CLUSTERS OF GALAXIES The Physics of the IGM: Cooling Flows.

CLUSTERS OF GALAXIES

The Physics of the IGM:Cooling Flows

Cooling FlowsCooling Flows Observational evidencesObservational evidences

The homogeneous model: one ρ and T at each radius

Observational evidence against homogeneous gasObservational evidence against homogeneous gas

The inhomogeneous model: Δρ and ΔT at each radius

The role of the magnetic fields in Cooling FlowsThe role of the magnetic fields in Cooling Flows

Estimates of dM/dt from imaging & spectral data

The fate of the cooling gasThe fate of the cooling gas

Cooling in Clusters

LX ngas2 Tg

1/2 Volume

E ngasKTg Volume

tcool E/LX Tg1/2 n-1

Cooling FlowsCooling Flows

tcool ≈ Tg1/2

np-1

For large radii np is small tcool »tHubble

In the core np is large tcool ~ tHubble

The gas within The gas within rrcoolcool will cool will cool

Cooling FlowsCooling Flows

When the gas coolsWhen the gas cools

The pressure becomes lowerThe pressure becomes lower

The gas flows inwards,The gas flows inwards,

The density increases in the The density increases in the centercenter

The gas cools even fasterThe gas cools even faster

Observational Evidences Observational Evidences for Cooling Flowsfor Cooling Flows

X-Ray ImagingX-Ray Imaging Surface brightness strongly peaked at the Surface brightness strongly peaked at the

centercenter


X-Ray ImagingX-Ray Imaging Surface brightness strongly peaked at the Surface brightness strongly peaked at the

centercenter

Peres et al. (1998)


X-Ray SpectraX-Ray Spectra Low ionization lines in soft X-ray spectraLow ionization lines in soft X-ray spectra

Canizares et al. (1984)


X-Ray SpectraX-Ray Spectra Temperature gradients towards the centerTemperature gradients towards the center

rcool

De Grandi & Molendi (2002)


X-Ray SpectraX-Ray Spectra Low energy absorption featuresLow energy absorption features

Allen et al. (1993)

T(r) NH(r)


X-Ray SpectraX-Ray Spectra Low ionization lines in soft X-ray spectraLow ionization lines in soft X-ray spectra

Temperature gradients towards the centerTemperature gradients towards the center

Low energy absorption featuresLow energy absorption features

No direct evidence of the gas motion, No direct evidence of the gas motion, resolution of X-ray detectors is insufficentresolution of X-ray detectors is insufficent

3 Dynamic regions:3 Dynamic regions:

1. r > rcool and tcool > tHubble Hydrostatic Equilibrium

2. rgal < r < rcool with rgal= radius at which the gas falls

within . potential well of the cD galaxy

3. r<rgal

Homogeneous ModelHomogeneous Model

Hot gas – one Tg and ng at each r – radiation

losses P decreases

Gas will flow inwards under the pressure Gas will flow inwards under the pressure of the overlaying gasof the overlaying gas

Region 2Region 2 ΔΦ/Δr is small radiation losses balanced by thermal energy +

PV vs>>vfree fall

The gas is in quasi-hydrostatic equilibrium Region 3Region 3

ΔΦ/Δr ≠ 0 gravitational energy balances radiation losses

r

Φ

rcoolrgal

21

3

Hydrodynamic equilibrium for Hydrodynamic equilibrium for Homogeneous ModelHomogeneous Model

1.1. Mass conservationMass conservation

2.2. Momentum conservationMomentum conservation

3.3. Energy conservationEnergy conservation

variation of H per variation of H per unit volume & timeunit volume & time

0vρrdrd

r1 22 constrπ4vρ

dtdM 2

drd

ρdrdP

)T(nρP

25

dtd

ρ 2

ρP

25

PVUH

energy radiated energy radiated per per

unit volume & timeunit volume & time

Entalphy=thermal E + work by P

M estimates forM estimates forHomogeneous modelHomogeneous model

Energy Energy loss rateloss rate

..

Hcool,X mμ

kT25

MρP

25

ML

Mass flow rateMass flow rateEnthalpyEnthalpy

. .

yr/M30030M

L%10L bol,Xcool,X

Peres et al. (1998)

..

A fraction of the gas A fraction of the gas

drops out the flow before drops out the flow before

reaching the centerreaching the center

Most of the cooling gas Most of the cooling gas never makes it to the never makes it to the centercenter

Observational evidences Observational evidences

against M=constagainst M=constThe surface brightness is not as peaked as would be expected if all the cooling gas were to The surface brightness is not as peaked as would be expected if all the cooling gas were to

reach the centerreach the center

M≠const M≠const M Mrrαα with with α≈α≈11

..

....

