# Presentation: 801763

## Cosmology with Galaxy Clusters

**Columbia University**

**Zolt****á****n Haiman  **

**Cosmology with X-ray Cluster Surveys                 Greenbelt,  15-16 January  2004**

**Collaborators:  ****Joe Mohr  (Illinois)        Justin Khoury (Columbia)**
**                                ****Wayne Hu (Chicago)      ****Sheng Wang (Columbia)**
**                                ****Gil Holder (Princeton)**

## Outline of Talk 

- Cosmological Sensitivity of Clusters            – why clusters?                                                          – current constraints
- Constraints from Future Samples                                                     – abundance evolution                                                – power spectrum
-        – SZ + X-ray synergy

## Current Cosmology Constraints

- M

- 

**Verde  www **
**(2003)**

**CMB**

**SN**

**LSS**

**(SCP)**

**(WMAP+)**

**(2dF)**

**strong degeneracy in any single experiment **

## Why Galaxy Clusters?

** ****Theory:**

- Clusters relatively simple objects.  Evolution of massive
- cluster abundance determined by gravity.  Clusters
- straddle the epoch of dark energy domination 0<z<3.

** ****Future observations:**

- Current samples of tens of clusters soon to be replaced
- by thousands of clusters with mass estimates in dedicated
- large (SZE, X-ray, weak lensing) surveys

** ****Why Do We Need Yet Another Cosmological Probe? **

- - Degeneracies differ from CMB, SNe, Galaxies
-  Systematics are different
-  Unique exponential dependence
-  Modelability

- (Impressive constraints - but dark energy still elusive)

## An advantage unique to clusters?

** ****A cluster sample can deliver **_**many**_** observables**

- X-ray flux                                SZE decrement
- Angular size                             Number of galaxies
- Spatial distribution (2d, 3d)     Lensing signatures

** ****We can construct **_**several**_** cosmology tests **

- dN/dz – abundance evolution
-               (including mass function dN/dM)
- P(k)   –  spatial power spectrum
-               (including Alcock-Paczynski)
- Scaling relations – between SZ/X-rays/sizes
-               (including dA measurement)

**Simultaneous determination of cosmological and**
**cluster structural parameters (with their evolution)**

**best?**

**better**

**good**

**Notes:**
Look for darth vader for “dark side”  

## Outline of Talk 

- Cosmological Sensitivity of Clusters            – why clusters?                                                          – current constraints
- Constraints from Future Samples                                                     – abundance evolution                                                – power spectrum
-        – SZ + X-ray synergy

## Local Cluster Abundance Constraints

-  63 bright X-ray clusters (REFLEX+)        - Soft X-ray flux limit 210-11 erg/s/cm2    - 20,000 sq. degrees (half sky),   z ~ 0

- M

- 8

**Reiprich & B****ö****hringer (2002)**
**             ****Pierpaoli et al. (2003)**

## Cluster Abundance Evolution Constraints

- 

- w

- using dN/dT evolution
- 24 clusters at z<0.3
- 19 clusters at z>0.3
- [marginalized over 8 ]

**Henry**
**et al. **
**(2004)**

- M

## Cluster Abundance Evolution Constraints

- w

- using dN/dT evolution
- 24 clusters at z<0.3
- 19 clusters at z>0.3
- [marginalized over 8 ]

**Henry**
**et al. **
**(2004)**

- M

**Depth important:**
**No constraints**
**from ~430 bright**
**clusters at 0<z<0.2**
**Schuecker et al (2001)**

## Summary of Current Results

**•****   ****Local Sample  ****of  ~ 100 clusters have constrained**
**    ****matter density and power spectrum normalization**
**    ****to accuracy comparable to other methods**

**•****   ****Similar results ****for ********M**** from cluster baryon fraction **
**    ****and mass/light arguments **

**•****  **** ****Dark energy constraints** **are not yet available, we **
**    ****need larger samples extending to larger distance (z~1)  **

**•****   ****Current systematics ****are dominated by M-T relation,**
**    ****around the level of statistical errors**

**Lin et al. (2003), Ostriker  et al. (2003)**

**Bridle et al. (2003)**

**Pierpaoli et al. (2003)**

**Schuecker et al. (2001), Henry (2004)**

## Outline of Talk 

- Cosmological Sensitivity of Clusters            – why clusters?                                                          – current constraints
- Constraints from Future Samples                                                     – abundance evolution                                                – power spectrum
-        – SZ + X-ray synergy

