What is the Fate of the Cooling Gas

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What is the Fate of the Cooling Gas?
G. M. Voit
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The Agenda

• Clusters bear the signature of galaxy formation
• Entropy is key property
• Global properties governed by cooling feedback
• Core entropy distribution offers clues to
  feedback mechanism

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Luminosity-Temperature Relation
If cluster structure were self-similar, then we
would expect L ? T2 However, cores of simulated
clusters radiate several times their thermal
energy over a Hubble time.
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Mass-Temperature Relation
Cluster masses derived from resolved X-ray
observations are also inconsistent with
simulations that do not include cooling and
feedback
M ? T1.5
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Why Entropy?
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Entropy A Review

• Definition of s Ds D(heat) / T
• Equation of state P Kr5/3
• Relationship to s s ln K3/2 const.
• Convective Stability ds/dr ? 0
• Useful Observable Tne-2/3 ? K
• Radiative cooling reduces Tne-2/3
• Heat input raises Tne-2/3

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Fundamentals of Cluster Structure

• Properties of relaxed cluster determined by
• shape of halo
• entropy
• distribution of
• intracluster gas

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The Entropy Floor
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Core Entropy of Clusters Groups
Core entropy of clusters is ? 100 keV cm2 at
r/rvir 0.1 Ponman et al. (1999)
Entropy Floor
Self-similar scaling
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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
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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)
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Entropy Modification
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L-T and the Cooling Threshold
Removal of all gas below the cooling threshold
reproduces L-T relation of clusters without
cooling flows
Voit Bryan (2001)
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Mass-Temperature Relation
Modified-entropy models based on the cooling
threshold also agree with observed M-T relation
Voit et al. (2002)
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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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Allowing for a cool core
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XMM Entropy Profiles
Entropy profiles of Abell 1963 (2.1 keV) and
Abell 1413 (6.9 keV) scale as T2/3 (?) K ?
r1.1 for r gt 0.1r200 Shallower slope at r lt
0.1r200 allows core luminosity to converge
Pratt Arnaud (2003)
dL
n2 L r3 ? T3 L (r/K)3
d ln r
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Intracluster Entropy Distributions
More realistic models need to account for gas
with cooling time less than a Hubble time
Voit et al. (2002)
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Core Temperature Gradient
Reproducing core temperature gradient requires
gas with a short cooling time
Voit et al. (2002)
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L-T and Cooling Flows
Gas below cooling threshold leads to modest
offset in L-T relation
Voit et al. (2002)
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What Regulates Core Entropy?
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Case 1 Thermal Conduction
Balancing cooling with conduction requires
r3 n2L(T) ? r2 f ?S (dT/dr) Setting
L(T) ? T1/2 and ?S ? T5/2 gives
r2 ? T3 n-2 K3 Balanced profile
K ? r2/3 (Central regions condense if
profile is steeper)
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Chandra Entropy Profiles K(r)
See Horner poster
a gt 2/3 in all cases
a 1 in most cases
Fitting formula K - K0 ? ra
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Where Conduction Fails
Conduction eliminates temperature gradients
below ?F (180 kpc) f1/2 (K/100 keV
cm2)3/2 Observations indicate K (300
keV cm2)(T/10 keV)2/3 (0.1r/r200) Conduction
cannot stop thermal instability within
r (18 kpc) f -1 (T/10 keV)-1/2 Condensatio
n phenomena appear within similar radius
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Case 2 Episodic Heating
Radiative cooling follows a heating episode
dK3/2/dt - T1/2L(T) ? T Isentropic
medium becomes nearly isothermal Kaiser Binney
(2003) find, for one realization
K - K0 ? Mg 0.3 General form depends on
potential heating mode Central entropy K0
indicates duty cycle
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Chandra Entropy Profiles K(Mg)
K0 10 keV cm2

• 0.3 - 0.6

Fitting formula K - K0 AMga
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What is the fate of the cooling gas?

• Cooling is essential to understanding global
  cluster properties
• Feedback seems necessary to prevent overcooling
  of baryons
• Conduction can inhibit condensation but cannot
  completely stop it
• Star-formation phenomena appear within radius at
  which conduction must fail
• Episodic heating may occur where conduction fails