THE X-RAY C-M RELATIONTHE 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

OUTLINEOUTLINE

1. INTRODUCTION

2. RESULTS AND c-M RELATION FOR X-RAY GROUPS

3. c-M RELATION OF THE EXTENDED LOCAL SAMPLE

4. c-M FOR THE SAMPLE OF 44 CLUSTERS AT z=0.1-0.3

5. CONCLUSIONS

DM DENSITY PROFILEDM DENSITY PROFILE

Navarro et al. 2004

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).

c-M RELATIONc-M RELATION

Bullock et al. 2001

•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).

c-M RELATIONc-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 (later modified by M08 to better match high mass end at higher z)

• the c-M relation is adequately parameterized by a power law over a large range in mass (D04, Shaw et al. 2006, M08)

• NFW a good fit to the mass profile

•c-M relation is consistent with no variation in c and with the gentle decline with increasing M expected from CDM (α = -0.040.03, P05).

Vikhlinin et al. 2006Pointecouteau et al. 2005

Clusters X-ray resultsClusters X-ray results

THE LOCAL SAMPLETHE LOCAL SAMPLE

•Improve significantly the constraints on mass profiles and c-M relation by analyzing a wider mass range with many more systems, in particular obtaining accurate mass constraints on relaxed systems with 1012 ≤ M ≤ 1014 Msun

•There were very few constraints on groups scale (1013 ≤ M ≤ 1014 Msun)

•In Gastaldello et al. 2007 we selected a sample of 16 objects in the 1-3 keV range from the XMM and Chandra archives with the best available data

X-RAY MASS DETERMINATIONX-RAY MASS DETERMINATION

• Spectra averaged within circular annuli• Normalization / shape of spectrum gives gas density

/ temperature

X-RAY MASS DETERMINATIONX-RAY MASS DETERMINATION1. Assume spherical symmetry2. Fit spectra with coronal plasma models and

obtain (deprojected) spectral quantities3. Fit parameterized functions to radial profiles of

gas density and temperature4. Assume hydrostatic equilibrium5. Calculate the radial mass profile

DATA ANALYSYSDATA ANALYSYS“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 HEGas density solution

We considered also the temperature solution

DATA ANALYSYSDATA ANALYSYS

•Fit gas density and temperature Fit gas density and temperature simultaneously assuming only simultaneously assuming only parameterizations for temperature and mass.parameterizations for temperature and mass.Advantages:Advantages:

•better constraints on Mbetter constraints on M•easy to interpret goodness of fiteasy to interpret goodness of fit

X-RAY SYSTEMATICSX-RAY SYSTEMATICS

1. HYDROSTATIC EQUILIBRIUM

2. MULTIPHASE GAS/PROJECTION EFFECTS IN CORES

3. DISCRETE SOURCES IN Es

4. BKG SUBTRACTION

5. DEPROJECTION AND FITTING PROCEDURES

RESULTSRESULTS•After accounting for the mass of the hot gas, NFW + stars is the best fit model

MKW 4

NGC 533

STARS

GAS

DM

RESULTSRESULTS•No detection of stellar mass due to poor sampling in the inner 20 kpc or localized AGN disturbance

A 2717

RESULTSRESULTS•No detection of stellar mass due to poor sampling in the inner 20 kpc or localized AGN disturbance

NGC 5044

Buote et al. 2002, Gastaldello et al. 2009

c-M relation for groupsc-M relation for groups

We obtain a slope α=-0.2260.076, c decreases with M at the 3σ level

THE LOCAL X-RAY c-M RELATION 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 (0.06-20) x 1014 Msun.

• A power law fit requires at high significance (6.6σ) that c decreases with increasing M (slope -0.172 ± 0.026)

• Normalization and scatter consistent with relaxed objects

THE LOCAL X-RAY c-M RELATION THE LOCAL X-RAY c-M RELATION

WMAP 1 yr Spergel et al. 2003

THE LOCAL X-RAY c-M RELATION THE LOCAL X-RAY c-M RELATION

WMAP 3yr Spergel et al. 2006

THE SAMPLE @ z = 0.1 – 0.3THE SAMPLE @ 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

COMPARISON OF METHODSCOMPARISON OF METHODS

COMPARISON OF METHODSCOMPARISON OF METHODS

c-M @ z = 0.1 – 0.3c-M @ z = 0.1 – 0.3

Slope steeper than predicted by simulations, it can not be constrained in the narrow mass range (all -0.50 ± 0.07, LEC -0.28 ± 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).

COSMOLOGICAL CONSTRAINTSCOSMOLOGICAL CONSTRAINTS

From the distribution of c and M using semi-analytic prescriptions calibrated through simulations, with the further constrain on the gas mass fraction, we obtain best fit values of σ8 = 1.0 ± 0.2 (0.83 ± 0.1 with the 11 LEC) and Ωm = 0.26 ± 0.02

11 LEC

26 w/ rs within the data

ALL 44

SUMMARY & CONCLUSIONSSUMMARY & CONCLUSIONS

•Mass constraints for X-ray bright groups/poor clusters in the local universe 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 potentially constrain cosmological parameters. Selection effects, response of DM to baryons (adiabatic contraction) and semi-analytic/ N-body simulations have to be better characterized and improved.