Constraining turbulence and conduction in the hot ICM through density perturbations^⋆

Max Planck Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, 85741 Garching, Germany
e-mail: mgaspari@mpa-garching.mpg.de

Received: 16 July 2013
Accepted: 3 October 2013

Abstract

Turbulence and conduction can dramatically affect the evolution of baryons in the universe; current constraints are however rare and uncertain. Using 3D high-resolution hydrodynamic simulations, tracking both electrons and ions, we study the effects of turbulence and conduction in the hot intracluster medium. We show how the power spectrum of the gas density perturbations (δ = δρ/ρ) can accurately constrain both processes. The characteristic amplitude of density perturbations is linearly related to the strength of turbulence, i.e. the 3D Mach number, as A(k)_δ,max = c   M, where c ≃ 0.25 for injection scale of 500 kpc. The slope of A_δ(k) in turn reflects the level of diffusion, dominated by conduction. In a non-conductive medium, subsonic stirring motions advect density with a similar nearly Kolmogorov cascade, E_δ(k) ∝ k^− 5/3. Increasing conduction (parametrized via the magnetic suppression f = 10^-3 → 1) progressively steepens the spectrum towards the Burgers-like regime, E_δ(k) ∝ k^-2. The slope is only weakly dependent on M. The turbulent Prandtl number defines the dynamic similarity of the flow; at scales where P_t ≡ t_cond/t_turb < 100, the power spectrum develops a significant decay, i.e. conduction stifles turbulent regeneration. The transition is gentle for highly suppressed conduction, f ≤ 10^-3, while sharp in the opposite regime. For strong conductivity (f ≥ 0.1), P_t ~ 100 occurs on spatial scales larger than the injection scale, globally damping density perturbations by a factor of 2−4, from large to small scales. The velocity spectrum is instead not much affected by conduction. The f ≥ 0.1 regime should also affect the appearance of X-ray images, in which Kelvin-Helmholtz and Rayleigh-Taylor rolls and filaments are washed out. In a stratified system, perturbations are characterized by a mixture of modes: weak/strong turbulence induces higher isobaric/adiabatic fluctuations, while conduction forces both modes towards the intermediate isothermal regime. We provide a general analytic fit which is applied to new deep Chandra observations of Coma cluster. The observed spectrum is best consistent with strongly suppressed effective isotropic conduction, f ≃ 10^-3, and mild subsonic turbulence, M ≃ 0.45 (assuming injection scale at ~250 kpc). The latter implies E_turb ≃ 0.11   E_th, in agreement with cosmological simulations and line-broadening observations. The low conductivity corroborates the survival of sharp features in the ICM (cold fronts, filaments, bubbles), and indicates that cooling flows may not be balanced by conduction.