Sculpting Cosmic Gas into Clusters

Transcript

1. Sculpting Cosmic Gas into Clusters Mike McCourt, Eliot Quataert, Ian Parrish, & Prateek Sharma October, 
2. Introduction Cold Gas Central Density Outer Temperature Conclusions Galaxy Clusters & the ICM stars (optical) hot gas (x-ray) Representative Numbers R ∼ 1 − 2 Mpc M ∼ 1014 − 1015 M T ∼ 5 × 107 K n ∼ 10−2 cm−3 Lx ∼ 1045 erg/s
3. Introduction Cold Gas Central Density Outer Temperature Conclusions Galaxy Clusters & the ICM stars (optical) hot gas (x-ray) Compare to the Milky Way… in hierarchical structure formation, objects are self-similar dark-matter halo filled with virialized gas lots of substructure, with largest galaxy in the center ~cosmic fraction of baryons most of the baryons are in gas, not stars gas density is much higher
4. Introduction Cold Gas Central Density Outer Temperature Conclusions Baryon Distrubution in Halos Andreon 2010 (cf. Dai et al. 2010, Giodini et al. 2009) 10 11 12 13 14 15 0.01 0.10 η≡ Mstar / Mvir / fb z=0 z=2 log 10 M halo (z) Conroy et al. 2009
5. Introduction Cold Gas Central Density Outer Temperature Conclusions Why Study Clusters? Unusual Regime for Plasma Physics / Fluid Dynamics R ∼ Mpc λmfp ∼ kpc rg ∼ 104 km Still understanding how plasmas behave in this limit closure debated (cf. Sharma et al. , Kunz et al. ) lots of new instabilities (HBI, MTI, HBO, RBO, …) Window into Galaxy Formation because of the higher density and longer path length, one can observe the virialized gas in clusters modelling x-ray emission → thermodynamic state can understand how the gas cools, forms stars, powers feedback, etc. Probes of Dark Energy Halo mass function sensitive to the expansion history of the universe, all the way to z ∼ 0
6. Introduction Cold Gas Central Density Outer Temperature Conclusions Why Study Clusters? Unusual Regime for Plasma Physics / Fluid Dynamics R ∼ Mpc λmfp ∼ kpc rg ∼ 104 km Still understanding how plasmas behave in this limit closure debated (cf. Sharma et al. , Kunz et al. ) lots of new instabilities (HBI, MTI, HBO, RBO, …) Window into Galaxy Formation because of the higher density and longer path length, one can observe the virialized gas in clusters modelling x-ray emission → thermodynamic state can understand how the gas cools, forms stars, powers feedback, etc. Probes of Dark Energy Halo mass function sensitive to the expansion history of the universe, all the way to z ∼ 0
7. Introduction Cold Gas Central Density Outer Temperature Conclusions Clusters as a Window into Galaxy Formation ermal State of the Gas Pressure Entropy Virgo Cluster (Million et al. 2010)
8. Outline “Sculpting Cosmic Gas into Clusters” Multiphase Gas ermal Instability (McCourt, Sharma, et al. ) Triggering of Feedback (Sharma, McCourt, et al. a) Central Density Non-Self-Similarity (Sharma, McCourt, et al. b) Baryon Fraction Outer Temperature Accretion History → T(r) (McCourt, Quataert, & Parrish) Conduction & Convection (Parrish, McCourt, et al. a)
9. How does cool gas form in clusters?
10. Introduction Cold Gas Central Density Outer Temperature Conclusions Atomic Gas in Clusters xray optical Fabian et al. 2011 Some clusters have neutral, ~ K gas colocated with the ionized, ~ K plasma!
11. Introduction Cold Gas Central Density Outer Temperature Conclusions Atomic Gas in Clusters Hydra A Abell  Abell  McDonald et al. 2010
12. Introduction Cold Gas Central Density Outer Temperature Conclusions ermal Instability in Clusters Conselice et al. 2005 Θ ≡ Net cooling rate ￿ ∂Θ ∂T ￿ P < ￿ ￿ermally unstable (Field ￿￿￿￿) Ay.
