General Introduction to Galaxy Clusters: Scaling Relations Brian McNamara University of Waterloo.

General Introduction to Galaxy Clusters: Scaling Relations

Brian McNamaraUniversity of Waterloo

Astronomical Units & Terminology

Kiloparsec Distance 1000 parsecs = 3x1021 cm

1053 erg Energy supernova explosion/GRB

Light year Distance 3.26 parsecs

Milky Way Diameter = 100,000 ly = 30 kpc

keV Temperature 1 keV = 1.16 x 107 K

dynes/cm2 Pressure cluster center P=10-10 dyne/cm2

10-16 Atm

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r2500 = 500kpcT

5keV

⎛

⎝ ⎜

⎞

⎠ ⎟

1

2

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M2500 = 2x1014 M⊕

T

5 keV

⎛

⎝ ⎜

⎞

⎠ ⎟

1

2

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r500 = 3.5 MpcT

5 keV

⎛

⎝ ⎜

⎞

⎠ ⎟

1

2

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M500 = 6x1015 M⊕

T

5keV

⎛

⎝ ⎜

⎞

⎠ ⎟

1

2

scaled to critical density of Universe

Why Study Galaxy Clusters?

• Cosmology - evolve by gravity: dominated by dark matter, non-gravitational processes

less dominant; sensitive to matter and dark energy density; scaling relations

- fair sample conjecture: baryons, dark matter, baryon fraction • Galaxy formation & Evolution - closed boxes: retain byproducts of stellar evolution; history of star formation

- uniform sampling in space & time - merging & perturbation: dynamical evolution of galaxies • Cosmic cooling problem - only few percent of baryons have condensed in clusters - cooling flows/feedback

What is a galaxy Cluster?

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

M3 + 2

0 30-491 50-792 80-1293 130-1994 200-2995 300>

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σ ≈300 −1000km s−1

Sizes 1-3 Mpc

Abell 1689 RC =4

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Mvir ≈ 3σ 2r /G ≈1015 h−1MΘ

Richness Classes

for

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σ ≈1000km s−1

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Mcl ≈1013 −1015 M⊕

Galaxy Cluster at X-ray & Visual wavelengths

X-ray visual

100 kpc

Lx = 1043 - 1045 erg s-1 Tgas = 107 - 108 K

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ρgas ≈10−1 −10−4 cm−3

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kTgas ≈ μmpσ2

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ε ∝ neni Te−hν / kTBremsstrahlung emissivity:





E = 0.1-15 keVEA = 922 cm2 @ 1 keVFOV = 33 x 33 arcminPSF ~ 4 arcsec FWHM

E = 0.5-10 keVEA = 600 cm2 @1.5 keVFOV = 16.9x16.9 arcminPSF = 0.5 arcsec FWHM

Chandra Xray Observatory XMM-Newton




are needed to see this picture.Wolter Type 1

Chandra’s mirrors

Grazing incidence optics

critical anglefew degrees

Fe L

Fe K

€

EM ≡ np∫ nedV€

s∝ε(E,T,Z)⊗R(E,φ)

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ε ∝ g(E,T,Z)T−1/ 2 exp(−E /kT)

Normalization:• ionization equilibrium• temperature sensitivity• metallicity sensitivity N > 8• Z ~ 1/3 solar

emitted spectrum observed spectrum

Arnaud 05

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Ix ∝ [1+ (r /rc )]−3β +

1

2

Multiple beta models: Ettori 2000

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ne (r) = n0[1+ (r /rc )2]−3β / 2

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Ix ∝ r−3

Beta Model

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β ≈2 /3ratio of energyper unit mass ingalaxies to that ingas

surface brightness:

electron density:

X-ray surface brighness profile

Gas Temperature: depth of potential well

Mushhotzky 2004

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σ ∝T 0.59±0.03

Normalization agrees with high temperature simulationsLow sigma clusters too hot; or sigma too low for T

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σ ∝ Tx

Abell 2390 €

M tot (< r) =kTr

Gμmp

d lnρ

d ln r+

d lnT

d ln r

⎛

⎝ ⎜

⎞

⎠ ⎟

€

ρ(r) = ρ 0 1+r

rc

⎛

⎝ ⎜

⎞

⎠ ⎟

2 ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

−3β / 2

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M tot (< r) =kr2

Gμmp

3βrT

r2 + rc2

−dT

dr

⎛

⎝ ⎜

⎞

⎠ ⎟

Mass Profiles

Gitti et al. 07

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d lnT

d ln r= 0

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β model

De Grandi & Molendi 01

Wise et al. 04

SN II

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α element enhanced (Si, S, Ne, Mg)

early enrichment z >> 0.5

top-heavy IMF?

