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 low 3D Mach number M \sim 0.25 , gravity waves mainly drive entropy perturbations , traced by preferentially tangential turbulence .
For M > 0.5 , sound waves start to significantly contribute , passing the leading role to compressive pressure fluctuations , 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 towards isotropic velocities .
Remarkably , regardless of the regime , the variance of density perturbations is comparable to the 1D Mach number , M _ { 1 D } \sim \delta \rho / \rho .
This linear relation allows 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 in general described by log-normal distributions ) act as effective tracers of the velocity field , broadly consistent 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 unaltered the velocity cascade .
The ratio of the velocity and density spectrum thus inverts the downtrend shown by the non-diffusive models , widening up to \sim 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 to calibrate the linear relation and to constrain relative perturbations down to just a few per cent .