Indirect measurements of gas velocities in galaxy clusters: effects of ellipticity and cluster dynamic state

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.