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Entropy in the ICM

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.

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Entropy in the ICM

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  1. Entropy in the ICM Michael Balogh University of Durham Institute for ComputationalCosmology University of Durham

  2. Collaborators • Mark Voit (STScI -> 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 > 0 Only radiative cooling can reduceTne-2/3 Only heat input can raiseTne-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 1014h-1MSun

  9. Entropy profiles Scaled entropy: (1+z)2 T-0.66 S Scaled entropy: (1+z)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? M=1015 M0 Isothermal model Preheated gas has a minimum entropy that is preserved in clusters Kaiser (1991) Balogh et al. (1999) Babul et al. (2002) Ko=400 keV cm2 300 200 100

  12. Balogh, Babul & Patton 1999 Babul, Balogh et al. 2002 10 Preheated model Ko=400 keV cm2 kT [keV] 1 Isothermal model 0.1 40 42 44 46 log10 LX [ergs s-1]

  13. 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 (K0/100keVcm2)-3/2 SN energy too low by at least a factor ~50

  14. 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

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

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

  17. 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)

  21. 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)

  22. 0.6 Katz & White (1993) 0.5 Lewis et al. (2000) 0.4 0.3 Pearce et al. (2000) 0.2 0.1 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)

  23. 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)

  24. 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 cooling+heating models Data from Horner et al., uncorrected for cooling flows McCarthy et al. in prep

  27. Simple cooling+heating 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

  29. T200 K200 = mmp (200fbrcr)2/3 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 1014h-1MSun

  31. 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. (M2-1)2 48/3Ksm M2 5 K1 vin2 3(4r1)2/3 Preheated smooth accretion • If pre-shock entropy K1≈Ksm, 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. Entropy gradients in groups

  35. Entropy in groups Scaled entropy (1+z)2T-0.66S Scaled entropy (1+z)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)

  36. Excess entropy in groups Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2

  37. Entropy gradients in groups Mo=5×1013 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 geff=5/3 geff=1.2 1 10 100 1000 Tlum (keV) K(0.1r200) keV cm2 Voit et al. 2003

  38. K(R200) ≈ 2.6 (d ln M / d ln t)-2/3 K200 ≈ 3.5 for 1013 h-1Mo ≈ 1.7 for 1015 h-1Mo 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

  39. Excess Entropy at R500 Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2

  40. 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

  41. 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

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