1. Lecture 2 IGM, Scaling Laws Clusters Cosmology Connection
CLUSTERS OF GALAXIES
Lecture 2
IGM, Scaling Laws
Clusters Cosmology Connection

2. Emission Processes of Clusters of Galaxies in the X-ray Band

3. Cluster Gas Density

4. Observables Relations T-M
Virial Equilibrium
Kinetic Energy for the gas
Thermodynamic
T-M relation

5. Status of The IGM T ~ 1-10 keV; Gas highly ionized
Age of Clusters ~ few Gyr; R ~ 1-2 Mpc
T ~ 1-10 keV; Gas highly ionized
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

6. Intracluster Medium Hydrostatic equilibrium (spherical symmetry)
We can measure the Cluster mass
Dynamical Properties of the Galaxies
King profile
Beta Profile
Isothermal Cluster

7. 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

8. Emission Processes of Clusters of Galaxies in the X-ray Band
Beside IGM contains
some metals (0.3 Solar)
They produce line emission

9. X-ray Observations Gas density Gas Temperature
Gas chemical composition
If assume hydrostatic equilibrium
Cluster Mass

10. Clusters –Cosmology connection
Clusters are useful cosmological tools

11. Evolution of N(M,z) to constrain cosmological parameters
Rosati, Borgani & Norman 03

12. Instead of M we can either use
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

13. Observables Relations T-M
Virial Equilibrium
Kinetic Energy for the gas
Thermodynamic
T-M relation

14. 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

15. 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

16. 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 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

17. 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

18. Observables Relations L-M
X-ray Luminosity

19. Observables Relations L-T
Theoretically
However from an observation point of view

20. 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

21. X-ray scaling laws: evolution

22. 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

23. Temperature Function & cosmological constraints
Markevitch 98
Henry 00

24. 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.

25. 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

26. 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

27. 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, X-ray/SZ clusters can answer in the next future

28. 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, X-ray/SZ clusters can answer in the next future
Mohr et al.

29. Clusters of Galaxies in the Microwaves
CMB+CLUSTERS
Sunyaev & Zel'dovich Effect

30. Sunyaev & Zel'dovich Effect

31. Sunyaev & Zel'dovich Effect