Entropy Evolution of the Gas in Cooling Flow Clusters

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Entropy Evolution of the Gas in Cooling Flow
Clusters

• Christian Kaiser
• Why is entropy a useful tool?
• Analytic solutions for evolving cooling flow
  clusters.
• Cold gas, a question of timing.

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Definition of entropy

• Entropy of N gas particles

Whats the point?
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Mass / entropy index power laws

• Observations show a simple power law relation
  between gas mass and entropy index

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Mass / entropy index power laws
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Mass / entropy index power laws
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Energy vs. entropy

• The rate of energy radiation is simple

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Analytical approach for quasi-hydrostatic state

• Equations

• Simplifications
• Cooling function,
• At t0, assume
• At all times,

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Time-dependent analytical solutions

• Entropy index

No assumption on grav. potential!
Pressure
Other gas properties follow from ideal gas
equation.
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Static distributions Density
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Static distributions Temperature
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Static distributions Mass/entropy index
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Numerical approach

• Is this all an artefact of the assumptions?
• Solve equations numerically.
• Assume proper cooling function.
• Use current state of Hydra cluster as starting
  point.
• Calculate distribution M(lt?) and use in
  subsequent timestep.

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Numerical solution

• M(lt?) stays a power law (nearly).

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Linear time evolution of ?

• Central entropy index as function of time.

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(Very) transient cold gas

• Gas temperature at cluster centre.
• Very small volume, hard to detect.

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Summary

• Entropy is easier to study than energy (and leads
  to an analytic solution).
• Radiative cooling leads to power law dependence
  of gas mass on entropy index.
• Cold gas only exists for a tiny fraction of the
  cooling phase of clusters.
• Episodic heating, possibly by AGN, is needed to
  avoid excessive cooling.
• Details in
• Kaiser Binney (2003)