Abstract

ABSTRACT While awaiting direct velocity measurements 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–Zel’dovich (SZ) y-parameter, and the characteristic Mach number of gas motions, M1d. In relaxed clusters, accounting for halo ellipticities reduces δρ/ρ or δP/P by a factor of up to 2 within r500c. We confirm a strong linear correlation between δρ/ρ (or δP/P) and M1d 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 M1d − δρ/ρ relation shows that it is almost linear for relaxed clusters, while for the unrelaxed ones, it is closer to $\delta \rho /\rho \propto M_{\rm 1d}^2$. In agreement with previous studies, we observe a strong correlation of M1d with radius. Correcting for these correlations leaves a residual scatter in M1d of ∼4(7) per cent for relaxed (perturbed) clusters. Hydrostatic mass bias correlates with M1d 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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