1. X-RAY BRIGHT GALAXY GROUPS AS COSMOLOGICAL TOOLS FABIO GASTALDELLO UNIVERSITY OF CALIFORNIA IRVINE D. BUOTE P. HUMPHREY L. ZAPPACOSTA J. BULLOCK W. MATHEWS UCSC F. BRIGHENTI BOLOGNA

2. OUTLINE 1.INTRODUCTION 2.THE GROUP SAMPLE 3.METHOD OF ANALYSIS 4.RESULTS AND c-M PLOT 5.COSMOLOGICAL IMPLICATIONS OF THE c-M PLOT 6.CONCLUSIONS

3. THE COSMOLOGICAL MODEL The current cosmological model, ΛCDM, has become established through a variety of observations (CMB, supernovae, galaxy surveys) which probe the large scale, high-z universe in linear clustering regime (δ ‹‹ 1) Testing the model on smaller scales, fully into the non-linear regime (δ ›› 1) will further our understanding of structure formation and evolution and refine the fundamental parameters of the cosmological model itself

4. WHAT SIMULATIONS TELL US Basic theory for the buildup of structure in the universe and the evolution of properties of gravitationally bound structures is well developed, it has been extensively simulated at increasingly high resolution and analytic formulations have been developed to describe their behavior (e.g., mass function: Jenkins et al. 2001). Density profiles of dark matter halos on all scales can be well approximated by a universal profile (Navarro, Frenk & White 1995, 1997)

5. NFW PROFILE c = r vir /r s with virial radius corresponding to overdensity of 101 for this talk and M vir characterize the profile Much debate about the exact inner slope (e.g. Moore et al. 1999), but a consistent view has now emerged in which real dispersion is expected between individual halos (e.g., Tasitsiomi et al. 2004). N04 (Navarro et al. 2004) Sersic-like model with no asymptotic value of the inner slope

6. NFW PROFILE The global fit and the concentration parameter c does not depend strongly on the innermost data points, r < 0.05 r vir (Bullock et al. 2001, B01; Dolag et al. 2004, D04).

7. c-M relation The central density in halo cores is found to reflect the mean density of the Universe at the time of halo formation. Since halos of increasing mass form at increasingly late epochs, the concentration parameter of halos at fixed redshift decreases with mass, with substantial intrinsic scatter independent of M (B01, D04, Shaw et al. 2006, Maccio’ et al. 2006). Bullock et al. 2001

8. c-M relation The median c-M relation for CDM halos is well described by the semi-analytic model proposed by B01, with 2 adjustable constants In the high mass “cluster” regime (M ≥ 10 14 M sun ) D04 find that the c-M relation is adequately parameterized by a power law

9. c-M relation The mass dependence is shallow and quite independent of cosmology; the normalization depends sensitively on the cosmological parameters, in particular σ 8 and w (D04,Kuhlen et al. 2005). Kuhlen et al. 2005

10. Concentrations for relaxed, early forming halos are larger by 10% compared to the whole population (Jing 2000, Wechsler 2002, Maccio’ 2006). They show also smaller scatter (σ logc ≈ 0.10 compared to 0.14) Wechsler et al. 2002 c-M relation

11. WHAT OBSERVATIONS TELL US This prediction is starting to be extensively tested at the scale of massive clusters (Pointecouteau et al. 2005, Vikhlinin et al. 2006, V06) both in term of the shape of the DM profile and the relation between the concentration parameter c and the virial mass M

12. NFW a good fit to the mass profile (Pointecouteau et al. 2005, V06) Pointecouteau et al. 2005

13. c-M relation for clusters using high quality XMM and Chandra data are consistent with no variation in c and with the gentle decline with increasing M expected from CDM ( α = - 0.04  0.03, Pointecouteau et al. 2005). Measurements slightly higher than average: highly relaxed clusters Pointecouteau et al. 2005 V06

14. c-M relation obtained using different techniques, e.g., redshift-space caustics (Rines & Diaferio 2006), weak gravitational lensing (Mandelbaum et al. 2006) are all consistent with no variation in c Rines & Diaferio (2006) Mandelbaum et al. (2006)

15. THE PROJECT Improve significantly the constraints on the c-M relation by analyzing a wider mass range with many more systems, in particular obtaining accurate mass constraints on relaxed systems with 10 12 ≤ M ≤ 10 14 M sun Our recent study of the mass profiles of 7 early type galaxies with Chandra indicates c-M values consistent with ΛCDM (Humphrey et al. 2006)

16. HIGHLIGHTS ON THE GALAXY SCALE … Humphrey et al. 2006

17. HIGHLIGHTS ON THE GALAXY SCALE … Humphrey et al. 2006

18. The contribution of the stellar mass NFW distribution apply only to the dark matter component and the baryons have a different distribution dominating the mass profile in the inner regions. Fitting an NFW model to DM NFW + stellar component can bias the result (Mamon & Lokas 2005) In addition adiabatic contraction (AC) could play a role i.e. DM halo responds to condensations of baryons into stars, which should cause the DM profile to contract adiabatically in the center (Blumenthal et al. 1986).