SN Ia

Metallicity Distribution

Typcal Gas Profiles

Borgani & Guzzo 01

Gladders & Yee 05

Optical: good for finding distant clusters poor measure of cluster properties

X-ray: good measure of cluster properties poor tracer beyond z ~ 1

“red sequence”

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δρ /ρ





Gaussian density perturbations

Hierarchical clustering

10 Mpc

Number density of clusters: amplitude of perturbations, aDegree of clustering:

a

€

Ncl ∝ a

€

Ωm

Virgo Consortium, Springel et al. 05

Galaxy Cluster

Cluster Scaling Relations

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Lx ∝ M 4 / 3(1+ z)7 / 2

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Lx ∝Tx2(1+ z)3 / 2

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M ∝Tx3 / 2(1+ z)−1

Observables in reverse order of difficulty: Lx, Tx, M

Simple assumptions: gravity, adiabatic compression, shocks

Departures from scaling relations: additional physics (cooling, feedback, etc.)

Evolution of scaling laws: Ettori et al. 04

Same internal structure, but distant clusters denser, smaller, more luminous

Implications:

examples:

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Lx ∝ ρ 2VΛ

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M ∝ ρV ∝ Mgas

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Λ∝T1/ 2 (T > 2 keV)

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Lx ∝ MρT1/ 2

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M ∝T1.5

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Lx ∝ ρT 2

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M ∝TR

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R∝T1/ 2

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M ∝T 3 / 2

Simulations + Observations

compare to scaling relations

problems: models deal primarily with DM mass observations deal with luminous baryons simulated & observed parameters (eg. T) do not always probe same quantity

strategy: find observational proxies for mass

Lx - easy to measure, sensitive to non-gravitational processes

Tx - difficult to measure except for brightest objects

M - even tougher

Mass Function constrains

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Ωm,σ 8

mean matter densityin units of critial density,amplitude of primordial density fluctuations

r2500

r500

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M ∝T1.5

Vikhlinin et al. 06Ettori et al. 04Arnaud 05

Scaling relation: M ~ T3/2

Mass-Temperature Relation

Issues:• Beta model fits• inner core• reference radius• redshift range

•small deviations from self similarity for cool clusters•normalization varies by ~30% between studies•least affected by non-gravitational physics•consistent wit self-similar evolution -Ettori et al. 04

Stanek et al. 06

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L∝ M1.59±0.05

scaling relation: L~M4/3

intercept

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∝Ωm1/ 2slope

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∝σ 8−4

Mass-luminosity Relation

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L∝ M p P = 1.59 +/- 0.05 Stanek et al. 06 = 1.88 +/- 0.43 Ettori et al. 04

too steep!

Luminosity-Temperature Relation

T (keV)

LX (

erg

s-1)

L ~ T2

gravity

L ~ T2.6 1. preheating2. feedback3. cooling

Markevitch 1998

1

5

10

3 5 10

Vikhlinin et al. 06Ettori & Fabian 99Ettori et al. 03

f gas

(r25

00 -

r 500

)

T(keV)

f gas

T(keV)

Baryon fraction as cosmological probe

assumption: universal fb

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fb = Ωb /Ωm

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fb = fgas + fgal

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Ωm = Ωb / fb = 0.30−0.03+0.04

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Ωb = 0.045h70−2 (from BBN & WMAP)

fgal ~ 0.016

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∴ fgas / fgal ≈10

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fgas ∝ (1+ z)2 d(h(z))A3 / 2

assume fgas = constant

Constraints on

€

Ωm,ΩΛ from fgas

Allen et al.

f ga

s (r

25

00)

ZZ€

€

h(z) = Ωm (1+ z)3 + ΩΛ

€

Ωm = 0.25

ΩΛ = 0.96

Allen et al.

