simulation turbulence in galaxy clusters insights on stochastic - PowerPoint PPT Presentation

simulation turbulence in galaxy clusters insights on stochastic acceleration and the impact of microphysics Francesco Miniati ETH-Zurich MPA, June 16 2015 (Munich) “The Matryoshka Run: Eulerian Refinement Strategy to Model Turbulence in Cosmic Structure” fm, ApJ 782 21 (2014) “The Matryoshka Run (II): Time Dependent Turbulence Statistics, Stochastic Particle Acceleration and Microphysics Impact in a Massive Galaxy Cluster” fm, ApJ 800 60 (2015)

motivations for turbulence acceleration • diffuse radio sources appear only in massive systems • they appear to be triggered by mergers / bi-modality (but see Enßlin+ 2011) • spectral curvature • source statistics suggests a lifetime of ca 1 Gyr • we don’t see gamma-rays that would suggest a secondary origin • other more sophisticated tests but like radial profile requiring some assumption about B or the like

outline • (computational modeling) • some properties of turbulence in galaxy clusters • particle acceleration by turbulence, impact of microphysics of weak shocks

Eulerian Refinement Strategy: Zoom-in + Matryoshka of grids ℓ L N ℓ n ℓ ∆ x ℓ 22 h -1 Mpc (h -1 Mpc) (h -1 kpc) 70 h -1 Mpc 0 240 512 2 470 1 120 512 2 235 240 h -1 Mpc 2 60 512 2 117 3 30 512 4 58.6 7.5 h -1 Mpc 4 15 1024 2 14.6 5 7.5 1024 -- 7.3 fm , ApJ 782, 21 (2014)

time: 11.9 Gyr time: 12.2 Gyr time: 12.6 Gyr time: 12.9 Gyr time: 13.3 Gyr time: 13.9 Gyr time: 14.2 Gyr time: 14.5 Gyr time: 14.8 Gyr

Statistics Hodge-Helmholtz decomposition ! (2) = 2 + ζ 2 v c = −∇ φ , ! ! v s = ∇ × A (2) S t , s S l , s ∇⋅ ! ∇ × ! ! φ = 1 v A = 1 v ∫ ∫ 2 d 3 r d 3 r , 4 π 4 π r r (von Karman & Howarth, 1938) fm , ApJ 800, 60 (2015)

Evolution of Turbulence fm , ApJ 800, 60 (2015)

Particle Acceleration ∂ ∂ f df dt − ∇ D xx ∇ f − 1 ∂ p = 0 ∂ p p 2 D pp transport eq. p 2 Δ p 2 Δ x 2 D pp ≡ 2 Δ t , D xx ≡ Fokker-Planck coeff. 2 Δ t ∂ Γ p ≡ ! ( ) = 4 D pp p = 1 p ∂ p p 2 D pp advection rate in p-space p 3 p 2

Particle Acceleration ∂ f ∂ ∂ f ∂ t − ∇ D xx ∇ f − 1 ∂ p = 0 ∂ p p 2 D pp p 2 Transit-Time-Damping (Fisk 1976, BL07): Non Resonant Mech. (Ptuskin 1988, BL07): • • 2 nd order Fermi process, particles resonate with fast stochastic acceleration due to velocity divergence MHD waves and get reflected by the mirror force according to the adiabatic process ! ! 3 ∇⋅ ! dp dt = − p ( ) dp ! dt = − p ⊥ B ⋅∇ v 2 B 2 v ⊥ B micro macro micro macro ζ 2 D pp = p 2 π I ϑ D pp = p 2 π I ϑ ⎛ ⎞ I ξ ( ) ( ) D pp = p 2 2 k L D ( ) 2 δ u c 2 2 δ u c 9 ζ 2 δ u c 16 c k E 16 c k E ⎜ ⎟ ⎝ ⎠ D c s 1 − ζ 2 ⎡ ⎤ d ξ ξ 1 − ζ 2 ⎛ ⎞ ζ 2 1 k c k c D / c s ∫ k c ∫ I ξ ≡ k E ≡ ≈ − 1 ⎢ ⎥ dkkW ( k ) k L ⎜ ⎟ ( ) 1 − ζ 2 ⎝ ⎠ 2 1 + ξ 2 δ u c ⎢ k L ⎥ ⎣ ⎦ k L D / c s

Spectra of Turbulent Cascade ) log kE k ( k − 1/2 Kraichnan k − 2/3 Kolmogorov k − 1 Burgers ( ) k=1/R vir log k

Spectra of Turbulent Cascade Brunetti & Jones 2014

Key Cascade Physics • the cascade of the compressional modes, Alfven vs Burgers: how much dissipation occurs during the cascade ? If enough to steepen the structure functions then the mechanisms become very inefficient • the slope of the cascade of compressional modes affects the value of the energy-averaged wave-vector which tends to k L as ζ ⟶ 1 i) ii) the cascade cutoff which can become much larger • the collisionality of the plasma; if thermal particles have their mfp reduced by micro instabilities (mirror, firehose…) , they won’t resonate with and damp the MHD waves anymore, only CRs do, so their acceleration efficiency increases dramatically ( ) 2 δ u c D pp = p 2 C D C W ξ k L 3 x CR c s

kraicknan’s kraicknan’s Tot AdC Tot AdC BL7 BL7k NR TTD cascade NR TTD cascade 8 8 GHz G for cutfoff + for cutfoff H z 1 1.4 GHz . 4 burgers’ and <k> E G H z 3 300 MHz 0 0 (simulation’s) M no micro H z slope instabilities GeV G e V for <k> E no micro instabilities Min ! Min ! loss l o s s H ( z ) H ( z ) burger’s kraicknan’s (simulation’s) BL11 Tot AdC Tot AdC BL7b x CR =10% NR TTD cascade cascade NR TTD " =100% 8 8 GHz G for cutfoff for cutfoff H z 1 1.4 GHz . 4 and <k> E and <k> E G H z 3 300 MHz 0 0 + independent M H z micro of micro GeV GeV instabilities instabilities set mfp Min ! loss Min ! loss H ( z ) H ( z ) fm , ApJ 800, 60 (2015)

Time evolution of spectral indexes kraicknan’s cascade kraicknan’s for cutfoff + cascade burgers’ for cutfoff (simulation’s) and <k> E slope no micro for <k> E instabilities no micro instabilities burger’s kraicknan’s (simulation’s) cascade cascade for cutfoff for cutfoff and <k> E and <k> E + independent micro of micro instabilities instabilities set mfp

takeaway result • the simulation model of the turbulence pins down an important ingredient entering the acceleration rate, which is the amount of compressional turbulent energy available for TTD or NR mechanisms • the microphysics of the ICM plasma, however, also enters the acceleration rates, and because we have fixed the above unknown, we can now expose its impact • the acceleration rates depend on at least the following microphysics (but possibly other as well) of: • the cascade of the compressional modes, Alfven vs Burgers: how much dissipation occurs during the cascade ? If enough to steepen the structure functions then the mechanisms become very inefficient • the collisionality of the plasma; if micro instabilities (mirror, firehose… ) reduce the thermal particles mfp then the acceleration efficiency is very high • we also need to understand the properties of magnetic fields