1. Combine Observations of Galaxy Clusters to Constrain Cosmological Parameters Heng Yu ( 余恒 ) & Zong-Hong Zhu Beijing Normal University 2008. 12.12

2. Outline 1.Background 2.Method 1: strong lensing cluster 3.Method 2: X-ray gas fraction 4.Method 3: S-Z effect 5.Results

3. Brief history 1901 Max Wolf discover Coma cluster 1933 Zwicky perceive the existence of dark matter from Coma cluster 1958 Abell published first galaxy cluster catalogue according to the Palomar Observatory Sky Survey (POSS) 1961-1968 Zwicky give his catalogue with different criteria

4. X-ray satellite History 1962 Aerobee Rocket USAF 2 -10 keV 1970-1973 Uhuru NASA 2-20 keV (1 st ) 1978-1981 Einstein NASA 0.2-3.5 keV 1990-1999 ROSAT Ge/US/UK 0.1 - 2.5 keV 1993-2000 ASCA Japan 0.4 -12 keV (CCD) 1999 Chandra NASA 0.1-10 keV 1999 XMM-Newton ESO 0.1-15 keV 2005 Sukuza Japan

5. X-ray Clusters Luminonious X-ray radiation T > 106 K ， P ≈ 1043 ～ 1045 erg/s Extended source β-model (Cavaliere et.al 1978) NFW (Navarro et.al 1997) double-β(Mohr et.al 1999) Thermal Bremsstrahlung spectrum 7keV Fe emission line

6. Bullet Cluster (2006): Direct Evidence of DM arXiv:astro-ph/0608407

7. Method 1: Giant Arcs in Lensing clusters

8. Gravitational lensing

9. Isothermal model β-model Hydrostatic density

10. Arcs Integrate to 2-D Critical surface mass density Here D is angular diameter distance, subscript s stands for source, and d the lens So when Σ>Σ cr clusters can generate arcs The position of tangential critical curve

11. Observational quantity Finally, from observation we can get And model can tell us then

12. What we need? Z d : redshift of cluster [Spectrum] θ arc (”) : position of arcs [Optical HST] T (keV) : gas temperature [X-ray Spectrum] β ： power index [X-ray surface Brightness] θ c : core radius of X-ray cluster Z arc : redshift of arcs [Spectrum]

13. Arc Sample D.J.Sand ApJ 2005 arXiv 0502528: find 104 tangential arcs and 4 radial arcs out of 128 GCs from HST WFPC2 Archive z arc : only 58 arcs out of 27 clusters have redshift value θ arc :

14. Z d & T Can be found directly at BAX BAX: the X-Rays Clusters Database This database contains information on 1579 groups and clusters of galaxies, and 298 clusters with available temperature measurements http://bax.ast.obs-mip.fr/http://bax.ast.obs-mip.fr/

15. Beta & theta_c Can be choosen In the “Physical data” frame Then we got the ADS link of all refered literature

16. Criteria 1) T > 4keV Regular X-ray Morphology (no merging as A2218)A2218 2)D ds / D s < 1 Angular distance should have physical significance 3)∑ /∑ cr ＞ 1 surface mass can genarate arcs

17. New Sample

18. 3-D Hubble Diagram

19. Dashed line: Old sample (Sereno 2004) Solid line: New sample

20. Method 2: Gas fraction

21. Gas mass X-ray gas mass fraction within r 2500 is constant with redshift NFW model

22. Optimization Algorithm Popular MCMC (Markov chain Monte Carlo) --CosmoMC Grid + Direct Search --Powell’s UOBYQA algorithm (using Numerical difference to approach directional derivative) --CONDOR http://www.applied-mathematics.net

23. Multigrid MCMC Grid-search Number of parameters: n Calculation amount: 10 2n 10 8 (fixed) n x 10 4

24. Method 3: S-Z effect WMAP temperature map with diamonds representing the position of nearby galaxy clusters

25. Precondition

26. Angular distance S X0 : X-ray surface brightness dT 0 : SZE decrement Lambda: X-ray cooling function 38 clusters 0.14 < z < 0.9 (Bonamente,2006)

27. Combination Result

28. Summary Lensing cluster, 9 points, sensitive to Ω Λ X-ray gas fraction,42 points, sensitive to Ω M and Direct Search algorithm is effective S-Z effect, 38 points, not big enough to do such constrain So Galaxy cluster is an expecting independent object for cosmological constrain !

29. Thanks! The real world is always complex, but we are approaching the truth !

30. A2218 Optical

31. A2218 X-ray Machacek, 2002 ApJ with Chandra