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Entropy in the ICM. Michael Balogh. University of Durham. Institute for Computational Cosmology University of Durham. Collaborators. Mark Voit (STScI -> Michigan) Richard Bower, Cedric Lacey (Durham) Greg Bryan (Oxford) Ian McCarthy, Arif Babul (Victoria). Outline. - PowerPoint PPT Presentation
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Entropy in the ICMEntropy in the ICM
Institute for Computational CosmologyUniversity of Durham
University of Durham
Michael Balogh
CollaboratorsCollaborators
• Mark Voit (STScI -> Michigan)– Richard Bower, Cedric Lacey
(Durham) Greg Bryan (Oxford)
• Ian McCarthy, Arif Babul (Victoria)
OutlineOutline
• Review of ICM scaling properties, and the role of entropy
• Cooling and heating
• The origin of entropy
• Lumpy vs. smooth accretion and the implications for groups
ICM Scaling propertiesICM Scaling properties
Luminosity-Temperature Luminosity-Temperature RelationRelation
If cluster structure were self-similar, then we would expect L T2
Preheating by supernovae & AGNs?
Mass-Temperature Mass-Temperature RelationRelation
Cluster masses derived from resolved X-ray observations are inconsistent with simulations
Another indication of preheating?
M
T1.
5
Definition of S: S = (heat) / T Equation of state: P = K5/3
Relationship to S: S = N ln K3/2 + const.
Useful Observable: Tne-2/3 K
Characteristic Scale:
Convective stability: dS/dr > 0
Only radiative cooling can reduce Tne-2/3
Only heat input can raise Tne-2/3
Entropy: A ReviewEntropy: A Review
K200 =T200
mp (200fbcr)2/3
Dimensionless Entropy From Dimensionless Entropy From SimulationsSimulations
Simulations without cooling or feedback show nearly linear relationship for K(Mgas) with
Kmax ~ K200
Independent of halo mass
(Voit et al. 2003)
Simulations from Bryan & Voit (2001)
Halos: 2.5 x 1013 - 3.4 x 1014 h-1 MSun
Entropy profilesEntropy profiles
Entropy profiles of Abell 1963 (2.1 keV) and Abell 1413 (6.9 keV) coincide if scaled by T0.65
Sca
led
en
trop
y: (
1+
z)2
T-1
S
Sca
led
en
trop
y: (
1+
z)2
T-0
.66
SRadius (r200) Radius (r200)
Pratt & Arnaud (2003)
Heating and CoolingHeating and Cooling
Preheating?Preheating?
Preheated gas has a minimum entropy that is preserved in clusters
Kaiser (1991)
Balogh et al. (1999)
Babul et al. (2002)
Isothermal modelM=1015 M0
Ko=400 keV cm2
300
200
100
Balogh, Babul & Patton 1999Babul, Balogh et al. 2002
log10 LX [ergs s-1]
kT [k
eV
]10
1
0.140 42 44 46
Isothermal model
Preheated modelKo=400 keV cm2
Does supernova feedback Does supernova feedback work?work?
• Local SN rate ~0.002/yr (Hardin et al. 2000; Cappellaro et al. 1999)
• An average supernova event releases ~1044 J
•Assuming 10% is available for heating the gas over 12.7 Gyr, total energy available is 2.5x1050 J
• This corresponds to a temperature increase of 5x104 K
•To achieve a minimum entropy K0 T/2/3:
/avg = 0.28 (K0/100 keV cm2)-3/2
Consider the energetics for 1011 Msun of gas:
SN energy too low by at least a factor ~50
Core Entropy of Clusters & Core Entropy of Clusters & GroupsGroups
Core entropy of clusters is 100 keV cm2
at r/rvir = 0.1
Self-similar scaling
Entropy “Floor”
Ponman et al. 1999
Entropy Threshold for CoolingEntropy Threshold for Cooling
Each point inT-Tne
-2/3 planecorresponds to a uniquecooling time
Entropy Threshold for CoolingEntropy Threshold for Cooling
Entropy at which
tcool = tHubble
for 1/3 solarmetallicity is identical toobserved coreentropy!
Voit & Bryan (2001)
Entropy History of a Gas Entropy History of a Gas BlobBlob
no cooling, no feedback
cooling & feedback
Gas that remains above threshold does not cool and condense.
Gas that falls below threshold is subject to cooling and feedback.