19. THE PROJECT Improve significantly the constraints on the c-M relation by analyzing a wider mass range with many more systems, in particular obtaining accurate mass constraints on relaxed systems with 10 12 ≤ M ≤ 10 14 M sun Our recent study of the mass profiles of 7 early type galaxies with Chandra indicates c-M values consistent with ΛCDM (Humphrey et al. 2006) There are very few constraints on groups scale (10 13 ≤ M ≤ 10 14 M sun ), where numerical predictions are more accurate because a large number of halo can be simulated.

20. In stark contrast with the situation for clusters, there is no X-ray selected, flux limitated sample to derive statistical constraints In Gastaldello et al. 2006 (astro-ph 0610134) we selected a sample of 16 objects from the XMM and Chandra archives with the best available data with no obvious disturbance, with a dominant elliptical galaxy at the center The best we can do to ensure hydrostatic equilibrium and recover mass from X-rays. SELECTION OF THE SAMPLE

23. DATA ANALYSIS We extracted concentric circular annuli located at the X-ray centroid and fitted 1T models (+ brem when needed) Bkg subtraction is crucial. Usual methods like simple use of bkg templates or double subtraction (Arnaud et al. 2002) have some flaws We completely model the various bkg components (Lumb et al. 2002), exploiting the fact that the source component, mainly characterized by the Fe-L shell, is clearly spectrally separated from the other bkg components

24. BKG MODELLING NGC 5044 offset Buote et al. 2004

25. DATA ANALYSIS Chandra is crucial in the inner region where a steep temperature gradient is present When data are available, we use Chandra in the core and XMM in the outer regions

26. DATA ANALYSIS Chandra is crucial in the inner region where a steep temperature gradient is present When data are available, we use Chandra in the core and XMM in the outer regions

27. From T and ρ profiles to mass profiles “Parametric mass method” is the principal approach of the study: we assume parameterizations for the temperature and mass profiles to calculate the gas density assuming HE Gas density solution We considered also the temperature solution

28. and the classical formulation of HE From T and ρ profiles to mass profiles

29. NGC 1550 We projected parameterized models of the 3D ρ and T thus obtained to the result obtained from our spectral analysis (the projected gas mass density is derived from the norm of the thermal spectral model), including the radial variation of the plasma emissivity  (T,Z Fe ). We use these models to evaluate the terms of the equation of hydrostatic equilibrium. Using an onion peeling deprojection (e.g., Fabian et al. 1981) gives consistent results with the above method

30. Mass Models For the mass models (applied to the gravitating matter) we consider NFW NFW + stars, modeled with a de Vaucolueurs model with effective radius measured in the K band by 2MASS (Jarrett et al. 2000) NFW +stars adiabatically contracted (AC) using code by O. Gnedin (Gnedin et al. 2004)

31. RESULTS After accounting for the mass of the hot gas, the resulting mass profiles are well described by a two component model, consisting of DM represented by NFW and stars from the central galaxy

35. RESULTS Adopting more complicated models, like introducing AC or N04 did not improve the fits. AC produces too low stellar mass-to- light ratios.

36. RESULTS After accounting for the mass of the hot gas, the resulting mass profiles are well described by a two component model, consisting of DM represented by NFW and stars from the central galaxy Adopting more complicated models, like introducing AC or N04 did not improve the fits. AC produces too low stellar mass-to- light ratios Not all the objects require stellar mass. When the radial range where the stellar component is relevant is adequately sampled by the X-ray data, this can be due to possible localized disturbances due to AGN activity (e.g., NGC 5044). Stellar M/L for the objects with best available data is 0.57  0.21, in reasonable agreement with SP synthesis models

37. Humphrey et al. 2006 Stellar M/L 0.76  0.24

38. c-M relation for groups We obtain a slope α=-0.226  0.076, c decreases with M at the 3σ level

39. In Buote et al. 2006 (astro-ph 0610135) we present the c-M relation for 39 systems ranging in mass from ellipticals to the most massive galaxy clusters (0.06-20) x 10 14 M sun. Together with the 23 objects of Humphrey et al. (2006) and Gastaldello et al. (2006), several clusters have been added: A2589 (Zappacosta et al. 2006) and the objects from V06 and Pointecouteau et al. (2006) THE X-RAY c-M RELATION

41. In Buote et al. 2006 (astro-ph 0610135) we present the c-M relation for 39 systems ranging in mass from ellipticals to the most massive galaxy clusters (0.06-20) x 10 14 M sun A power law fit requires at high significance (6.6σ) that c decreases with increasing M THE X-RAY c-M RELATION

42. WMAP 1 yr Spergel et al. 2003

43. THE X-RAY c-M RELATION WMAP 3yr Spergel et al. 2006

44. In Buote et al. 2006 (astro-ph 0610135) we present the c-M relation for 39 systems ranging in mass from ellipticals to the most massive galaxy clusters (0.06-20) x 10 14 M sun A power law fit requires at high significance (6.6σ) that c decreases with increasing M The WMAP 3 yr model is rejected at > 99.99% and the reason of its poor performance is the low value of σ 8 (0.74), combined with the action of the tilt of the power spectrum and the lower value of Ω m. It can be reconciled if w ≈ -0.8 THE X-RAY c-M RELATION

47. CONCLUSIONS Mass constraints for X-ray bright groups derived from good quality Chandra and XMM data can be of the same quality as obtained for hot, massive clusters. This crucial mass regime has provided the crucial evidence of the decrease of c with increasing M c-M relation offers interesting and novel approach to constrain cosmological parameters