## Galaxy Cluster Abundance

**Dependence on cosmological parameters**

**growth**
**function**

**power**
**spectrum (********8****, M-r)**

**Jenkins**
**et al. 2001**

**comoving**
**  ****volume**

**mass**
**limit**

**mass**
**function**

**# of clusters per**
** ****unit area and z:**

**mass function:**

**      ****overall**
**normalization**

**       ****Hubble volume**
**N-body simulations**
**in three cosmologies**
**cf: Press-Schechter**

## Different Sensitivity to M  and w

**overall scaling and ********8  ****change**

**Haiman, Mohr & Holder (2001)**

**redshift**

**0**

**1**

**2**

**3**

**dN/dz/12 deg****2**

**redshift**

**0**

**1**

**2**

**3**

**volume (low-z)  + growth (high-z)**

**w=-1**

**w=-0.6**

**w=-0.2**

## Power & Complementarity 

**Constraints using dN/dz**
**of ~10,000 clusters in a**
**wide angle X-ray survey**
**(SPT gives similar results)**

**Planck measurements**
**of CMB anisotropies **

**2,400 Type Ia SNe**
**from SNAP**

- M

- 

******M**** to   ~1%**
********** ****to   ~10%**

_**Power comparable**_** to:**

**J.Mohr/Z.Haiman   + DUO**

## Dark Energy Constraints

**Using 6000**** ****deg****2  ****X-ray**
**~10,000 clusters**
**between 0 < z ****≲ 1**
**(****marginalized over **
**H****0**** and **8**)**

**Planck measurement**
**of CMB anisotropies **
**and polarization**

- M

- w

******M**** to   ~1%**
**w   to    ~10%**

**J.Mohr + DUO**

## Time-dependence of w(z)

** ****w(z)=w****0**** + w****1****z**
** ****Fixed mass limit of 2****×10****14 ****h****-1 ****M****⊙**
** ****4000 square degrees    **
** ****Errors from 4x4 Fisher matrix**
**          ****WMAP                     w****0**** = -0.8**
**          ********CDM                      w****1**** = 0.3**
**        ********  ****= 0.01                 ********  = 0.01**
**        ********8**** = 0.006                ********8**** = 0.005**
**        ********w****0**** = 0.12                 ********w****0**** = 0.10**
**        ********w****1**** = 0.25                 ********w****1**** = 0.19**
**                  ****(0.04)                         (0.03)**
** ****Combine with P(k)**

**Work in progress**
**with J. Khoury **
**         ****S. Wang **
**        ****(Columbia)**
**    ****& M. May **
**        ****(Brookhaven)**
**      **
**see also:**
** ****Weller et al. (2002)**
** ****Battye & Weller (2003)**

**“****raw” errors**

**Notes:**
Justin’s 4x4 Fisher errors:  Omega= 0.011     sigma8= 0.0056      w0= 0.12      w1= 0.25

## Outline of Talk 

- Cosmological Sensitivity of Clusters            – why clusters?                                                          – current constraints
- Constraints from Future Samples                                                     – abundance evolution                                                – power spectrum
-        – SZ + X-ray synergy

## Cluster Power Spectrum

**Dependence on cosmological parameters**

**cluster**
**bias**

**growth**
**function**

**redshift**
**distortion**

**transfer**
**function**

**Observable:**

**inverse**
**volume**

**Radial modes:**

**Transverse modes:**

**Angular diameter distance**

**Hubble constant**

**Redshift distortion:**

**Scales with growth function**

**Geometry!**
**(w/ physical**
** ****scale info)**

**}**

**initial**
**spectrum**

## Cluster Power Spectrum

**•****   ****Galaxy clusters highly biased: **
**     **
**                   ****Large amplitude for P****C****(k) = b****2 ****P(k)**
**                   ****Cluster bias as calculable as mass function**
**                       **

**•****   ****Expected statistical errors on P(k):**
**                  ****FKP (Feldman, Kaiser & Peacock 1994)**
**                 “****signal-to-noise” increased by b****2 ****~25**
**                   ****c.f. SDSS spectroscopic sample b****2 ****~1**

**Notes:**
Check effective bias (old email)

## Cluster Power Spectrum - Accuracies

**Z. Haiman / DUO**

**~8,000 clusters total**
**   ****(~2700 in each of **
**      ****three redshift bins)**
**  ****P(k) determined to **
**  ****roughly the same**
**  ****accuracy in each z-bin**
**  ****Accuracies: **
**    ********k/k=0.1  ****→ 10%**
**    ****k<0.2        → 3%**
**NB: baryon “wiggles” **

- k[h Mpc –1]

- P(k) [h –3 Mpc 3]

- [h Mpc –1]

**Notes:**
Check baryon 2-sigma (old email)

## Effects of Neutrinos on Power Spectrum

**Courtesy W. Hu**

**Courtesy W. Hu**

**Neutrino Mass**** **

**Generalized Dark Matter**

**e.g. m********=0.2eV   [************h****2****≈ ****0.002]**

**Pure P(k) “shape test”**

**CMB**

**P(k)**

**w[dm]********0**

**Notes:**
Converting neutrino mass to Omega neutrino...
Degenerate with tilt ??

## (M vs  ) from Cluster Power Spectrum

**Haiman/Hu/Cooray + DUO**

**Use 3D power spectrum**
**of 10,000 clusters**
**DUO improves CMB**
**neutrino limits:**
**factor of ~10 over WMAP**
**factor of ~2 over Planck**
**(because of degeneracy **
** ****breaking)**