Voit et al. 2001
Entropy Threshold for CoolingEntropy Threshold for Cooling
Updated measurements show that entropy at 0.1r200 scales as
K0.1 T 2/3
in agreement with cooling threshold models
Voit & Ponman (2003)
L-T and the Cooling L-T and the Cooling ThresholdThreshold
Gas below the cooling threshold cannot persist
Voit & Bryan (2001)Balogh, Babul & Patton (1999)Babul, Balogh et al. (2002)
log10 LX [ergs s-1]
kT [k
eV
]
10
1
0.1
40 42 44 46
Also matched by preheated, isentropic cores
L-T and the Cooling L-T and the Cooling ThresholdThreshold
Gas below the cooling threshold cannot persist
Voit & Bryan (2001)Balogh, Babul & Patton (1999)Babul, Balogh et al. (2002)
log10 LX [ergs s-1]
kT [k
eV
]
10
1
0.1
40 42 44 46
Also matched by preheated, isentropic cores
Mass-Temperature Mass-Temperature relationrelation
Both pre-heating and cooling models adequately reproduce observed M-T relation
● Reiprich et al. (2002) Babul et al. (2002) Voit et al. (2002)
The overcooling problemThe overcooling problem
Balogh et al. (2001)
Observations imply */b 0.05
f co
ol
0.1
0.6
0.5
0.4
0.3
0.2
Fraction of condensed gas in simulations is much larger, depending on numerical resolution
Pearce et al. (2000)
Lewis et al. (2000)
Katz & White (1993)
kT (keV)1 10
Observed fraction
Heating-Cooling TradeoffHeating-Cooling Tradeoff
Many mixtures of heating and cooling can explain L-T relation
If only 10% of the baryons are condensed, then ~0.7 keV of excess energy implied in groups
Voit et al. (2002)
Heating + CoolingHeating + Cooling
McCarthy et al. in prep
Start with Babul et al. (2002) cluster models, which have isentropic cores
Allow to cool for time t in small timesteps, readjusting to hydrostatic equilibrium after each step
Develops power-law profile with K r1.1
Entropy profiles of CF Entropy profiles of CF clustersclusters
McCarthy et al. in prep
Observed cooling flow clusters show entropy gradients in core
Well matched by dynamic cooling model from initially isentropic core
Obser
vatio
ns
Model
Simple cooling+heating Simple cooling+heating modelsmodels
McCarthy et al. in prep
Data from Horner et al., uncorrected for cooling flows
Simple cooling+heating Simple cooling+heating modelsmodels
McCarthy et al. in prep
Data from Horner et al., uncorrected for cooling flows
Non-CF clusters well matched by preheated model of Babul et al. (2002)
CF cluster properties matched if gas is allowed to cool for up to a Hubble time
The origin of entropyThe origin of entropyVoit, Balogh, Bower, Lacey & Bryan ApJ, in press astro-ph/0304447
Important Entropy ScalesImportant Entropy Scales
K200 =T200
mp (200fbcr)2/3
Characteristic entropy scale associated with halo mass M200
Ksm =v2
acc
(4in)2/3
Entropy generated by accretion shock
(Mt)2/3
(d ln M / d ln t)2/3
Dimensionless Entropy From Dimensionless Entropy From SimulationsSimulations
How is entropy generated initially?
Expect merger shocks to thermalize energy of accreting clumps
But what happens to the density?
(Voit et al. 2003)
Simulations from Bryan & Voit (2001)
Halos: 2.5 x 1013 - 3.4 x 1014 h-1 MSun
Smooth vs. Lumpy AccretionSmooth vs. Lumpy Accretion
Smooth accretion produces ~2-3 times more entropy than hierarchical accretion(but similar profile shape)
SMOOTH
LUMPY
Voit et al. 2003
Preheated smooth Preheated smooth accretionaccretion
• If pre-shock entropy K1≈Ksm, gas is no longer pressureless
=(M2-1)2
M2
48/3Ksm
5 K1
K2 ≈ Ksm + 0.84K1, for Ksm/K1» 0.25
+ 0.84K1 vin
2
3(41)2/3 ≈
Note adiabatic heating decreases post-shock entropy
Lumpy accretionLumpy accretion
• Assume all gas in haloes with mean density fbcr
K(t) ≈ (1/ fbcr)2/3 Ksm(t)
≈ 0.1 Ksm(t)
Two solutions: K vin2/
1. distribute kinetic energy through turbulence (i.e. at constant density)
2. vsh ≈ 2 vac (i.e. if shock occurs well within R200)
Entropy gradients in Entropy gradients in groupsgroups
Entropy in groupsEntropy in groups
Entropy profiles of Abell 1963 (2.1 keV) and Abell 1413 (6.9 keV) coincide if scaled by T0.65
Cores are not isentropic
Sca
led
en
trop
y (1
+z)
2T
-1S
Sca
led
en
trop
y (1
+z)
2T
-0.6
6S
Radius (r200) Radius (r200)
Pratt & Arnaud (2003)
Excess entropy in groupsExcess entropy in groups
Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2
Entropy gradients in Entropy gradients in groupsgroups
1 10 0.1
1
1
0
Tlum (keV)
Lx/
T3
lum (
10
42 h
-3 e
rg s
-1 k
eV
-3
Lx/
T3
lum (
10
42 h
-3 e
rg s
-1 k
eV
-3
Mo=5×1013 h-1 Mo
eff=5/3
eff=1.2
100 1000
0
.1
1
10
1
00
0
K(0.1r200) keV cm2
Voit et al. 2003
Excess entropy at RExcess entropy at R200200
Entropy gradients in groups with elevated core entropy naturally leads to elevated entropy at R200
Voit et al. 2003
eff = 1.2
eff = 1.3
≈ 2.6K(R200)
K200
(d ln M / d ln t)-2/3
≈ 3.5 for 1013 h-1Mo
≈ 1.7 for 1015 h-1Mo
Excess Entropy at RExcess Entropy at R500500
Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2
Smooth accretion on Smooth accretion on groups?groups?
Groups are not isentropic, but do match the expectations from smooth accretion models
Relatively small amounts of preheating may eject gas from precursor haloes, effectively smoothing the distribution of accreting gas.
Self-similarity broken because groups accrete mostly smooth gas, while clusters accrete most gas in clumps
ConclusionsConclusions• Feedback and cooling both required to match cluster
properties and condensed baryon fraction
• Smooth accretion models match group profiles
• Difficult to generate enough entropy through simple shocks when accretion is clumpy
• Similarity breaking between groups and clusters may be due to the effects of preheating on the density of accreted material