2025ApJ...985..248R

The hot plasma in galaxy clusters, the intracluster medium, is expected to be shaped by subsonic turbulent motions, which are key for heating, cooling, and transport mechanisms. The turbulent motions contribute to the nonthermal pressure, which, if not accounted for, consequently imparts a hydrostatic mass bias. Accessing information about turbulent motions is thus of major astrophysical and cosmological interest. Characteristics of turbulent motions can be indirectly accessed through surface brightness fluctuations. This study expands on our pilot investigations of surface brightness fluctuations in the Sunyaev-Zel'dovich and in X-ray data by examining, for the first time, a large sample of 60 clusters using both SPT-SZ and XMM-Newton data and spans the redshift range 0.2 < z < 1.5, thus constraining the respective pressure and density fluctuations within 0.6R₅₀₀. We deem density fluctuations to be of sufficient quality for 32 clusters, finding mild correlations between the peak of the amplitude spectra of density fluctuations and various dynamical parameters. We infer turbulent velocities from density fluctuations with an average Mach number ${{ \mathcal M }}_{\,\rm{3D}\,}=0.52\pm 0.14$, in agreement with numerical simulations. For clusters with inferred turbulent Mach numbers from fluctuations in both pressure, ${{ \mathcal M }}_{\,\rm{P}\,}$, and density, ${{ \mathcal M }}_{\rho }$, we find broad agreement between ${{ \mathcal M }}_{\,\rm{P}\,}$ and ${{ \mathcal M }}_{\rho }$. Our results suggest either a bimodal or a skewed unimodal Mach number distribution, with the majority of clusters being turbulence-dominated (subsonic) while the remainder are shock-dominated (supersonic).