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