Turbulent density and pressure fluctuations in the stratified intracluster medium

Turbulent gas motions are observed in the intracluster medium (ICM). The ICM is density-stratified, with the gas density being highest at the centre of the cluster and decreasing radially outwards. As a result of this, Kolmogorov (homogeneous, isotropic) turbulence theory does not apply to the ICM. The gas motions are instead explained by anisotropic stratified turbulence, with the stratification quantified by the perpendicular Froude number (Fr-perpendicular to). These turbulent motions are associated with density and pressure fluctuations, which manifest as perturbations in X-ray surface brightness maps of the ICM and as thermal Sunyaev-Zeldovich effect (SZ) fluctuations, respectively. In order to advance our understanding of the relations between these fluctuations and the turbulent gas velocities, we have conducted 100 high-resolution hydrodynamic simulations of stratified turbulence (256(2) x 384-1024(2) x 1536 resolution elements), in which we scan the parameter space of subsonic rms Mach number (M), Fr-perpendicular to, and the ratio of entropy and pressure scale heights (R-PS = H-P/H-S), relevant to the ICM. We develop a new scaling relation between the standard deviation of logarithmic density fluctuations (sigma(s), where s = ln (rho/)), M, and Fr-perpendicular to, which covers both the strongly stratified (Fr-perpendicular to << 1) and weakly stratified (Fr-perpendicular to << 1) turbulence regimes: sigma(2)(s) = ln(1 + b(2)M(4) + 0.10/(Fr-perpendicular to + 0.25/root Fr-perpendicular to)(MRPS)-M-2-R-2), where b similar to 1/3 for solenoidal turbulence driving studied here. We further find that logarithmic pressure fluctuations sigma((ln P/ < P >)) are independent of stratification and scale according to the relation sigma(2)((ln P)) = ln(1 + b(2)gamma M-2(4)), where (P) over bar = P/< P > and gamma is the adiabatic index of the gas. We have tested these scaling relations to be valid over the parameter ranges M = 0.01-0.40, Fr-perpendicular to = 0.04-10.0, and R-PS = 0.33-2.33.

Automated summary

This text discusses turbulent gas motions in the intracluster medium (ICM) and their dependence on density stratification. The relationships between turbulent properties and density/pressure fluctuations are explored, revealing scaling relations that are valid over certain parameter ranges.