the ICM Power Spectrum:

Transcription

1 the ICM Power Spectrum: probing the gas physics of galaxy clusters Massimo Gaspari Max Planck Institute for Astrophysics Collaborators: E. Churazov, D. Nagai, E. Lau, I. Zhuravleva, R. Sunyaev

2 Power Spectrum CMB - observations Photon-baryon fluid CMB temperature: Planck coll acoustic oscillations If sound waves are synchronized, the same behavior can be simulated in the ICM

3 Power Spectrum ISM - observations ISM density: Armstrong et al Kolmogorov slope (classic turbulence) over 10 decades in wavenumber! E k / k 5/3... same for the solar wind: Woo & Armstrong 1979, Marsch & Tu 1990

4 Power Spectrum ICM - observations Only a few ICM studies: suggest Kolmogorov trend (or slightly shallower) ICM pressure: Schuecker et al (Coma) ICM density: Churazov et al (Coma) ICM density: Sanders et al (AWM7)

5 3D high-res simulations [astrophysical experiment] Gaspari & Churazov 2013 Gaspari et al for numerical details init from observed profiles (Coma) Massive hot galaxy cluster: T0 = 8.5 kev, Mvir ~ M ʘ, R500 ~ 1.4 Mpc UG (100 mil. cells) avoid AMR diffusion dx 2.6 kpc (~ electron mean free path) 3D hydrodynamics: III order PPM (FLASH4) Main physics tested: TURBULENCE: M ~ THERMAL CONDUCTION: f ~ electron - ion equilibration

6 turbulence ICM is never in perfect HSE: mergers, cosmic flows, galaxy motions, feedback processes Observations & simulations: e.g. Norman & Bryan 1999, Schuecker et al. 2004, Lau et al. 2009, Vazza et al. 2009, 2011, Churazov et al. 2008, de Plaa et al. 2012, Gaspari et al. 2012, Sanders & Fabian 2013,... kpc Eturb ~ 3-30% Eth tested range: Mach ~ OU spectral driving in Fourier space (Linj ~ kpc) natural turbulent cascade to smaller scales Gaspari et al v mid-plane slice massive galaxy cluster

7 ICM Power Spectrum Turbulent velocity (total) A(k) p P (k)4 k 3 = p E(k) k Density perturbations (relative to the underlying radial profile) higher conductivity Gaspari & Churazov 2013 Gaspari et al. 2014

8 1. ps normalization: rising with turbulent motions / Mach 1D

9 PS normalization Gaspari et al % 3D velocity 12% f=0 18% Density f=1 Mach ~ 0.75 Mach ~ 0.5 Mach ~ 0.25 globally self-similar over Mach and L inj / Mach 1D (< 1)

10 g-waves vs p-waves BUOYANCY SOUND! 4! 2 c 2 s k 2 +! 2 BV c 2 s k 2? =0 linearized perturbed HD - dispersion relation (Balbus & Soker 1990) p-waves g-waves turbulence frequency Mach P/P Mach 1D stronger compression (p-waves) buoyancy frequency (Brunt Väisälä) stronger buoyancy (g-waves) K/K Mach 1D massive cluster (Gaspari et al. 2014) cluster gradients are radial

11 g-waves > p-waves g-waves p-waves but in both cases / Mach 1D Gaspari et al K/K P/P P/P & K/K isobaric hydro (towards) adiabatic

12 velocity anisotropy marker of the dominant regime Gaspari et al stronger turbulence (Mach > 0.5): towards isotropy g-waves (Mach < 0.5): mild tangential anisotropy

13 2. ps slope: tracing velocity field & shaped by transport processes

14 tracers of the velocity field Gaspari et al D velocity all quantities develop a cascade Extreme/fully passive case: e.g. entropy: T DS Dt T Kolmogorov-Obhukov-Corrsin E tracer (k) / E + v rs 0... but deviations: weak compression, radial gradients, different diffusivity (nonlinear sims are required)

15 thermal conduction Transfer of heat via plasma electrons: heating rate per unit volume r F cond = r (apple rt e ) core of Coma t di l 2 /D Spitzer (1962) conductivity: apple ' f Te 5/2 ln ei t turb t e-i equilibration magnetic suppression (unresolved small scales highly tangled B-field): f ~ Ruszkowski & Oh 2010,11 saturation t cond f=0.1 (fast) plasma micro-instabilities (mirror, firehose, etc.) + line divergence geometric suppression (electrons move along B-field lines) (Gaspari & Churazov 2013)

16 density cascade damped by conduction Gaspari & Churazov 2013 steepening ~ Kolmogorov ~ Burgers higher conductivity E k / k 5/3! k 2 strong decay if turbulent Prandtl P t D turb D cond = t cond t turb < 100

17 velocity cascade unaffected by conduction 3D velocity density PS/velocity PS ratio: & varying M and L Gaspari et al Kolmogorov no conduction & varying M and L velocity PS/ density PS linear relation holds in cosmological (hydro) simulations strong conduction Decoupling: ratio widens up to 5! Zhuravleva et al. 2014

18 Density fluctuations (real space) δρ/ρ mid-plane cuts M ~ 0.25 Gaspari & Churazov 2013 hydro isobaric fluctuations f = f = 0.01 log-normal PDF f = 0.1 isothermal fluctuations

19 SBx weighting Gaspari & Churazov 2013 hydro f = 0.1 M ~ 0.5 M ~ 0.5 SBx image perturbations + global profile smoothening: KH + RT rolls washed out X-ray emission-weighted (projected) velocity dispersion non-black regions: Astro-H will be able to detect turbulent velocities > 200 km s 1 (using the Fe XXV line) Gaspari et al. 2014

20 real case: Coma Cluster Gaspari & Churazov 2013; Churazov et al (in prep.) mild turbulence: ~500 ks M ' 0.45 L 250 kpc E turb ' 0.11 E th (as in cosmological sims & line-broadening constraints) strongly suppressed conduction: f 10 3 Kolmogorov slope plasma microinstabilities and line divergence below electron mean free path are important (consistent with cold fronts, filaments, bubbles) (cooling flows can not be balanced by conduction)

21 Summary Power spectrum of ICM perturbations is a powerful tool to probe baryon physics. Highly unexplored: many deep XMM/Chandra observations already available. Astro-H and Athena+ major advancements: σv ~ 100 km/s δρ/ρ ~ a few %. 3D high-res. simulations/experiments: we are working on MHD, viscosity, cooling, other physics. PSρ normalization: linear relation (easy conversion) δρ/ρ Mach1D Weak turbulence (M < 0.5) gravity-waves (tangential bias; isobaric): δk/k ~ Mach1D Strong turbulence (M > 0.5) pressure-waves (isotropic; adiabatic): δp/p ~ Mach1D PSρ slope overall traces the velocity cascade (deviations: compressibility, radial gradients), but decouples if diffusion processes are not suppressed: conduction damps ρ/t perturbations (smooth SBx images), not velocities. Steepening Kolmogorov to Burgers-like slope (as Pt < 100). (Real) Coma mild turbulence: Mach 0.4 & suppressed conduction: f 10-3.