1. GH2005 Gas Dynamics in Clusters
Craig Sarazin
Dept. of Astronomy
University of Virginia
Cluster Merger Simulation
A85 Chandra (X-ray)

2. Clusters of Galaxies ~4 Mpc diameter ~1015 M total mass
Largest gravitationally bound systems in Universe
100’s of bright galaxies, 1000’s of faint galaxies
~4 Mpc diameter
~1015 M total mass

4. Intracluster Gas
Majority of observable cluster mass (majority of baryons) is hot gas
Temperature T ~ 108 K ~ 10 keV
Electron number density ne ~ 10-3 cm-3
Mainly H, He, but with heavy elements (O, Fe, ..)
Mainly emits X-rays
LX ~ 1045 erg/s, most luminous extended X-ray sources in Universe
Age ~ 2-10 Gyr

5. Physical State of Intracluster Gas: Local Thermal State
Mainly ionized, but not completely
State of
free particles (kinetic equilibrium)?
bound vs. free electrons
(ionization equilibrium)?
bound electrons (excitation)?
free continuum
bound levels

6. Kinetic Equilibrium Free electrons, protons, other ions
Coulomb collisions → thermodynamic equil.

7. Kinetic Equilibrium Coulomb collision time scales t(e,e) ~ 105 yr
t(p,p) ~ 4 x 106 yr
t(p,e) ~ 2 x 108 yr
all < age (>109 yr)
Kinetic equilibrium, Maxwellian at T
Equipartition Te=Tp
(except possibly at shocks)

8. Ionization Equilibrium
Collisional ionization
e- + X+i → e- + e- + X+i+1
Radiative, dielectronic recombination
e- + X+i+1 → X+i + photon(s)
(not e- + e- + X+i+1 → e- + X+i )
Not thermodynamic equilibrium (Saha)!
Collisional ionization equilibrium
independent of density ne
depends only on temperature T
(except perhaps in shocks)

9. Ionization Equilibrium
Iron
XXV = Fe+24 (helium-like iron)

10. Excitation Equilibrium
bound levels
Collisional excitation
Radiative de-excitation
(line emission)
No collisional de-excitation
(density too low)
No local density diagnostics in spectrum e
photon

11. X-ray Emission Processes
Continuum emission
Thermal bremsstrahlung, ~exp(-hn/kT)
Bound-free (recombination)
Two Photon
Line Emission
(line emission)
Ln ∝ en (T, abund) (ne2 V)
In ∝ en (T, abund) (ne2 l)

12. X-ray Spectrum

13. The Intracluster Medium as a Fluid
Mean-free-path λe ~ 20 kpc < 1% of diameter → fluid
(except possibly in outer regions, near galaxies, or at shocks and cold fronts)

14. The Intracluster Medium as a Fluid (cont.)
Specify local:
Density (r or ne)
Pressure P
Internal energy or temperature T
Velocity v
Ideal gas P = n k T
(except for nonthermal components;
cosmic rays, magnetic fields)

15. Transport Properties Due to finite mean free path thermal conduction
viscosity
diffusion and settling of heavy elements

16. Heat Conduction Spitzer heat conductivity
Strongly dependent on temperature Q ∝ T7/2

17. Heat Conduction (cont.)
600 kpc
10 Gyr

18. Heat Conduction (cont.)
If unsuppressed, heat conduction very important in
centers of clusters,
or where there are large temperature gradients
cooling cores
cold fronts
near galaxies with gas

19. Magnetic Fields in Clusters
B ~ mG → PB « Pgas in general in clusters
Electron, ions gyrate around magnetic
field lines
rg ≈ 108 cm « scales of interest
Act like effective mean free path,
make ICM more of a fluid
Suppress transport properties ⊥ B
Could greatly reduce thermal conduction,
but depends on topology of B fields B e

20. Heating and Cooling of ICM
What determines temperature T?
Why is ICM so hot?
What are heating processes?
gravitational heating
nongravitational heating (SNe, AGNs)
What are cooling processes?

21. Why is gas so hot?
Clusters have huge masses, very deep gravitational potential wells
Any natural way of introducing gas causes it to move rapidly and undergo fast shocks
infall galaxy ejection
All intracluster gas is shocked at ~2000 km/s

22. Cluster Mergers
Clusters from hierarchically, smaller things form first, gravity pulls them together
Abell 85 Chandra

23. Merger Shocks
Main heating mechanism of intracluster gas

24. Simple Scaling Laws for Gravitational Heating (Kaiser 1986)
Gas hydrostatic in gravitational potential
kT ~ mmp GM/R
Clusters formed by gravitational collapse
〈rcluster ~ 180 rcrit (zform)
Most clusters formed recently, zform ~ now
Baryon fraction is cosmological value, most baryons in gas
R ∝ ( M / rcrit0 )1/3 ∝ M1/3
T ∝M2/3
LX ∝T2

