| Περίληψη: | While awaiting direct velocity measurement of gas motions in the hot intracluster medium, we rely on indirect probes, including gas perturbations in galaxy clusters. Using a sample of ∼80 clusters in different dynamic states from Omega500 cosmological simulations, we examine scaling relations between the fluctuation amplitudes of gas density, δρ/ρ, pressure, δP/P, X-ray surface brightness, Sunyaev-Zeldovich (SZ) y-parameter, and the characteristic Mach number of gas motions, M<sub>1d</sub>. In relaxed clusters, accounting for halo ellipticities reduces δρ/ρ or δP/P by a factor of up to 2 within r<sub>500c</sub>. We confirm a strong linear correlation between δρ/ρ (or δP/P) and M<sub>1d</sub> in relaxed clusters, with the proportionality coefficient η≈1. For unrelaxed clusters, the correlation is less strong and has a larger η≈1.3±0.5 (1.5±0.5) for δρ/ρ (δP/P). Examination of the power-law scaling of M<sub>1d</sub> with δρ/ρ shows that it is almost linear for relaxed clusters, while for the unrelaxed ones, it is closer to δρ/ρ∝M<sup>2</sup><sub>1d</sub>, supporting an increasing role of non-linear terms and compressive modes. In agreement with previous studies, we observe a strong correlation of M<sub>1d</sub> with radius. Correcting for these correlations leaves a residual scatter in M<sub>1d</sub> of ∼4(7) per cent for relaxed (perturbed) clusters. Hydrostatic mass bias correlates with M<sub>1d</sub> as strongly as with δρ/ρ in relaxed clusters. The residual scatters after correcting for derived trends is ∼6−7 per cent. These predictions can be verified with existing X-ray and SZ observations of galaxy clusters combined with forthcoming velocity measurements with X-ray microcalorimeters.
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