Transcript Slide 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
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
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
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)
NFW PROFILE
c = rvir/rs with virial radius corresponding to overdensity of 101
for this talk and Mvir 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
NFW PROFILE
The global fit and the concentration parameter c does not
depend strongly on the innermost data points, r < 0.05 rvir
(Bullock et al. 2001, B01; Dolag et al. 2004, D04).
c-M relation
Bullock et al. 2001
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).
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 ≥ 1014 Msun) D04 find
that the c-M relation is adequately parameterized by a power
law
c-M relation
Kuhlen et al. 2005
The mass dependence is shallow and quite independent of cosmology;
the normalization depends sensitively on the cosmological parameters,
in particular σ8 and w (D04,Kuhlen et al. 2005).
c-M relation
Wechsler et al. 2002
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 (σlogc ≈ 0.10
compared to 0.14)
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
Pointecouteau et al.
2005
NFW a good fit to the mass profile (Pointecouteau et al. 2005, V06)
Pointecouteau et al. 2005
V06
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
Rines & Diaferio (2006)
Mandelbaum et al. (2006)
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
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 1012 ≤ M ≤ 1014 Msun
•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)
HIGHLIGHTS ON THE GALAXY SCALE …
Humphrey et al. 2006
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).
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 1012 ≤ M ≤ 1014 Msun
•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 (1013 ≤ M ≤ 1014 Msun) ,
where numerical predictions are more accurate because a large number
of halo can be simulated.
SELECTION OF THE SAMPLE
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.
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
BKG MODELLING
NGC 5044 offset
Buote et al. 2004
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
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
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
From T and ρ profiles to mass profiles
and the classical formulation of HE
From T and ρ profiles to mass profiles
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,ZFe). 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
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)
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
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-tolight ratios.
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-tolight 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
Humphrey et al. 2006
Stellar M/L 0.760.24
c-M relation for groups
We obtain a slope α=-0.2260.076, c decreases with M at the 3σ level
THE X-RAY c-M RELATION
• 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 1014 Msun. 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
THE X-RAY c-M RELATION
• 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 1014 Msun
• A power law fit requires at high significance (6.6σ) that c
decreases with increasing M
THE X-RAY c-M RELATION
WMAP 1 yr
Spergel et
al. 2003
THE X-RAY c-M RELATION
WMAP 3yr
Spergel et
al. 2006
THE X-RAY c-M RELATION
• 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 1014 Msun
• 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 σ8 (0.74), combined with
the action of the tilt of the power spectrum and the lower value
of Ωm. It can be reconciled if w ≈ -0.8
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