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What is the Fate of the Cooling Gas?

What is the Fate of the Cooling Gas?. G. M. Voit. 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. Luminosity-Temperature Relation.

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What is the Fate of the Cooling Gas?

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

  2. 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

  3. 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.

  4. 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

  5. Why Entropy?

  6. 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 reducesTne-2/3 Heat input raisesTne-2/3

  7. Fundamentals of Cluster Structure • Properties of relaxed cluster determined by: • shape of halo • entropy • distribution of • intracluster gas

  8. The Entropy “Floor”

  9. 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

  10. Entropy Threshold for Cooling Each point in T-Tne-2/3 plane corresponds to a unique cooling time

  11. Entropy Threshold for Cooling Entropy at which tcool = tHubble for 1/3 solar metallicity is identical to observed core entropy! Voit & Bryan (2001)

  12. 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

  13. 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)

  14. Entropy Modification

  15. 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)

  16. Mass-Temperature Relation Modified-entropy models based on the cooling threshold also agree with observed M-T relation Voit et al. (2002)

  17. 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)

  18. Allowing for a cool core

  19. 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 > 0.1r200 Shallower slope at r < 0.1r200 allows core luminosity to converge Pratt & Arnaud (2003) dL ~ n2Lr3T3L (r/K)3 d ln r

  20. Intracluster Entropy Distributions More realistic models need to account for gas with cooling time less than a Hubble time Voit et al. (2002)

  21. Core Temperature Gradient Reproducing core temperature gradient requires gas with a short cooling time Voit et al. (2002)

  22. L-T and Cooling Flows Gas below cooling threshold leads to modest offset in L-T relation Voit et al. (2002)

  23. What Regulates Core Entropy?

  24. Case #1: Thermal Conduction Balancing cooling with conduction requires r3 n2L(T) ~ r2f S (dT/dr) Setting L(T)  T1/2 and S  T5/2 gives r2  T3n-2~ K3 Balanced profile: K r2/3 (Central regions condense if profile is steeper)

  25. Chandra Entropy Profiles: K(r) See Horner poster a > 2/3 in all cases a ~ 1 in most cases Fitting formula: K - K0 ra

  26. 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 Condensation phenomena appear within similar radius

  27. 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 Mg0.3 General form depends on potential & heating mode Central entropy K0 indicates duty cycle

  28. Chandra Entropy Profiles: K(Mg) K0 ~ 10 keV cm2 • ~ 0.3 - 0.6 Fitting formula: K - K0 = AMga

  29. 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

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