1. Observational Constraints on Galaxy Clusters and DM Dynamics Doron Lemze Tel-Aviv University / Johns Hopkins University Collaborators : Tom Broadhurst, Yoel Rephaeli, Rennan Barkana, Keiichi Umetsu, Rick Wagner, & Mike Norman 21/9/10

2. Overview: Observational constraints on galaxy clusters. Study case: the high-mass cluster A1689 DM Dynamics Lemze, Broadhurst, Rephaeli, Barkana, & Umetsu 2009 Lemze, Rephaeli, Barkana, Broadhurst, Wagner, & Norman 2010

3. Subaru/suprime-cam VLT/VIMOS The measuring instruments Hubble Strong lensing Weak lensing Imaging of cluster galaxies Cluster galaxies spectroscopy

4. cD galaxy 00.5’ Lemze, Barkana, Broadhurst & Rephaeli 2008

5. Galaxy surface number density About 1900 cluster members.

6. Velocity-Space Diagram Velocity caustics method: Diaferio & Geller 1997 Diaferio 1999 About 500 cluster members.

7. Methodology Jeans eq. Velocity anisotropy Galaxy surface number density Projected velocity dispersion The unknowns: M is taken from lensing

8. Galaxy surface number density data points : 20 Projected velocity dispersion data points : 10 The number of free parameters : 5 --------------------------------------- dof : 25 Galaxy surface number density fit Projected velocity dispersion fit The fit results

9. Galaxy number density profile

10. Velocity anisotropy profile

11. Galaxy velocity anisotropy data vs. simulations Arieli, Rephaeli, & Norman 2010

12. Mass profiles Here M is not taken from lensing!

13. The high concentration problem Broadhurst et al. 2008 Zitrin et al. 2010

14. A1689MS2137 Can we trust the high value found? Comerford & Natarajan 2007

15. Virial mass vs. concentration parameter Here M is not taken from lensing!

16. Comerford & Natarajan 2007 Hennawi et al. 2007 Bullock et al. 2007 62 clusters Building statistical samples

17. Duffy et al. 2007 10 halos per data bin N-body simulations using WMAP5 parameters X-ray measurements Building statistical samples

18. Johnston et al. 2007 Weak lensing measurements of stacked SDSS groups and galaxy clusters In agreement with Mandelbaum et al. 2006 Large samples

19. Conclusions W e e s t i m a t e d f o r t h e f i r s t t i m e a d e t a i l e d 3 D v e l o c i t y p r o f i l e. W e f o u n d t h a t t h e c a u s t i c m a s s i s a g o o d e s t i m a t i o n f o r t h e m a s s p r o f i l e. O u r t h r e e i n d e p e n d e n t e s t i m a t e s f o r t h e m a s s p r o f i l e a r e c o n s i s t e n t w i t h e a c h o t h e r. W e c o n s t r a i n e d t h e v i r i a l m a s s u s i n g g a l a x y p o s i t i o n s a n d v e l o c i t i e s d a t a. W e d e d u c e d h i g h v a l u e s f o r t h e c o n c e n t r a t i o n p a r a m e t e r u s i n g t w o i n d e p e n d e n t m e t h o d s.

20. DM dynamics Question: how one can determine DM dynamics when “DM spectroscopy” is hard to obtain? Answer: by using a surrogate Measurement. The first Choice should be other kind of collisionless particles - galaxies. The orbit of a test particle in a collisionless gravitational system is independent of the particle mass. This would presumably imply that once hydrostatic equilibrium is attained, most likely as a result mixing and mean field relaxation, DM and galaxies should have the same mean specific kinetic energy, i.e.,, where

21. Host et al. 2009 DM velocity anisotropy Best-fit value:

22. DM density All other colors DM density Galaxy density Total matter density Best-fit values:

23. Model-dependent Model-independent The collisionless profile

24. Model-independent Model-dependent The velocity bias profile

25. Conclusions W e o b t a i n t h e m e a n v a l u e o f t h e D M v e l o c i t y a n i s o t r o p y p a r a m e t e r, a n d t h e D M d e n s i t y p r o f i l e. r ∼ 1 / 3 r _ v i r s e e m s t o b e a t r a n s i t i o n r e g i o n i n t e r i o r t o w h i c h c o l l i s i o n a l e f f e c t s s i g n i f i c a n t l y m o d i f y t h e d y n a m i c a l p r o p e r t i e s o f t h e g a l a x y p o p u l a t i o n w i t h r e s p e c t t o t h o s e o f D M i n A 1 6 8 9

28. Comerford & Natarajan 2007 Hennawi et al. 2007 Bullock et al. 2007 ??C is measured using lensing and X-ray??? 62 clusters Building statistical samples

29. Duffy et al. 2007 10 halos per data bin N-body simulation using WMAP5 parameters – lower sigma_8 X-ray measurements

30. X-ray data Assuming a gas density profile Double model Assuming a temperature profile Isothermal Fitting a double Surface brightness model Where a single model is For gas in hydrostatic equilibrium,, and. For the isothermal assumption: where For obtaining the mass profile: Lensing data What has been done previously? Assuming a DM profile NFW

32. Doron Lemze Tel-Aviv University Collaborators : Tom Broadhurst, Rennan Barkana, Yoel Rephaeli, Keiich Umetsu Collaborators :

33. Johnston et al. 2007 Weak lensing measurements of stacked SDSS groups and galaxy clusters In agreement with Mandelbaum et al. 2006 Large samples Black points are from the shear profile fits for the L200 luminosity bins and the red points are from the N200 richness bins.

34. In Rachel MandelbaumRachel Mandelbaum, Uros Seljak, Christopher M. Hirata 2008Uros SeljakChristopher M. Hirata Astro-ph 0805.2552v20805.2552v2 FIG. 5: The best-fit c(M) relation at z = 0.22 with the 1 allowed region indicated. The red points with errorbars show the best-fit masses and concentrations for each bin when we fit them individually, without requiring a power-law c(M) relation. The blue dotted lines show the predictions of [39] for our mass definition and redshift, for theWMAP1 (higher) and WMAP3 (lower) cosmologies. The prediction for theWMAP5 cosmology falls in between the two and is not shown here. Their measurements are actually lower than the theoretical model Eventhough they have used WMAP1 (which gives a lower curve see Duffy et al. 2007). This indicate that they stack the clusters without Exactly center them ontop of each other and didn’t separate the background From the cluster galaxy good. These two effect lowers the concentration value.