• geometrical test• precise mass estimates over z• biases in aperture size, f constancy• priors: H0,

€

Ωbh2

mass & luminosity function sensitivity to

€

Ωm,Λ

Eke et al. 92 Mullis et al. 04M

N(M

) 1015

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Ωm =1

€

Ωm = 0.3,ΩΛ = 0.7

Lx

N(L

)

Evolution: Lx > 5x1044 erg s-1 z > 0.5

Summary

• Clusters close to self-similar population (M-T)• Dark matter profile universal: theory solid• Gas scaling steeper than predicted:

problem: baryon physics: cooling, heating

• Cosmological parameters from clusters in concordance with SNIa, WMAP, etc.

The Cosmic Cooling Problem and Galaxy Formation in Cooling Clusters

B.R. McNamaraUniversity of Waterloo

Balogh et al. 01

Cosmic Cooling Problem

Model Predictions

Observations 0.07h

fewer condensed baryonsthan models predict

cooling is a runaway process

Benson et al 03

Bower et al. 06

CDM hierarchy fails to account for bulge luminosities

K-band luminosity function

more luminous, massive halos have larger cooling timesfails to explain turnover in luminosity function

DM halo

Rees Ostriker 77, Binney 77, White Rees 78

feedback

no feedback

Cosmic Star Formation Rate Density “anti-hierarchical?”

Juneau et al. 2005

galaxy clusters galaxy/SMBH formation

963 10GyrBang!

**

*

**

*

*

*

*

*

*

*

*

**

*--- “Cooling flows” redshift < 0.3 (Rafferty et al. 2006)

cD galaxies:struggle against cooling & star formation

Juneau et al. 05



cD Galaxies are not “old, red, dead”

NGC 1275 in Perseus

Conselice et al. 01

SFR = 15 Mo yr -1

X-rays Emerging from the cool core of a galaxy cluster

M ~ Lx / T ~Mgas/tcool ~100-1000 Mo yr-1. Mspec < 10-100 Mo yr-1.radiative cooling losses spectroscopic limit

cD galaxy

Rcool =100 kpctcool~108 yr

X-ray Spectroscopy: Cooling 5-10 times less than predicted but not zero

Peterson et al. 2003

XMM-Newton 1999 --

Implication: Heating, feedback

Fe XVII

Structure of a Cool Cluster Core

Cooling RegionNe = 10-2 cm-3

Rcool ~ 50-100 kpc

Starburstgalaxy

X-ray Cavities

100 kpc

3 Mpc

Hot AtmosphereT = 108 KNe = 10-3 cm-3

Condensation Regiontcool < 7x108 yrRcond ~ 10 - 30 kpc

conduction

Rafferty et al. 07see also Edwards et al. 07

star formation correlates central cooling time < 1 Gyr

blue

tcool ~7 x 108 yr

Star formation rate in Abell 1835 consistent with net cooling rate

R-band U-band Starburst

McNamara et al. 06

SFR = 100 - 200 Mo yr-1 = Lx,spec

1011 Mo of Gas

Edge & Frayer 2002

Spitzer Mid-IR Starburst Spectrum of Abell 1835

de Messieres, O’Connell, McNamara, et al. in prep.

Star formation

old stars

< 50 kpc across

Calculating Star Formation Rates

tAP < 1 GyrMAP =108-1010 Mo

Standard cooling flow

Nebular filaments

cD galaxy

Bruzual-Charlot 06

Starburst associated with coolest keV gas

tcool = 3x108 yr

kT

coolin

g t

ime (

Gyr)

M< 200 Mo yr-1 .

.

tcool~tdyn

is the gas multiphase here?

r r

tSFR~



Optical, radio, X-ray



Perseus MS0735.6+7421

E ~1059 erg E ~ 1062 erg

1’ = 200 kpc

1’= 20 kpc

Fabian et al. 05 McNamara et al. 05

M=1.3 shock

weak shock

ghost cavity

Gitti et al. 07

Gravitational Binding Energy Released by SMBH

rt = r/v

20/40

€

δU = MgδR = VρgδR = −Vdp

dRδR = −Vδp

cavity enthalpy thermalized in wake of rising cavity

gravitational potential energyturned into kinetic energy

€

M = ρV

€

dp /dr = −ρg€

H = E + pV =γ

γ −1pV

enthalpy = internal energy+work

McNamara & Nulsen 07, ARAA

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dE = Tds − pdV (therm #1)