13. Introduction Cold Gas Central Density Outer Temperature Conclusions ermal Instability in Clusters Conselice et al. 2005 Is the ICM ermally Unstable? ermal instability suppressed in cooling-flows (Balbus & Soker ) Some equilibria may be thermally stable (e. g. Kunz et al. ) Many heating mechanisms are thermally unstable (Gaspari et al. ) Multi-phase gas seen in many clusters (McDonald et al. , ) Assume local thermal instability
14. Introduction Cold Gas Central Density Outer Temperature Conclusions How Does ermal Instability Saturate? (Assuming it exists…) log 10 (ρ/ρ0 ) z/H tcool/tff = 1/10 x/H −1 0 1 0 1 2 3 −2 −1 0 1 log 10 (ρ/ρ0 ) z/H tcool/tff = 10 x/H −1 0 1 0 1 2 3 −1.0 −0.5 0.0 McCourt et al. 2012 ermal Instability does not necessarily imply Multi-phase gas.
15. Introduction Cold Gas Central Density Outer Temperature Conclusions How Does ermal Instability Saturate? (Assuming it exists…) log 10 (ρ/ρ0 ) z/H tcool/tff = 1/10 x/H −1 0 1 0 1 2 3 −2 −1 0 1 log 10 (ρ/ρ0 ) z/H tcool/tff = 10 x/H −1 0 1 0 1 2 3 −1.0 −0.5 0.0 McCourt et al. 2012 ermal Instability does not necessarily imply Multi-phase gas. See cold gas when tcool /tff 10
16. Introduction Cold Gas Central Density Outer Temperature Conclusions Physics of the Saturation t/tTI δρ/ρ rms 0 5 10 15 10−3 10−2 10−1 1 10 Linear Theory tTI /tff = 1/10 tTI /tff = 1 tTI /tff = 10 Perturbations initially grow exponentially… …Saturate when tsink ∼ tcool Final amplitude ∝ (tcool /tff )−1 is is a non-linear effect McCourt et al. 2012
17. Introduction Cold Gas Central Density Outer Temperature Conclusions Application to Hα Filaments Expect multiphase gas when tcool /tff 
18. Introduction Cold Gas Central Density Outer Temperature Conclusions Application to Hα Filaments V V V V V V V V V v v v v v v v V v r (Mpc) tcool/tff 10−3 10−2 10−1 1 10 102 103 Extended Hα No Extended Hα min(tcool) (Gyr) min(tcool/tff) Abell 133 Abell 478 Abell 496 Sersic 159-03 Abell 1991 Abell 2597 Abell 1795 Hydra A Centaurus Abell 85 Abell 644 Abell 4059 Abell 1650 Abell 2029 Abell 2142 Abell 744 10−2 10−1 1 10 1 10 102 Extended Hα No Extended Hα McCourt et al. 2012
19. Introduction Cold Gas Central Density Outer Temperature Conclusions Feedback Regulation Feedback and cooling self-regulate to the critical threshold for non-linear thermal stability: min(tcool/tff) ∼ 10
20. Introduction Cold Gas Central Density Outer Temperature Conclusions Feedback Regulation ermal Instability Develops Cold Gas Accretes Residual Cold Gas No ermal Instability 10 kpc r (kpc) t (Gyr) M int . M cold . M (M sun /yr) . M hot . Sharma, McCourt et al. 2012a
21. Introduction Cold Gas Central Density Outer Temperature Conclusions Feedback Regulation Feedback and cooling self-regulate to the critical threshold for non-linear thermal stability: min(tcool/tff) ∼ 10
22. What determines the density of the gas in the centers of clusters?
23. Introduction Cold Gas Central Density Outer Temperature Conclusions Motivation: Non-Self-Similarity Assume that the gas properties scale with the dark matter: ρ ∼ M0 T ∼ M/r ∼ M2/3 L ∼ ρ2T1/2r3 ∼ T2 T2 T3 Gas in the centers of clusters has lower density and higher entropy than gravitational self-similar models predict. (more so for lower masses.)
