Combine Observations of Galaxy Clusters to Constrain Cosmological Parameters

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 • Background • Method 1: strong lensing cluster • Method 2: X-ray gas fraction • Method 3: S-Z effect • 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 (1st) • 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, subscripts stands for source, and d the lens So when Σ>Σcrclusters 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? • Zd: redshift of cluster [Spectrum] • θarc (”) : position of arcs [Optical HST] • T (keV) : gas temperature [X-ray Spectrum] • β：power index [X-ray surface Brightness] • θc: core radius of X-ray cluster • Zarc: 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 zarc : only 58 arcs out of 27 clusters have redshift value θarc :

14. Zd & 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/

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) 2) Dds / Ds < 1 Angular distance should have physical significance • ∑/∑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 r2500 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. Grid-search MCMC Multigrid Number of parameters: n Calculation amount: 102n 108 (fixed) n x 104

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

25. Precondition

26. Angular distance • SX0 :X-ray surface brightness • dT0 :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 ΩΛ • X-ray gas fraction,42 points, sensitive to ΩM andDirect 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