The relation between gas density and velocity power spectra in galaxy clusters: High-resolution hydrodynamic simulations and the role of conduction

Exploring the power spectrum of fluctuations and velocities in the intracluster medium (ICM) can help us to probe the gas physics of galaxy clusters. Using high-resolution 3D plasma simulations, we study the statistics of the velocity field and its intimate relation with the ICM thermodynamic perturbations. The normalization of the ICM spectrum (related to density, entropy, or pressure fluctuations) is linearly tied to the level of large-scale motions, which excite both gravity and sound waves due to stratification. For a low 3D Mach number M similar to 0.25, gravity waves mainly drive entropy perturbations, which are traced by preferentially tangential turbulence. For M > 0.5, sound waves start to significantly contribute and pass the leading role to compressive pressure fluctuations, which are associated with isotropic (or slightly radial) turbulence. Density and temperature fluctuations are then characterized by the dominant process: isobaric (low M), adiabatic (high M), or isothermal (strong conduction). Most clusters reside in the intermediate regime, showing a mixture of gravity and sound waves, hence drifting toward isotropic velocities. Remarkably, regardless of the regime, the variance of density perturbations is comparable to the 1D Mach number, M-1D similar to delta rho/rho. This linear relation allows us to easily convert between gas motions and ICM perturbations (delta rho/rho < 1), which can be exploited by the available Chandra, XMM data and by the forthcoming Astro-H mission. At intermediate and small scales (10-100 kpc), the turbulent velocities develop a tight Kolmogorov cascade. The thermodynamic perturbations (which can be generally described by log-normal distributions) act as effective tracers of the velocity field, in broad agreement with the Kolmogorov-Obukhov-Corrsin advection theory. The cluster radial gradients and compressive features induce a flattening in the cascade of the perturbations. Thermal conduction, on the other hand, acts to damp the thermodynamic fluctuations, washing out the filamentary structures and steepening the spectrum, while leaving the velocity cascade unaltered. The ratio of the velocity and density spectrum thus inverts the downtrend shown by the non-diffusive models, as it widens up to similar to 5. This new key diagnostic can robustly probe the presence of conductivity in the ICM. We produce X-ray images of the velocity field, showing how future missions (e. g. Astro-H, Athena) can detect velocity dispersions of a few 100 km s(-1) (M > 0.1 in massive clusters), allowing us to calibrate the linear relation and to constrain relative perturbations down to just a few percent.