24. Introduction Cold Gas Central Density Outer Temperature Conclusions Feedback Regulation Feedback and cooling self-regulate to the critical threshold for non-linear thermal stability: min(tcool/tff) ∼ 10
25. Introduction Cold Gas Central Density Outer Temperature Conclusions Excavating Cool Cores r / r vir t cool / t f f 10 30 100 3 1
26. Introduction Cold Gas Central Density Outer Temperature Conclusions Excavating Cool Cores self-sim ilar r / r vir t cool / t f f 10 30 100 3 1
27. Introduction Cold Gas Central Density Outer Temperature Conclusions Excavating Cool Cores self-sim ilar entropy core r / r vir t cool / t f f upper limit 10 30 100 3 1
28. Introduction Cold Gas Central Density Outer Temperature Conclusions Excavating Cool Cores r / r vir ρ self-sim ilar entropy core r / r vir t cool / t f f upper limit 10 30 100 3 1
29. Introduction Cold Gas Central Density Outer Temperature Conclusions Core Size w/ Mass 3 × 1014 1 × 1013 6 × 1012 1 × 1012 High-Mass Halos High Temperature Long Cooling Time ⇒ small core Low-Mass Halos Lower Temperature Shorter Cooling Time ⇒ large core (Minimum) Core size determined by ermal Instability
30. Introduction Cold Gas Central Density Outer Temperature Conclusions Applications Also: gas fraction core size & entropy stellar mass baryon fraction Assuming global thermal balance, these properties are ~independent of the feedback mechanism Sharma, McCourt, et al. 2012b
31. What determines the temperature of the gas at large radii in clusters?
32. Introduction Cold Gas Central Density Outer Temperature Conclusions Motivation Simionescu et al. (2011) ∇T < 0 ⇒ MTI tcond ∼ r2 vir /χ ∼ 1 Gyr tage
33. Introduction Cold Gas Central Density Outer Temperature Conclusions Motivation 0.2 10 9 8 7 0.0 0.4 r (Mpc) T (keV) 0.6 0.8 1.0 Initial 1 1.5 2.5 3.5 Parrish et al. (2008) In simulations of isolated clusters, the ICM becomes isothermal after ~Gyr.
34. Introduction Cold Gas Central Density Outer Temperature Conclusions Model: Entropy Generation at the Shock r sh r ta 1 2 v2 i = GMsh rsh − GMsh rta ρv = 1 4πr2 sh dM dt + Jump Conditions → K(rsh ) (e. g. Voit et al. 2003)
35. Introduction Cold Gas Central Density Outer Temperature Conclusions Adiabatic Evolution r/rsh T/Tvir slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 In the case of Adiabatic Evolution, this is a simple problem. T(0) = Tvir T(out) = Tsh Temperature Gradient set by Accretion Rate (tdyn × d ln M/dt)
36. Introduction Cold Gas Central Density Outer Temperature Conclusions Adiabatic Evolution r/rsh T/Tvir slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn slow accretors: ˙ M M /t dyn fast accretors: ˙ M ∼ M/tdyn 0.0 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 In the case of Adiabatic Evolution, this is a simple problem. T(0) = Tvir T(out) = Tsh Temperature Gradient set by Accretion Rate (tdyn × d ln M/dt)
37. Introduction Cold Gas Central Density Outer Temperature Conclusions Dispersion in Accretion Histories r/rvir 0.0 0.25 0.5 0.75 1014M r/rvir 0.0 0.25 0.5 0.75 1.0 1015M r/rvir T/Tvir 0.0 0.25 0.5 0.75 0.0 0.5 1.0 1.5 1014.5M Accretion histories from McBride et al. 2009
38. Introduction Cold Gas Central Density Outer Temperature Conclusions Effect of Conduction r/rvir 0.0 0.25 0.5 0.75 1014M r/rvir 0.0 0.25 0.5 0.75 1.0 1015M r/rvir T/Tvir 0.0 0.25 0.5 0.75 0.0 0.5 1.0 1.5 1014.5M Accretion histories from McBride et al. 2009
39. Introduction Cold Gas Central Density Outer Temperature Conclusions Application: MTI & Non- ermal Pressure Support t = 0 t = 4 tbuoy t = 6 tbuoy t = 10 tbuoy t = 30 tbuoy McCourt et al. 2011, Parrish et al. 2012a,b suggest that convection produces ~ tens of  turbulent pressure support.