€

dH = Tds + Vdp0 adiabatic, radiative losses negligible

€

δH = Vδp Kinetic energy in wake = enthalpy lost by rising cavity

Cluster Outflows: AGN Powered

Starburst winds: < 1042 erg s-1

AGN outflows: 1044 -1046 erg s-1 Ecav,shock = 1059 - 1062 erg

Mout ~ Mdisp/tcav = 1010 Mo/108 yr ~ 100 Mo yr-1.

H alpha

Fabian et al. 03 Blanton et al. 01eg., Crawford, Hatch, & Co

conduction ?

Star formation rate consistent with net cooling rate

R-band U-band

Starburst

McNamara et al. 06

SFR = 100 - 200 Mo yr-1 = Lx,spec

1011 Mo of GasEdge & Frayer 2002

Abell 1835

cavitiescavitiesE cavity = 1.7 x 1060 erg

Ecavity = 1.7x1060 erg

Pcavity = 1.4 x 1045 erg s-1 ~ Lx,cool

Heating & Cooling Diagram

Rafferty et al. 06 Birzan et al. 04

jet power

X-ray cooling luminosity

Heating-cooling Diagram for gEs

pV4pV

16pV

Nulsen et al. in prep.

All quenched!

gE & groups

cD clustersongoing star formation

quenched“old, red, dead”



QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

gEs from Nulsen et al. 06

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

cold accretionRafferty 06

Bondi accretionAllen 06

Heating-Cooling Diagram

optical/UV star formation rate

coolingFuse

mass continuity

Rafferty et al. 06

Cooling rates approaching SFRs

Voigt & Fabian 04

Conditions conducive to AGN-regulated feedback loop

1) tcool ~ 108 yr 2) LAGN ~ Lx 3) Entropy floors

Rafferty et al. 06Birzan et al. 04

Voit & Donahue 05Donahue et al. 06Voit 05

SMBH Specific Accretion per Event

€

M•

BH =ε

0.1

⎛

⎝ ⎜

⎞

⎠ ⎟−1 Pcavity

5.67x1045 erg s−1

⎛

⎝ ⎜

⎞

⎠ ⎟M⊕yr−1

€

⟨MBH ⟩•

≈ 0.16 M⊕ yr−1

(clusters)

~ doubled in mass

€

ΔMBH / MBH

Accretion Mechanisms

Bondi- only low mass systems

Stars - intermittent, not enough

Gas - likely, but hard to regulate

Rafferty et al. 06

• sub-Eddington

Black Hole Mass vs Bulge Mass

Gebhardt et al. 00

Bulge Mass vs SMBH Mass

Gebhardt et al. 00Kormendy et al. 03

SMBH mass 10-3 bulge mass “Magorrian Relation”~

Ferrarese & Merritt 00

10% conversion efficiency

Magorrian Relation

Bulge Growth Rate vs SMBH Growth RateRafferty et al.

06 Abell 1835

AGN dominated

.

Starburst dominated

Shock

M=1.34

E=9x1060 erg s-1

t=140 Myr

Radio: Lane et al. 04

Low Radio Frequency Traces Energy

74 MHzWise et al. 07

shock

6 arcmin

380 kpc

Hydra A

Wise et al. 07

1061 erg

Nulsen et al. 05

tshock= 140 Myr

tbuoy= 220 Myr

tbuoy > tshock

Cluster scale heating events

MS0735.7+7421

Gitti et al. 07

E = 1/4 - 1/3 keV/baryon

Lx

Excess: ~ 1 keV/baryon

Others: Herc A, Hydra A

Summary

• SFRs approaching XMM/Chandra cooling rates

• SFR thermostatically controlled by AGN

AGN

• Regulate cooling & star (galaxy) formation• Exponential turnover in galaxy luminosity function• Prevent baryon “over cooling”• Excess entropy (preheating)?

Challenge: How do cavities heat, enthalpy, shocks, ?

General Introduction to Galaxy Clusters: Scaling Relations Brian McNamara University of Waterloo.

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