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## Entropy in the ICM

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**Entropy in the ICM**Michael Balogh University of Durham Institute for ComputationalCosmology University of Durham**Collaborators**• Mark Voit (STScI -> Michigan) • Richard Bower, Cedric Lacey (Durham) Greg Bryan (Oxford) • Ian McCarthy, Arif Babul (Victoria)**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**Luminosity-Temperature Relation**If cluster structure were self-similar, then we would expect L T2 Preheating by supernovae & AGNs?**Mass-Temperature Relation**Cluster masses derived from resolved X-ray observations are inconsistent with simulations Another indication of preheating? M T1.5**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**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**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)**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**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]**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**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**Entropy Threshold for Cooling**Each point in T-Tne-2/3 plane corresponds to a unique cooling time**Entropy Threshold for Cooling**Entropy at which tcool = tHubble for 1/3 solar metallicity is identical to observed core entropy! Voit & Bryan (2001)**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**Entropy Threshold for Cooling**Updated measurements show that entropy at 0.1r200 scales as K0.1T 2/3 in agreement with cooling threshold models Voit & Ponman (2003)**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)**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)**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)**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)**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)**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**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**Simple cooling+heating models**Data from Horner et al., uncorrected for cooling flows McCarthy et al. in prep**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**The origin of entropy**Voit, Balogh, Bower, Lacey & Bryan ApJ, in press astro-ph/0304447**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**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**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**(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**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)**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)**Excess entropy in groups**Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2**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**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**Excess Entropy at R500**Entropy “measured” at r500 (~ 0.6r200) exceeds the amount hierarchical accretion can generate by hundreds of keV cm2**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**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