40. Introduction Cold Gas Central Density Outer Temperature Conclusions Application: MTI & Non- ermal Pressure Support r/rvir 0.0 0.25 0.5 0.75 1014M r/rvir 0.0 0.25 0.5 0.75 1.0 1015M T/Tvir 0.0 0.5 1.0 1.5 r/rvir (M/α)2 0.0 0.25 0.5 0.75 0.0 0.25 0.5 0.75 1014.5M
41. Introduction Cold Gas Central Density Outer Temperature Conclusions Conclusions ermal Instability Assuming that the ICM is thermally unstable, multi-phase gas forms only when tcool/tff 10. Cooling and feedback self-regulate to the critical threshold for stability. Density Cores ermal instability sets a density ceiling (or entropy floor) for the gas ⇒ non-self-similarity. Temperature Gradients A cluster’s accretion rate determines its temperature gradient is temperature gradient persists even with thermal conduction Importance of the MTI may be non-monotonic with halo mass. (× M is the sweet spot).
42. Backup Slides
43. Introduction Cold Gas Central Density Outer Temperature Conclusions Cosmological Constraints from Clusters Weinberg et al. 2012
44. Introduction Cold Gas Central Density Outer Temperature Conclusions Previous Ideas pre-heating heat gas before the cluster forms necessary amount of heating depends on halo mass selective removal of low-entropy gas (e. g. Voit & Bryan 2001) need a way to target low-entropy gas need to explain what the threshold is Neither of these ideas accounts for feedback heating. (Clusters must be globally stable.)
45. Introduction Cold Gas Central Density Outer Temperature Conclusions Heating Fluctuations tTI/tff = 10 z/H 1 2 3 tTI/tff = 1 tTI/tff = 1/10 Fiducial z/H 1 2 3 100% Fluct. x/H z/H −1 0 1 0 1 2 3 x/H −1 0 1 x/H 300% Fluct. −1 0 1
46. Introduction Cold Gas Central Density Outer Temperature Conclusions Density Perturbations 5 5 5 5 5 tti/tff δρ/ρ rms 10−1 1 10 10−2 10−1 1 10
47. Introduction Cold Gas Central Density Outer Temperature Conclusions Including Conduction λF ∝ (ˆ b ⋅ ˆ k) × (χe t￿ɪ)￿￿￿ e 5), to the point where the magnetic pressure n the filaments. The regions over which the ed are coincident with, but significantly longer on of the cold filaments. The field enhancement freezing as the cooling plasma is compressed o the initial field direction in the nonlinear state by contrast, in one at 1.43 Gyr (Figur state in two dimen regions to becom (because of the s 0 x(kpc) t=0.95 Gyr 0 20 40 −1 −0.5 0 x(kpc) z(kpc) t=0.475 Gyr 0 20 40 0 20 40 −0.13 −0.12 −0.11 −0.1 plots of log10 temperature (in keV) for the fiducial run (MWC) at linear (0.475 Gyr; left) he arrows show the magnetic field direction. this figure is available in the online journal.) Sharma et al. 2010 V V V ¥ ¥ ¥ V ¥ anisotropic isotropic tχ/tff tTI/tff Cold Fraction (by Mass) 10−1 1 10−2 10−1 1 10 √ 2 √ 2 √ 2/10 10 √ 2 √ 2 McCourt et al. 2012
48. Introduction Cold Gas Central Density Outer Temperature Conclusions Including Conduction, cont. tχ /tff = ∞ z/H -2 -1 0 1 2 3 tχ /tff = 10 √ 2 tχ /tff = √ 2 tχ /tff = √ 2/4 tχ /tff = √ 2/10 tTI/tff = 10−0.75 z/H -2 -1 0 1 2 3 tTI/tff = 10−0.25 x/H z/H −3 −2 −1 0 1 2 -3 -2 -1 0 1 2 3 x/H −3 −2 −1 0 1 2 x/H −3 −2 −1 0 1 2 x/H −3 −2 −1 0 1 2 x/H tTI/tff = 1 3 −3 −2 −1 0 1 2
49. Introduction Cold Gas Central Density Outer Temperature Conclusions r/rvir 0.0 0.25 0.5 0.75 1014M r/rvir 0.0 0.25 0.5 0.75 1.0 1015M T/Tvir 0.0 0.5 1.0 1.5 r/rvir (M/α)2 0.0 0.25 0.5 0.75 0.0 0.25 0.5 0.75 1014.5M