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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
€
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?
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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:
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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
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Chandra’s mirrors
Grazing incidence optics
critical anglefew degrees
Fe L
Fe K
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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
€
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
€
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
€
d lnT
d ln r= 0
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β model
De Grandi & Molendi 01
Wise et al. 04
SN II
€
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
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Gaussian density perturbations
Hierarchical clustering
10 Mpc
Number density of clusters: amplitude of perturbations, aDegree of clustering:
a
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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
€
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
€
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
€
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
€
∴ fgas / fgal ≈10
€
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
€
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
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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~
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Optical, radio, X-ray
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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
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M = ρV
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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)
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dH = Tds + Vdp0 adiabatic, radiative losses negligible
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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”
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gEs from Nulsen et al. 06
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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, ?