- M h2

- **** h2

**DUO+Planck Accuracy**
**          ************h****2 ****~ 0.002**

**Notes:**
Check what was marginalized (tilt?)

## Cluster Power Spectrum - Summary

**•****   ****High bias of galaxy clusters enables accurate**
**    ****measurement of cluster P(k):**
**                  ********k/k=0.1  ****→ P(k) to 10%  at k=0.1**
**                      ****k<0.2        → P(<k) to 3%**

**•****   ****Expected statistical errors from Clusters+Planck:**
**                  ************h****2  ****~ 0.002   “shape test”        **

**•****   ****Pure geometric tests can be constructed ****(Wayne Hu’s talk)**** **
**                  ****use features as ‘standard rods’**
**                     ****combine with CMB**

**•****   ****Enough “signal-to-noise” to consider 3-4 z- or M-bins:**
**                  ****evolution of clustering**
**                     ****peak bias theories / non-gaussianity**

**Notes:**
Check effective bias (old email)

## dN/dz + P(k): Time-dependence of w(z)

** ****w(z)=w****0**** + w****1****z / (1+z)     cf WMAP fiducial model**
** ****Mass limit to mimic X-ray survey (~****10****14****-10****15**** M****⊙****)**
** ****10,000 square degrees     **
** ****Errors from 6x6 Fisher matrix**
**               ****dN/dz             P(k)            dN/dz +**
**               ****alone              alone           P(k)**
******w****1****         0.52                 0.67           0.15**
******w****0****         0.15                 0.14           0.048**
******          ****0.014               0.017          0.006**
******8****         0.007               0.019          0.0033**
******H****0****         0.30                 0.26           0.015**
******n****s****          0.07                 0.05           0.05**

** ****Work in progress with S.Wang & J. Khoury (Columbia)**
**                                        ****M. May (Brookhaven)           **
** ****Majumdar & Mohr (2003)**

## Outline of Talk 

- Cosmological Sensitivity of Clusters            – why clusters?                                                          – current constraints
- Constraints from Future Samples                                                     – abundance evolution                                                – power spectrum
-        – SZ + X-ray synergy

## SZE and X-ray Synergy

**Molnar, Haiman, Birkinshaw & Mushotzky 2004,   ApJ,  in press**

** ****Assuming 10% angular diameter (D****A****) measurements **
**  ****of 100 clusters at 0<z<1.5   (0.5<z<1 has most power)**
** ****combined with 12 deg****2**** SZA sample**

- M

- M

- 

- w

## Observables in Future Surveys

**SZ decrement:**

**X-ray flux:**

**weak lensing shear....**

## (S ,TX) scaling relations + dN/dz test 

**work in preparation**

**Using a sample**
**of ~200 clusters**
- Different Mmin - 0
- degeneracies

-  can check on
-      systematics

## SZE and X-ray Synergy

**Verde, Haiman & Spergel 2002**

- S **-** TX** scaling relation expected to have small scatter:**
**                 ****(1)**** SZ signal robust    ****(2)**** effect of cluster ages**

**Using scaling relations, we can simultaneously**
**Probe cosmology and test cluster structure**

**SZ decrement vs Temperature**

**SZ decrement vs Angular size**

## “Fundamental Plane”: (S ,TX, )

**Verde, Haiman & Spergel (2002)**

**Plane shape**
**sensitive to **
**cosmology**
**and cluster**
**structure**
** **
**    ******
**Tests the**
**origin of**
**scatter **

## SZ and X-ray Synergy - Summary

**     ****SZ decrement and X-ray flux depend on different **
**     ****combinations of cosmological parameters**
**                 **

**•****   ****SZ + X-ray  yields angular diameter distance **
**                     ****equivalent to SNe , so complementary to dN/dz  **
**                     ****~100 clusters with ~10% distance errors     **

**•****   ****SZ vs X-ray scaling relations carry cosmological info**
**                  ****complementary to dN/dz **
**                     ****still to be worked out**

**•****   ****Physical origin of ****scatter can be investigated**
**                  ****Is age dispersion contributing to scatter?**
**                     ****If so, then (SZ-FX) should be much tighter **
**                     ****than either of the above vs. size**

**Molnar, Haiman, Birkinshaw & Mushotzky (2004),  ApJ,  in press**

**(with L. Verde)**

**Verde, Haiman & Spergel (2002)**

**Notes:**
Check effective bias (old email)

## Conclusions 

**Clusters are a tool of  “precision cosmology”                      ****a unique blend of cosmological tests, combining    volume, growth function, and mass-observable**
**Using dN/dz, P(k)  complementary to other probes                ****e.g.:   (********M****,w) , (********M****, ************ ****), (********M****, ************ ****) planes  vs CMB and SNe**
**Combining above tests and SZ/XR can tackle systematics              ****solving for cosmology AND cluster  parameters?       **