GH2005 Gas Dynamics in Clusters Craig Sarazin Dept. of Astronomy University of Virginia A85 Chandra...
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Transcript of GH2005 Gas Dynamics in Clusters Craig Sarazin Dept. of Astronomy University of Virginia A85 Chandra...
GH2005Gas Dynamics in Clusters
Craig SarazinDept. of Astronomy
University of Virginia
A85 Chandra (X-ray)Cluster Merger
Simulation
Clusters of Galaxies
• Largest gravitationally bound systems in Universe
• 100’s of bright galaxies, 1000’s of faint galaxies
• ~4 Mpc diameter
• ~1015 M total mass
• 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
Intracluster Gas
• Mainly ionized, but not completely
• State of• free particles (kinetic
equilibrium)?• bound vs. free
electrons(ionization equilibrium)?
• bound electrons (excitation)?
Physical State of Intracluster Gas:
Local Thermal State
free continuum
bound levels
• Free electrons, protons, other ions• Coulomb collisions → thermodynamic
equil.
Kinetic Equilibrium
),(1800),()/(),(
),(43),(/),(
yrcm10K10
103),(
40)/ln(ln
ln8)(23
)2,1(
1
33
2/3
85
minmax
422
2122
2/31
eeeemmep
eeeemmpp
nTee
bb
eZZnmkTm
ep
ep
e
• Coulomb collision time scales(e,e) ~ 105 yr(p,p) ~ 4 x 106 yr(p,e) ~ 2 x 108 yrall < age (>109 yr)
Kinetic equilibrium, Maxwellian at TEquipartition Te=Tp
(except possibly at shocks)
Kinetic Equilibrium
• Collisional ionizatione- + X+i → e- + e- + X+i+1
• Radiative, dielectronic recombinatione- + 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)
Ionization Equilibrium
Ionization Equilibrium
Iron
XXV = Fe+24 (helium-like iron)
• Collisional excitation• Radiative de-excitation
(line emission)• No collisional de-excitation
(density too low)
No local density diagnostics in spectrum
Excitation Equilibrium
ee e
bound levels
photon
• Continuum emission• Thermal bremsstrahlung,
~exp(-h/kT)• Bound-free (recombination)• Two Photon
• Line Emission(line emission)
L∝ (T, abund) (ne2 V)
I∝ (T, abund) (ne2 l)
X-ray Emission Processes
X-ray Spectrum
The Intracluster Medium as a Fluid
ln8)(3
4
22/3
enkT
eep
kpccm10K10
231
33
2
8
enT
Mean-free-path λe ~ 20 kpc < 1% of diameter → fluid
(except possibly in outer regions, near galaxies, or at shocks and cold fronts)
The Intracluster Medium as a Fluid
(cont.)• Specify local:
• Density (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)
Transport Properties• Due to finite mean free path
• thermal conduction• viscosity• diffusion and settling of heavy
elements
Heat Conduction• Spitzer heat conductivity
• Strongly dependent on temperature Q ∝ T7/2
cgsK10
105
31.1
sec)/(ergs/cm
2/5
813
2/1
2
T
mkT
kn
TQ
eee
Heat Conduction (cont.)
600 kpc
10 Gyr
Heat Conduction (cont.)If unsuppressed, heat conduction very
important in centers of clusters,
or where there are large temperature gradients
cooling corescold frontsnear galaxies with gas
Magnetic Fields in ClustersB ~ G → PB « Pgas in general in clustersElectron, ions gyrate around magnetic
field linesrg ≈ 108 cm « scales of interest
• Act like effective mean free path,make ICM more of a fluid
• Suppress transport properties ⊥ BCould greatly reduce thermal conduction,
but depends on topology of B fields
B
e
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?
• 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
Why is gas so hot?