Peres et al. (1998)

(Fabian, Nulsen &Canizares 1984)

@ T≈10@ T≈106 6 K tK tcoolcoolttss The cool blobs decouple The cool blobs decouple

from the flow and:from the flow and:

1.1. Fall ballistically?Fall ballistically?

2.2. Stay in place as cold gas?Stay in place as cold gas?

3.3. Stay in place and form stars?Stay in place and form stars?

In-homogeneous Model In-homogeneous Model (Nulsen (Nulsen

’86)’86)

Different phases T,Different phases T,ρρ coexist at every r coexist at every r

Phases are in Pressure equilibrium (ts<tcool)

The phases comove with <v> « vThe phases comove with <v> « vss, , B field ties the B field ties the different phases togetherdifferent phases together

Heat conduction btw phases must be suppressed, again B fields have been invoked

SummarySummary

Gas that is already highly inhomogeneous cools and flows inward under the pressure of the gas immediately on top.

The different phases are in pressure equilibrium and comove The different phases are in pressure equilibrium and comove (B field).(B field).

When a given phase cools below ≈106K it falls out of pressure equilibrium while the other phases continue to flow inwards

Cold gas deposition occurs on the whole CF region with Cold gas deposition occurs on the whole CF region with similar similar for different clusters (dM(r)/dt for different clusters (dM(r)/dtrrαα))

The origin of the density inhomogeneity is unclear:The origin of the density inhomogeneity is unclear:

1.1. fossil of the past stripping from galaxies (Soker et al. ’91)fossil of the past stripping from galaxies (Soker et al. ’91)

2.2. former mergers btw substructures with different T and former mergers btw substructures with different T and ρρ

1.1. From Imaging data From Imaging data within the context of the in-homogeneous model within the context of the in-homogeneous model

ΔΔLLjj, luminosity in a given radial shell and M, luminosity in a given radial shell and Mj j mass mass flow rate in the same shell are related through a flow rate in the same shell are related through a linear formula linear formula from this, values M can be from this, values M can be computedcomputed

2.2. From Spectral dataFrom Spectral data

stricly valid for homogeneous model, reasonable stricly valid for homogeneous model, reasonable

approx. for inhomogeneous model (Wise & Sarazin ’93)approx. for inhomogeneous model (Wise & Sarazin ’93)

dTT

TM

m

kL

T

HcoolX

max

)(

)()(,

02

5

M estimates forM estimates forin-homogeneous modelin-homogeneous model

..

.

..

Comparison btw. MComparison btw. Mss and Mand MII

Allen (2000)

.. ..

The role of B fields The role of B fields

Tangled field inhibit thermal conduction by increasing the particle mean free path

Once a blob has cooled down to ~ 10Once a blob has cooled down to ~ 106 6 K K radiation cooling becomes very fast radiation cooling becomes very fast

ρ ≈ constant, T decreases, Pgas decreases repressurizing shocks are partially repressurizing shocks are partially

suppressed by the Psuppressed by the PBB

At T ~ 106 K trecon ≈ tcool magnetic energy will

be converted into thermal energy thereby slowing down the collapse of the blobs.

The fate of theThe fate of thecooling gascooling gas

Cooling flow is a frequent phenomenon (~ 60%-Cooling flow is a frequent phenomenon (~ 60%-70%)70%)

Cooling flow is a persistent phenomenonCooling flow is a persistent phenomenon

1.1. MMaccacc ≈≈ 10 101212 M Msun sun [M/(100M[M/(100Msunsun/yr)] (Sarazin /yr)] (Sarazin

’89)’89)

2.2. MMaccacc « M « Mcluster cluster ≈ 10≈ 101414-10-101515 M Msunsun

3.3. MMaccacc comparable to mass of the cD galaxy comparable to mass of the cD galaxy

..


(A) Ionized

Cold gasCold gas (B) Neutral

(C) Molecular

(A) Lines observed in optical and UV indicate that ionized gas is present « Macc


(A) Ionized


(C) Molecular


(B) 21 cm observations in central galaxies give MHI 109 Msun


(A) Ionized


(C) Molecular


(B) 21 cm observations in central galaxies give MHI 109 Msun

(C) Recent obs. (Edge 2002) have detected molecular gas for the first time, again « Macc

SUMMARYSUMMARY

B fields play an important role in CFB fields play an important role in CF

A dominating fraction of galaxy clusters feature CFA dominating fraction of galaxy clusters feature CF

Analysis of X-ray images and spectra lead to consistent Analysis of X-ray images and spectra lead to consistent

determination of mass deposition rates.determination of mass deposition rates.

From X-ray observations we find that CF deposit large From X-ray observations we find that CF deposit large

quantities of cold gasquantities of cold gas

At larger wavelenghts we do not find At larger wavelenghts we do not find .. evidence of such large masses evidence of such large masses

the fate of the cooled gas is unknownthe fate of the cooled gas is unknown

It is somewhat disturbing that all It is somewhat disturbing that all crucial evidences for cooling flows crucial evidences for cooling flows comes from X-ray datacomes from X-ray data

Even in the X-rays we do not have Even in the X-rays we do not have direct observational evidence of:direct observational evidence of:

1.1. flowing gasflowing gas

2.2. multiphase gas at one multiphase gas at one

radiusradius

CLUSTERS OF GALAXIES The Physics of the IGM: Cooling Flows.

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