2007

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## Near Term Cluster Surveys

- X-ray serendipitous surveys with XMM and Chandra
- SZE surveys with SZA, AMI and APEX
- NIR surveys with FLAMINGOS
- Optical surveys with SDSS, RCS2, etc
- These will set the stage for the longer term, precision studies of the dark energy using clusters

- SF '04- Mohr

## 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

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## Photometric Redshifts and Cluster Followup

- DUO (wide) will survey the SDSS region in the north, so photo-z’s should be available out to z~0.6
- The SPT 4000 deg2 survey will yield roughly 29,000 clusters (assumes WMAP+ cosmology, the standard structure formation model and our current estimates of the survey cluster flux limi)t.  So we expect to find roughly 7 clusters per deg2
- Followup will be carried out for several reasons:
- Photometric redshift estimates (optical and/or NIR)
*Accuracy is acceptable (****z~0.02 with shallow SDSS data to z=0.6). Similar accuracy with deeper two-band photometry to z=1 (Yee and Gladders)*
*g’, r’, i’ and z’ photometry to 10 sigma depth of 24.6, 24.1, 24 and 23.6 would be sufficient for determining redshifts of those clusters at z~1.3 (>95% of our SPT sample)*
*Such a survey on the Blanco 4m with a  3deg**2** camera would take approximately 500 nights*
*Higher redshift (most interesting but <1/deg**2**) systems will likely require NIR data*
- Additional, independent mass estimates
*galaxy light or number, weak lensing, X-ray hydrostatic masses possible*
- Determine completeness and contamination in cluster sample
*Compare cluster lists in SZE, optical, NIR, and X-ray for a subset of the survey*

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## Dark Energy Survey

- Dark Energy Science
- Four independent constraints on the dark energy
*Cluster survey- SPT *
- (and perhaps DUO X-ray survey as well)
*Cosmic shear*
*Galaxy angular power spectrum*
*SNe Ia distance measurements*
- Dark Energy Collaboration
*Fermilab- Camera building*
- Annis, Flaugher, Lin, Kent, Peoples, Wester, Dodelson, Stebbins, Stoughton, and Tucker
*U Illinois- Data Management, Data Acquisition*
- Brunner, Karliner, Mohr, Plante, Selen and Thaler
*U Chicago- Cluster and weak lensing science components*
- Carlstrom, Frieman, Hu, Sheldon and Wechsler
*LBNL/UC Berkeley- Red sensitive detectors, SNe science component *
- Aldering, Roe, Levi and Perlmutter
*CTIO- Telescope & Camera Operations, SNe science component*
- Smith, Suntzeff, Abbott and Walker
- Mike Gladders (Carnegie Observatories)

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## Dark Energy Camera

- Camera build and data management preparations begin 2005
- 3deg2 prime focus camera, ~60 2kX4k 15 micron (0.26 arcsec) LBNL SNAP-like devices
- 2.1degree diameter corrector on Blanco 4m
- First survey season begins fall 2008 and runs through end of 2012
- Dark energy survey data released to public
- Full dataset is 100TB + four 1Tpix images + Catalogs
- Reduced exposures released 1 year after observation
- Co-added sky images in four bands released at half-way point and at survey end

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## 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

- SF '04- Mohr

## 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*

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## 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**
**Lima & Hu 2004**
- Wang et al 2004

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

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## 	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
You have 100 mass measurements, each accurate to 30% (1 sigma) and distributed evenly in mass and redshift from 0.3 to 1.2. These come from detailed observational studies from X-ray or other methods (in each redshift bin we effectively have a single mass measurement accurate to 10% at 1 sigma)

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*
*You have 100 mass measurements, each accurate to 30% (1 sigma) and distributed evenly in mass and redshift from 0.3 to 1.2. These come from detailed observational studies from X-ray or other methods (in each redshift bin we effectively have a single mass measurement accurate to 10% at 1 sigma)*
- 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

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## 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% 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

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## Survey Self-calibration and Cosmology

*Implications:*
- The most robust cluster mass estimates will be statistical estimates derived from the properties of tens of thousands of clusters.  Large samples over large, contiguous areas of the sky are required.  Direct mass estimates are advantageous, if they are unbiased at better than 10% level.
- 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.
- 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.
- Problems such as an increasing AGN contribution to cluster flux or changes in the fraction of clusters with cool cores with redshift (or mass) are simply self-calibrated out
*Improvements and cross checks:*
- There is additional dark energy information to be had by including (a) the mass function as a function of redshift together (see Hu 2003) with (b) the cluster power spectrum with CMB calibration.  There are many levels of redundancy in this approach.
- The best fit cosmology and mass-observable relation can be used to predict the observed cluster mass function as a function of redshift.  Level of agreement with theoretical dark matter mass functions will be direct test of robustness

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## What Calculations are Needed Between Now and Then?

- The cluster mass function and bias-mass relation
- Test universality of Jenkins or Sheth-Tormen mass function
- Add baryons (15% component) to large volume simulations
- Develop better cluster detection algorithms
- Multiwavelength techniques are key
- Must tune algorithms using realistic noise
- Understand survey selection in detail
- Requires large volume, medium resolution simulations with baryons

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