1. Entropy Generation in the ICM Institute for Computational Cosmology University of Durham Michael Balogh

2. Collaborators Mark Voit (STScI -> Michigan) –Richard Bower, Cedric Lacey (Durham) –Greg Bryan (Oxford) Frazer Pearce, Brendan Hogg (Nottingham)

3. Definition of S:  S =  (heat) / T Equation of state:P = K  5/3 Relationship to S:S = N ln K 3/2 + const. Useful Observable:Tn e -2/3  K Convective stability: dS/dr > 0 Only radiative cooling can reduce Tn e -2/3 Only heat input can raise Tn e -2/3 Entropy: A Review

4. Important Entropy Scales K 200 = T 200  m p (200f b  cr ) 2/3 Characteristic entropy scale associated with halo mass M 200 K sm = v 2 acc  (4  in ) 2/3 Entropy generated by cold, smooth accretion shock  (Mt) 2/3 (d ln M / d ln t) 2/3

5. 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 10 13 - 3.4 x 10 14 h -1 M Sun

6. Smooth vs. Lumpy Accretion Smooth accretion produces ~2 times more entropy than hierarchical accretion (but similar profile shape) SMOOTH LUMPY Voit et al. (2003)

7. Preheated smooth accretion If pre-shock entropy K 1 ≈K sm, gas is no longer pressureless = (M 2 -1) 2 M 2 4 8/3 K sm 5 K 1 K 2 ≈ K sm + 0.84K 1, for K sm /K 1 » 0.25 + 0.84K 1 v in 2 3(4  1 ) 2/3 ≈ Note adiabatic heating decreases post-shock entropy

8. Preheating and smooth accretion M(t o )=10 14 h -1 M o K mod K sm K 200 K1K1 2 1.5 1 0.5 0 0 0.5 1 f g =M g /f b M 200 K (10 34 erg cm 2 g- 5/3 ) 2 1.5 1 0.5 0 0 0.5 1 f g =M g /f b M 200 K (10 34 erg cm 2 g- 5/3 ) M(t o )=10 13 h -1 M o K mod K sm K 200 K1K1 K c (T 200 ) Voit et al. 2003 Early accretion is isentropic; leads to nearly-isentropic groups

9. Entropy in groups Entropy profiles of Abell 1963 (2.1 keV) and Abell 1413 (6.9 keV) coincide if scaled by T 0.65 Cores are not isentropic Scaled entropy (1+z) 2 T -1 S Scaled entropy (1+z) 2 T -0.66 S Radius (r 200 ) Pratt & Arnaud (2003)

10. Excess Entropy at R 500 Entropy “measured” at r 500 (~ 0.6r 200 ) exceeds the amount hierarchical accretion can generate by hundreds of keV cm 2 Voit & Ponman (2003)

11. 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

12. Lumpy accretion Assume all gas in haloes with mean density  f b  cr K(t) ≈ (  1 /  f b  cr ) 2/3 K sm (t) ≈ 0.1 K sm (t) Two solutions: K  v in 2 /   1. distribute kinetic energy through turbulence (i.e. at constant density) 2. v sh ≈ 2 v ac (i.e. if shock occurs well within R 200 )

13. Binary merger models initial distribution final To double mass, need entropy jump of 1.6. For realistic power spectrum, self-similarity requires 1.59<K 2 /K 1 <2 Maximum velocity model

14. Realistic mass spectrum Entropy generation is still insufficient to preserve initial profile. Low density gas highly shocked to greater and greater entropy

15. SPH Simulations Simulations of galaxy mergers to study entropy generation –1:1, 1:8 and 1:16 mergers –vary impact parameter, infall velocity –explore effect of preheating

16. Post-merger remnant 1:8 merger Density Collision direction 10 Mpc

17. Post-merger remnant 1:8 merger Entropy 10 Mpc

18. Post-merger remnant 1:8 merger Entropy change 10 Mpc

19. Simulations f gas Entropy Post-merger Pre-merger Even the small merger is able to generate substantial entropy Surprisingly, appears to result in a simple shift to the entropy distribution… by factor of 1.6!

20. Conclusions Smooth accretion onto groups may explain higher entropy gas in those systems Lumpy accretion: may be difficult to generate enough entropy through accretion shocks alone –but simulations are encouraging: entropy production appears to be simple