Transcript Slide 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 OUTLINE 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 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 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). Bullock et al. 2001 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 (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) Clusters X-ray results Pointecouteau et al. 2005 Vikhlinin et al. 2006 • 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). THE 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 DETERMINATION • Spectra averaged within circular annuli • Normalization / shape of spectrum gives gas density / temperature X-RAY MASS DETERMINATION 1. 2. 3. 4. 5. Assume spherical symmetry Fit spectra with coronal plasma models and obtain (deprojected) spectral quantities Fit parameterized functions to radial profiles of gas density and temperature Assume hydrostatic equilibrium Calculate the radial mass profile DATA 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 HE Gas density solution We considered also the temperature solution DATA ANALYSYS •Fit gas density and temperature simultaneously assuming only parameterizations for temperature and mass. Advantages: •better constraints on M •easy to interpret goodness of fit X-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 RESULTS •After accounting for the mass of the hot gas, NFW + stars is the best fit model STARS GAS MKW 4 DM NGC 533 RESULTS •No detection of stellar mass due to poor sampling in the inner 20 kpc or localized AGN disturbance A 2717 RESULTS •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 groups We obtain a slope α=-0.2260.076, c decreases with M at the 3σ level 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 (0.0620) 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 WMAP 1 yr Spergel et al. 2003 THE LOCAL X-RAY c-M RELATION WMAP 3yr Spergel et al. 2006 THE 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 METHODS COMPARISON OF METHODS c-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 CONSTRAINTS 26 w/ rs within the data ALL 44 11 LEC 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 SUMMARY & 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.