1. THE X-RAY C-M RELATION FABIO GASTALDELLO INAF-IASF MILANO, UCI
D. BUOTE, S. ETTORI, P. HUMPHREY, L. ZAPPACOSTA, A. LECCARDI, S. MOLENDI, M. ROSSETTI, J. BULLOCK, M. MENEGHETTI, W. MATHEWS, F. BRIGHENTI

2. OUTLINE INTRODUCTION: c-M AS COSMOLOGICAL TOOL
c-M RELATION FOR THE LOCAL SAMPLE
c-M FOR THE SAMPLE OF 44 CLUSTERS AT z=
CONCLUSIONS

3. DM DENSITY PROFILE
The concentration parameter c do not depend strongly on the innermost data points, r < 0.05 rvir (Bullock et al. 2001, B01; Dolag et al. 2004, D04).
Navarro et al. 2004

4. c-M RELATION c slowly declines as M increases (slope of -0.1)
Constant scatter (σlogc ≈ 0.14)
the normalization depends sensitively on the cosmological parameters, in particular σ8 and w (D04;Kuhlen et al. 2005; Macciò et al. 2008,M08).
For halos of fixed mass, the concentration parameter increases with decreasing redshift because the background density drops, and we have the c-z relation
Bullock et al. 2001

5. c-M RELATION Macciò et al. 2008
Quantify the slope, which is expected to be -0.1
The dependence on the two parameters is due to the fact that halos tend to form earlier.
The presence of dark energy is firmly established observationally (SNIa, CMB, power spectrum of galaxy clustering, baryon fraction of galaxy clusters), but measuring its equation of state and developing a theoretical understanding of its nature are two of the biggest outstanding problems in cosmology today
Macciò et al. 2008

6. X-RAY MASS DETERMINATION
Introduction with NFW and cosmological relevance of the c-M relation with current observational results
Lack of results in the group mass range which spurred the work I’m presenting here.
Method of analysis (bkg subtraction, potential approach to HE equation, care to addressing systematics)
Group results
Cosmological implications of the extended sample ranging from ellipticals to massive clusters (Buote et al. 2006)
Spectra averaged within circular annuli
Normalization / shape of spectrum gives gas density / temperature

7. X-RAY MASS DETERMINATION
A) Deproject with no need to assume parametrized quantities for gas quantities but smoothing required to obtain a physical mass profile (smoothed inversion)
Introduction with NFW and cosmological relevance of the c-M relation with current observational results
Lack of results in the group mass range which spurred the work I’m presenting here.
Method of analysis (bkg subtraction, potential approach to HE equation, care to addressing systematics)
Group results
Cosmological implications of the extended sample ranging from ellipticals to massive clusters (Buote et al. 2006)
B) Forward-fitting: fit gas density and temperature simultaneously assuming only parameterizations for density (or T or entropy) and mass
Buote & Humphrey 11

8. RESULTS
After accounting for the mass of the hot gas, NFW (+ stars) is the best fit model
STARS
GAS
MKW 4 DM
NGC 533

9. THE LOCAL X-RAY c-M RELATION
Buote, Gastaldello et al. 2007: c-M relation for 39 systems ranging in mass from ellipticals to the most massive galaxy clusters ( ) x 1014 Msun.
A power law fit requires at high significance (6.6σ) that c decreases with increasing M (slope ± 0.026)
Normalization and scatter consistent with relaxed objects
I will explain later what the lines in various colors are

10. THE LOCAL X-RAY c-M RELATION
The solid blue line is the best fitting power-law model while the dotted blue lines represent the 1 sigma scatter. The estimated intrinsic scatter in log c is 0.1020.04
Green line is the D04 model for higher mass halos with K=3.5, while the red line is the fit to lower mass halos with K=3.1
Within the context of WMAP 1 year
WMAP 1 yr Spergel et al. 2003

11. THE LOCAL X-RAY c-M RELATION
Green line is the D04 model for higher mass halos with K=3.5, while the red line is the fit to lower mass halos with K=3.1
Within the context of WMAP 3 year
WMAP 3yr Spergel et al. 2006

12. c-M relation for groups
The values of concentration and mass obtained by the best fit NFW+stars model are plotted here. The best fitting power law obtained with the BCES estimator is plotted in red along with the B01 model for sigma_8 = 0.9.
It is this mass range which provides crucial evidence that c decreases with M
The intrinsic scatter is low, 0.030.02 which agrees with CDM only if these halos are very relaxed, reinforcing the selection for HE equilibrium
We obtain a slope α=-0.2260.076, c decreases with M at the 3σ level

13. THE z = 0.1 – 0.3
In Ettori, Gastaldello et al. (2010) we used the sample from Leccardi & Molendi (2008), all hot clusters (kT > 3.3 keV) in the range 0.1 < z < 0.3, with detailed temperature profiles secured by performing accurate background modelling
Even though clusters showing evidence of recent and strong interactions were excluded, we have not only regular and relaxed clusters in the sample. They are characterized by the entropy ratios, following Leccardi et al. (2010), which are closely related to the dynamical disturbance
A 2204 LEC
A 1763 HEC

14. z = 0.1 – 0.3

15. z = 0.1 – 0.3
Slope steeper than predicted by simulations, it can not be constrained in the narrow mass range (all ± 0.07, LEC ± 0.15).
Normalization in agreement.
Constraints improve when considering only clusters with rs within the data and only LEC clusters. Concentration biased high in disturbed systems (e.g., Lau et al. 2009).

16. COSMOLOGICAL CONSTRAINTS

17. OPEN ISSUES HYDROSTATIC EQUILIBRIUM SELECTION EFFECTS
RADIAL RANGE OF DATA TO OBTAIN MASS PROFILE
THEORETICAL/SIMULATION PREDICTION
ADIABATIC CONTRACTION

18. BIAS IN HE DERIVED c
Lau et al. (2009)
TURBULENT PRESSURE RISING W/ RADIUS AND MORE IMPORTANT IN DISTURBED OBJECTS. SEE RASIA ET AL., MENEGHETTI ET AL.

19. SELECTION EFFECTS
A proper comparison between the theoretical c-M relations with observations requires the observed and simulated halos be selected in a consistent manner. Bear that in mind when we will compare these predictions with the X-ray selection of the most relaxed objects.
Wechsler et al. 2002
De Boni et al. 2013
WHAT ARE WE REALLY SELECTING WHEN WE SELECT “RELAXED” OBJECTS ?

20. RADIAL RANGE OF DATA RXJ 1159 Humphrey et al. (2012)
The original discussion in Mamon and Lokas is suited to elliptical galaxies, infact the x-axis is labeled by the DeV effective radius. This contribution has to be modeled even for higher mass systems, in particular X-ray bright groups which generally have a dominant central elliptical galaxies
Another effect discussed in the literature is adiabatic contraction. Recent observational results calls into question whether AC operates as predicted
RXJ 1159
Humphrey et al. (2012)

21. SUMMARY & CONCLUSIONS
c-M relation as determined from X-rays has provided independent evidence of hierarchical structure formation, in particular when fitted over a wide range of masses
c-M relation offers interesting and novel approach to potentially constrain cosmological parameters. Selection effects, HE, radial range of the data, response of DM to baryons (adiabatic contraction) and semi-analytic/ N-body simulations are open issues which have to be better characterized and improved.