gh2005 gas dynamics in clusters craig sarazin dept. of astronomy university of virginia a85 chandra...
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GH2005Gas Dynamics in Clusters
Craig SarazinDept. of Astronomy
University of Virginia
A85 Chandra (X-ray)Cluster Merger
Simulation
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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
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• 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
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• 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
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• 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
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• 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
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• 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
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Ionization Equilibrium
Iron
XXV = Fe+24 (helium-like iron)
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• 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
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• 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
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X-ray Spectrum
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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)
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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)
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Transport Properties• Due to finite mean free path
• thermal conduction• viscosity• diffusion and settling of heavy
elements
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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
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Heat Conduction (cont.)
600 kpc
10 Gyr
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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
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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
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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?
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• 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
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Clusters from hierarchically, smaller things form first, gravity pulls them together
Cluster Mergers
Abell 85 Chandra
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Main heating mechanism of intracluster gas
Merger Shocks
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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
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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
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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)
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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
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Nongravitational Entropy• Purely gravitational heating (entropy
from merger shocks) gives scalingK ∝T ∝ M2/3
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Cluster and Group Entropies at 0.1 Rvir
(Lloyd-Davies et al. 2000)
K ∝T gravity
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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
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Entropy vs. Radius
(Ponman et al. 2003)
gravity
data
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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
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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
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Universal Pre-Heating of Intergalactic Gas?
• Lyman forest clouds at z ~ 2 → much of IGM relatively cool
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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
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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
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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
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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
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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
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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
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Hydrostatic Equilibrium
spherical )(1
2rrGM
drd
drdP
P
Isothermal (T = constant)
)()(ln
ln11
00
rkT
mr
mkT
mkT
P
p
pp
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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
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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
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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
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Beta Model (cont.)
2/132
2
2/32
0
1)(
parameter fitting asbut treat
1
)(
cX
galp
c
rr
rI
kT
m
rr
r
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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
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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
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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