All intracluster gas is shocked at ~2000 km/s
Clusters from hierarchically, smaller things form first, gravity pulls them together
Cluster Mergers
Abell 85 Chandra
Main heating mechanism of intracluster gas
Merger Shocks
Simple Scaling Laws for Gravitational Heating (Kaiser 1986)
• Gas hydrostatic in gravitational potential
kT ~ mp GM/R• Clusters formed by gravitational
collapse⟨cluster ~ 180 crit (zform)
• Most clusters formed recently, zform ~ now
• Baryon fraction is cosmological value, most baryons in gas
R ∝ ( M / crit0 )1/3 ∝ M1/3
T ∝M2/3
LX ∝T2
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
Nongravitational Heating and Entropy
• If heating done now, need ~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/5/3) + s0
P = kT/( mp)define
K ≡ kT/(ne)2/3 keV cm2
(s ∝ln K)
Specific Entropy - Advantages• Lagrangian variable, moves with gas,
mirrors history of each gas parcel• For any reversible change to gas,
remains constantds/dt = 0, dK/dt = 0
• Reversible changes: slow compression or expansion
• Irreversible changes include:• shocks• heating• cooling
Nongravitational Entropy• Purely gravitational heating (entropy
from merger shocks) gives scalingK ∝T ∝ M2/3
Cluster and Group Entropies at 0.1 Rvir
(Lloyd-Davies et al. 2000)
K ∝T gravity
Nongravitational Entropy• Purely gravitational heating (entropy
from merger shocks) gives scalingK ∝T ∝ M2/3
• Observed clusters and groups require extra entropy
K ~ 125 keV cm2
• Entropy increases outwards in clusters. convectively stable
Entropy vs. Radius
(Ponman et al. 2003)
gravity
data
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~ 1.6 ZSi (Esn/1051 ergs) keV ≲ 0.3
keV (Loewenstein 2000)
Probably a bit low, but possible
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 = MBH .
Provides enough energy, if a significant part deposited in ICM
Universal Pre-Heating of Intergalactic Gas?
• Lyman forest clouds at z ~ 2 → much of IGM relatively cool
Radiative Cooling of ICM• Main cooling mechanism is
radiation, mainly X-rays
L = (T,abund) ne2
ergs/cm3/s
T ≳ 2 kev, ∝T1/2 Thermal
bremsstrahlungT ≲ 2 keV, ∝T-0.4
X-ray lines
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
GyrK10cm10
692/1
8
1
33
Tnt ecool
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
GyrkeV2cm keV130
1412/3
2
TK
tcool
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
Hydrodynamics
state ofequation
cooling) & (heatingentropy
(Euler)on conservati momentum 0
y)(continuiton conservati mass 0)(
pmkT
P
LHDtDs
T
PDtDv
vt
Add viscosity, thermal conduction, … Add magnetic fields (MHD) and cosmic rays Gravitational potential from DM, gas, galaxies
Sound Crossing Time• Sound speed
• Sound crossing time
Less than age → unless something happens (merger, AGN, …),
gas should be nearly hydrostatic
km/sK10
1500
35
2/1
8
2
Tc
PPc
s
s
yrMpcK10
106.62/1
88
DTts
Hydrostatic Equilibrium
spherical )(1
2rrGM
drd
drdP
P
Isothermal (T = constant)
)()(ln
ln11
00
rkT
mr
mkT
mkT
P
p
pp
Cluster Potentials
ssss
svir
svir
ss
sdm
rrr
rr
rrM
rr
rrc
rr
rr
r
)1ln(4)(
kpc400 Mpc,2
clusters,for 5/
1
)(
3
2
NFW (Navarro, Frenk, & White 1997)
ln NFW
r-1
ln r
r-3
Analytic King Model (approximation to isothermal sphere
Cluster Potentials (cont.)
kpc2002/
1
)( 2/32
0,
sc
c
dmdm
rr
rr
r
r-3
ln NFW
King
r-1
flat core
ln r
Beta Model(Cavaliere & Fusco-Femiano 1976)
Assume King Model DM potential Alternatively, assume galaxies follow King Model, and have isotropic, constant velocity dispersion
drd
mkT
drd
dr
d
p
galgal
lnln2
2/32
0,
1
)(
c
galgal
rr
r
Beta Model (cont.)
2/132
2
2/32
0
1)(
parameter fitting asbut treat
1
)(
cX
galp
c
rr
rI
kT
m
rr
r
Beta Model (cont.)
XMM/Newton A1413 Pratt & Arnaud
Beta model
Fit outer parts of clusters
(Multiple beta models)
≈ 2/3
∝ r -2
IX ∝ r -3
Hydrostatic Equilibrium (cont.)Adiabatic (Polytropic) Models
)1/(1
00
000
)()(
)( ,
)(1)1(1
)(
11
1 isothermal
5/3 1 polytropic
3/5 if adiabatic
TrTr
TTr
TrT
Tmk
P
P
p
Cluster Temperature ProfilesChandra
(Vikhlinin et al 2005)
• Rapid T rise with r at center (100 kpc, “cooling core”)
• T flat to 0.125 rvir
• Slow T decline with r at large radii
~ 1.2