Constraining turbulence and conduction in the hot ICM through density
  perturbations
  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 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)_max = 0.25 M. The slope of A(k) in
turn reflects the level of conduction. In a non-conductive medium, subsonic
stirring motions advect density with a similar nearly Kolmogorov cascade.
Increasing conduction (via magnetic suppression f = 0.001-1) progressively
steepens the spectrum towards the Burgers-like regime. The turbulent Prandtl
number defines the dynamic similarity of the flow; at scales where Pt < 100,
the spectrum develops a significant decay. The transition is gentle for highly
suppressed conduction, f < 0.001, while sharp in the opposite regime. For
strong conductivity (f > 0.1), Pt ~ 100 occurs on spatial scales larger than
the injection scale. The velocity spectrum is instead not much affected by
conduction. The f > 0.1 regime affects the appearance of X-ray images, in which
Kelvin-Helmholtz and Rayleigh-Taylor rolls and filaments are washed out. In a
stratified system, 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. The observed spectrum is best consistent
with strongly suppressed effective isotropic conduction, f = 0.001, and mild
subsonic turbulence, M = 0.45 (with injection at ~250 kpc). 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.