25. Need for Nongravitational Heating
Scaling laws disagree with observations, particularly for lower mass systems (groups)
Gas distributions are too extended, may have cores
Explanations:
nongravitational heating, puffs up gas distribution
inhomogeneous gas and radiative cooling removes cooler gas

26. Nongravitational Heating and Entropy
If heating done now, need e ~2 keV per particle
For preheating, or more complex history, better variable is amount of extra entropy per particle
s = (3/2) k ln (P/r5/3) + s0
P = rkT/( mmp)
define
K ≡ kT/(ne)2/3 keV cm2
(s ∝ln K)

27. Specific Entropy - Advantages
Lagrangian variable, moves with gas, mirrors history of each gas parcel
For any reversible change to gas, remains constant
ds/dt = 0, dK/dt = 0
Reversible changes: slow compression or expansion
Irreversible changes include:
shocks
heating
cooling

28. Nongravitational Entropy
Purely gravitational heating (entropy from merger shocks) gives scaling
K ∝T ∝ M2/3

29. Cluster and Group Entropies at 0.1 Rvir
K ∝T gravity
(Lloyd-Davies et al. 2000)

30. Nongravitational Entropy
Purely gravitational heating (entropy from merger shocks) gives scaling
K ∝T ∝ M2/3
Observed clusters and groups require extra entropy
K ~ 125 keV cm2
Entropy increases outwards in clusters. convectively stable

31. Entropy vs. Radius
data
gravity
(Ponman et al. 2003)

32. Heating by Supernovae
Core-collapse supernovae, massive stars, during period of galaxy formation, galactic winds
Type Ia supernovae, older binary stars, more continuous
Supernovae also make heavy elements
e ~ 1.6 ZSi (Esn/1051 ergs) keV ≲ 0.3 keV (Loewenstein 2000)
Probably a bit low, but possible

33. Heating by AGN
Need energy deposited in ICM: large scale kinetic energy (jets) and particles, not radiation from AGN
Clusters → E & S0 galaxies → radio galaxies and radio QSOs
Estimate total energy input from MBH today, MBH ∝ Mbulge . Assume MBH due to gaseous accretion, E = e MBH .
Provides enough energy, if a significant part deposited in ICM

34. Universal Pre-Heating of Intergalactic Gas?
Lyman a forest clouds at z ~ 2 → much of IGM relatively cool

35. Radiative Cooling of ICM
Main cooling mechanism is radiation, mainly X-rays
L = L(T,abund) ne2
ergs/cm3/s
T ≳ 2 kev, L ∝ T1/ Thermal bremsstrahlung
T ≲ 2 keV, L ∝ T-0.4
X-ray lines

36. Radiative Cooling (cont.)
Cooling time (isobaric, constant pressure)
Longer than Hubble time in outer parts of clusters
Short in centers of ~1/2 clusters, “cooling flows”, tcool ~ 3 x 108 yr

37. Pre-Cooling vs. Pre-Heating
Cooling time, in terms of entropy:
Shorter than Hubble time for K ≲ 130 kev cm2
If clusters start with gas with a wide range of entropies, low entropy gas cools out, leaves behind high entropy gas (Voit & Bryan 2001)
Cooled gas → galaxy formation, stars

38. Heating of ICM - Summary
Most of energy in large clusters due to gravity, mergers of clusters
Smaller clusters, groups, centers of clusters → significant evidence of nongravitational heating
Due to galaxy and star formation, supernovae, formation of supermassive BHs
ICM/IGM records thermal history of Universe

39. Hydrodynamics
Add viscosity, thermal conduction, … Add magnetic fields (MHD) and cosmic rays Gravitational potential f from DM, gas, galaxies

40. Sound Crossing Time Sound speed Sound crossing time
Less than age → unless something happens (merger, AGN, …),
gas should be nearly hydrostatic

41. Hydrostatic Equilibrium
Isothermal (T = constant)

42. Cluster Potentials NFW (Navarro, Frenk, & White 1997) r-1 ln r NFW r-3

43. Cluster Potentials (cont.)
Analytic King Model (approximation to isothermal sphere
NFW
King
r-1
flat core
ln r
ln r
r-3

44. Beta Model (Cavaliere & Fusco-Femiano 1976)
Assume King Model DM potential Alternatively, assume galaxies follow King Model, and have isotropic, constant velocity dispersion

45. Beta Model (cont.)

46. Beta Model (cont.) Fit outer parts of clusters (Multiple beta models)
≈ 2/3
∝ r -2
IX ∝ r -3
Beta model
XMM/Newton A Pratt & Arnaud

47. Hydrostatic Equilibrium (cont.)
Adiabatic (Polytropic) Models

48. Cluster Temperature Profiles
Rapid T rise with r at center (100 kpc, “cooling core”)
T flat to rvir
Slow T decline with r at large radii
g ~ 1.2
Chandra
(Vikhlinin et al 2005)