Entropy in the ICM

1
Entropy in the ICM
Michael Balogh
University of Durham
Institute for Computational Cosmology University
of Durham
2
Collaborators

• Mark Voit (STScI -gt Michigan)
• Richard Bower, Cedric Lacey (Durham) Greg Bryan
  (Oxford)
• Ian McCarthy, Arif Babul (Victoria)

3
Outline

• 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

4
ICM Scaling properties
5
Luminosity-Temperature Relation
If cluster structure were self-similar, then we
would expect L ? T2 Preheating by supernovae
AGNs?
6
Mass-Temperature Relation
Cluster masses derived from resolved X-ray
observations are inconsistent with
simulations Another indication of preheating?
M ? T1.5
7
Entropy A Review
Definition of S DS D(heat) / T Equation of
state P Kr5/3 Relationship to S S N ln K3/2
const. Useful Observable Tne-2/3 ? K
Characteristic Scale Convective
stability dS/dr gt 0 Only radiative cooling can
reduce Tne-2/3 Only heat input can raise Tne-2/3
T200
K200
mmp (200fbrcr)2/3
8
Dimensionless Entropy From Simulations
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
9
Entropy profiles
Scaled entropy (1z)2 T-0.66 S
Scaled entropy (1z)2 T-1 S
Radius (r200)
Radius (r200)
Entropy profiles of Abell 1963 (2.1 keV) and
Abell 1413 (6.9 keV) coincide if scaled by T0.65
Pratt Arnaud (2003)
10
Heating and Cooling
11
Preheating?
Isothermal model
M1015 M0
Preheated gas has a minimum entropy that is
preserved in clusters Kaiser (1991) Balogh et
al. (1999) Babul et al. (2002)
Ko400 keV cm2
300
200
100
12
Balogh, Babul Patton 1999 Babul, Balogh et al.
2002
10
Preheated model
Ko400 keV cm2
kT keV
1
Isothermal model
0.1
40
42
44
46
log10 LX ergs s-1
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Does supernova feedback work?
Consider the energetics for 1011 Msun of gas

• 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/r2/3
• r/ravg 0.28 (K0/100 keV cm2)-3/2

SN energy too low by at least a factor 50
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Core Entropy of Clusters Groups
Core entropy of clusters is ? 100 keV cm2 at
r/rvir 0.1
Entropy Floor
Self-similar scaling
Ponman et al. 1999
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Entropy Threshold for Cooling
Each point in T-Tne-2/3 plane corresponds to a
unique cooling time
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Entropy Threshold for Cooling
Entropy at which tcool tHubble for 1/3
solar metallicity is identical to observed
core entropy!
Voit Bryan (2001)
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Entropy History of a Gas Blob
Gas that remains above threshold does not cool
and condense. Gas that falls below threshold is
subject to cooling and feedback.
no cooling, no feedback
cooling feedback
Voit et al. 2001
18
Entropy 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)
19
L-T and the Cooling Threshold
10
kT keV
1
0.1
40
42
44
46
log10 LX ergs s-1
Also matched by preheated, isentropic cores
Gas below the cooling threshold cannot persist
Balogh, Babul Patton (1999) Babul, Balogh et
al. (2002)
Voit Bryan (2001)
20
L-T and the Cooling Threshold
10
kT keV
1
0.1
40
42
44
46
log10 LX ergs s-1
Also matched by preheated, isentropic cores
Gas below the cooling threshold cannot persist
Balogh, Babul Patton (1999) Babul, Balogh et
al. (2002)
Voit Bryan (2001)
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Mass-Temperature relation
Both pre-heating and cooling models adequately
reproduce observed M-T relation
? Reiprich et al. (2002) Babul et al.
(2002) Voit et al. (2002)
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The overcooling problem
Observations imply W/Wb ? 0.05
fcool
Fraction of condensed gas in simulations is
much larger, depending on numerical resolution
Observed fraction
1
10
kT (keV)
Balogh et al. (2001)
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Heating-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)
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Heating Cooling
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
McCarthy et al. in prep
25
Entropy profiles of CF clusters
Observed cooling flow clusters show entropy
gradients in core Well matched by dynamic
cooling model from initially isentropic core
Model
Observations
McCarthy et al. in prep
26
Simple coolingheating models
Data from Horner et al., uncorrected for cooling
flows
McCarthy et al. in prep
27
Simple coolingheating models
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
McCarthy et al. in prep
28
The origin of entropy
Voit, Balogh, Bower, Lacey Bryan
ApJ, in press
astro-ph/0304447
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Important Entropy Scales
Characteristic entropy scale associated with halo
mass M200
v2acc
Entropy generated by accretion shock
Ksm
3 (4rin)2/3
(Mt)2/3
?
(d ln M / d ln t)2/3
30
Dimensionless Entropy From Simulations
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
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Smooth vs. Lumpy Accretion
SMOOTH
LUMPY
Smooth accretion produces 2-3 times more entropy
than hierarchical accretion (but similar profile
shape)
Voit et al. 2003
32
Preheated smooth accretion

• If pre-shock entropy K1Ksm, gas is no longer
  pressureless

K2 Ksm 0.84K1, for Ksm/K1 0.25
0.84K1

Note adiabatic heating decreases post-shock
entropy
33
Lumpy accretion

• Assume all gas in haloes with mean density Dfbrcr
• K(t) (r1/ Dfbrcr)2/3 Ksm(t)
• 0.1 Ksm(t)
• Two solutions K ? vin2/r
• 1. distribute kinetic energy through turbulence
  (i.e. at constant density)
• 2. vsh 2 vac (i.e. if shock occurs well within
  R200)

34
Preheating and smooth accretion
M(to)1013h-1Mo
Kmod
Ksm
K1
K200
Kc(T200)
Early accretion is isentropic leads to
nearly-isentropic groups
Voit et al. 2003
35
Entropy gradients in groups
36
Entropy in groups
Scaled entropy (1z)2T-0.66S
Scaled entropy (1z)2T-1S
Radius (r200)
Radius (r200)
Entropy profiles of Abell 1963 (2.1 keV) and
Abell 1413 (6.9 keV) coincide if scaled by
T0.65 Cores are not isentropic
Pratt Arnaud (2003)
37
Excess entropy in groups
Entropy measured at r500 ( 0.6r200) exceeds
the amount hierarchical accretion can generate by
hundreds of keV cm2
38
Entropy gradients in groups
Mo51013 h-1 Mo
Lx/T3lum (1042 h-3 erg s-1 keV-3
0.1 1 10
0.1 1 10 1000
Lx/T3lum (1042 h-3 erg s-1 keV-3
geff5/3
geff1.2
1 10
100 1000
Tlum (keV)
K(0.1r200) keV cm2
Voit et al. 2003
39
Excess entropy at R200
Entropy gradients in groups with elevated core
entropy naturally leads to elevated entropy at
R200
geff 1.2
geff 1.3
Voit et al. 2003
40
Excess Entropy at R500
Entropy measured at r500 ( 0.6r200) exceeds
the amount hierarchical accretion can generate by
hundreds of keV cm2
41
Smooth accretion on 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

42
Conclusions

• 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