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Using 3D high-resolution hydrodynamic simulations, tracking both electronsand ions, we study the effects of turbulence and conduction in the hotintracluster medium. We show how the power spectrum of the gas densityperturbations can accurately constrain both processes. The characteristicamplitude of density perturbations is linearly related to the strength ofturbulence, i.e. the 3D Mach number, as A(k)_max = 0.25 M. The slope of A(k) inturn reflects the level of conduction. In a non-conductive medium, subsonicstirring motions advect density with a similar nearly Kolmogorov cascade.Increasing conduction (via magnetic suppression f = 0.001-1) progressivelysteepens the spectrum towards the Burgers-like regime. The turbulent Prandtlnumber defines the dynamic similarity of the flow; at scales where Pt < 100,the spectrum develops a significant decay. The transition is gentle for highlysuppressed conduction, f < 0.001, while sharp in the opposite regime. Forstrong conductivity (f > 0.1), Pt ~ 100 occurs on spatial scales larger thanthe injection scale. The velocity spectrum is instead not much affected byconduction. The f > 0.1 regime affects the appearance of X-ray images, in whichKelvin-Helmholtz and Rayleigh-Taylor rolls and filaments are washed out. In astratified system, weak/strong turbulence induces higher isobaric/adiabaticfluctuations, while conduction forces both modes towards the intermediateisothermal regime. We provide a general analytic fit which is applied to newdeep Chandra observations of Coma. The observed spectrum is best consistentwith strongly suppressed effective isotropic conduction, f = 0.001, and mildsubsonic turbulence, M = 0.45 (with injection at ~250 kpc). The lowconductivity corroborates the survival of sharp features in the ICM (coldfronts, filaments, bubbles), and indicates that cooling flows may not bebalanced by conduction.

Constraining turbulence and conduction in the hot ICM through density perturbations