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Report
CLUSTERS OF GALAXIES
IGM, and Scaling Laws
Emission Processes of Clusters
of Galaxies in the X-ray Band
Status of The IGM
Age of Clusters ~ few Gyr; R ~ 1-2 Mpc
T ~ 1-10 keV; Gas highly ionized; density 10-3cm-3
Electrons free mean path
Gas may be treated as a fluid
Timescale for Coulomb Collisions
Electrons are in kinetic equilibrium
Maxwellian velocity distribution
Timescale for soundwave propagation
Gas is in hydrostatic equilibrium
Intracluster Medium
Hydrostatic equilibrium (spherical symmetry)
We can measure the Cluster mass
Dynamical Properties of the Galaxies
Isothermal Cluster
King profile
Beta Profile
Emission Processes of Clusters
of Galaxies in the X-ray Band
•The IGM is a Plasma
•Electrons are accelerated by the ions
•They emit for Bremsstrahlung
•Electrons are in kinetic equilibrium (Maxwellian V distr. )
•Cluster emission is mainly thermal Bremsstrahlung
Emission Processes of Clusters
of Galaxies in the X-ray Band
Beside IGM contains
some metals (0.3 Solar)
They produce line emission
X-ray Observations
•Gas density
•Gas Temperature
•Gas chemical composition
•If assume hydrostatic equilibrium
Cluster Mass
Clusters –Cosmology
connection
Clusters are useful cosmological tools
Evolution of N(M,z) to constrain
cosmological parameters
Rosati, Borgani & Norman 03
But: matter is dark & we need light to
see/count/measure galaxy clusters…
Instead of M we can either use
LX  ngas2 (T) Volume
or
Tgas
Cluster Gas Density
Observables Relations
L-M
X-ray Luminosity
Observables Relations
T-M
Virial Equilibrium
Kinetic Energy for the gas
Thermodynamic
T-M relation
X-ray scaling laws: M  T3/2
Evrard, Metzler & Navarro (1996) use gasdynamic simulations to assess the
accuracy of X-ray mass estimations & conclude that within an overdensity
between 500 and 2500, the masses from -model are good. The scatter can
be reduced if M is estimated from the tight M-T relation observed in
simulations:
M500 = 2.22e15 (T/10 keV)3/2 h50-1 Msun
-model
law
X-ray scaling laws: M  T3/2
Nevalainen et al. (2000) using a ASCA (clusters: 6) & ROSAT
(groups: 3) T profiles: (i) in the 1-10 keV range, M1000  T 1.8
[preheating due to SN?], but (ii) at T>4 keV, M1000  T 3/2 [they
claim, but measure 1.80.5 at 90%…] & norm 50% [!!!] lower than
EMN :
EMN96
X-ray scaling laws: M  T3/2
Finoguenov et al. (2001) use a flux-limited sample of 63 RASS
clusters (T mainly from ASCA) & 39 systems btw 0.7-10 keV with
ASCA T profile.
(i) Steeper profile than 3/2,
high scatter in groups
(ii) deviations from simulations
due to pre-heating [makes flat
ngas] & z_formation
(iii) M from -model:  depends
on T
EMN96
X-ray scaling laws: M  T3/2
Allen et al. (2001): 7 massive clusters observed with
Chandra, M2500-T2500 relation.
slope of 1.52  0.36 &
normalization lower
than 40%.
ME01
Observables Relations
L-T
Theoretically
However from an observation point of view
X-ray scaling laws: self-similar?
We have a consistent picture at T>3 keV, but also
evidence that cool clusters/groups may be not just
a scaled version of high-T clusters [review in Mulchaey
2000]
T3
T5
X-ray scaling laws: evolution
Luminosity Function
Local (left) & high-z (right) XLF: no evolution evident
below 3e44 erg/s, but present at 3 level above it (i.e.
more massive systems are rare at z>0.5)
Rosati et al. 03
Temperature Function & cosmological
constraints
Markevitch 98
Henry 00
Cosmology in the WMAP era
1-st year results of the temperature
anisotropies in the CMB from MAP
(Bennett et al., Spergel et al 03) put alone
constraints on tot, bh2, mh2.
Cosmology in the WMAP era
However, the final answer to the cosmology quest is not
given:
• the cosmological parameters in CMB are degenerate…
complementary
• the equation of state of Dark Energy & its evolution
with redshift is not known
• given that, we can play the reverse game: fix the
cosmology & see what your cosmology-dependent data
require
Cosmology in the WMAP era
In non-flat cosmologies, there is degeneracy in m- space (e.g. =0 is
consistent with MAP results, but requires H0=32 and tot=1.28…).
To get tighter & non-degenerated constraints, one needs to add
something else, like, P(k) from 2dF & Lyman- forest, Hubble KP, SN Ia,
clusters survey…: complementarity
Allen etal 02
Cosmology in the WMAP era
The equation of state of the Dark Energy & its evolution with
time: only post-MAP CMB surveys (i.e. Planck in 2007), SN Ia, Xray/SZ clusters can answer in the next future
Cosmology in the WMAP era
The equation of state of the Dark Energy & its evolution with
time: only post-MAP CMB surveys (i.e. Planck in 2007), SN Ia, Xray/SZ clusters can answer in the next future
Mohr et al.
Clusters of Galaxies
in the Microwaves
CMB+CLUSTERS
Sunyaev & Zel'dovich Effect
Sunyaev & Zel'dovich Effect
Sunyaev & Zel'dovich Effect

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