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

While awaiting direct velocity measurement of gas motions in the hot intracluster medium, we rely on indirect probes, including perturbations galaxy clusters. Using a sample $\sim 80$ clusters different dynamic states from Omega500 cosmological simulations, examine scaling relations between fluctuation amplitudes density, $\delta\rho/\rho$, pressure, $\delta P/P$, X-ray surface brightness, Sunyaev-Zeldovich (SZ) y-parameter, and characteristic Mach number motions, $M_{\rm 1d}$. In relaxed clusters, accounting for halo ellipticities reduces $\delta\rho/\rho$ or P/P$ by factor up to 2 within $r_{500c}$. We confirm strong linear correlation (or P/P$) 1d}$ with proportionality coefficient $\eta \approx 1$. For unrelaxed is less has larger $\eta\approx 1.3\pm 0.5$ ($1.5\pm0.5$) ($\delta P/P$). Examination power-law shows that it almost while ones, closer $\delta\rho/\rho\propto M_{\rm 1d}^2$, supporting an increasing role non-linear terms compressive modes. agreement previous studies, observe radius. Correcting these correlations leaves residual scatter 4 (7)$ per cent (perturbed) Hydrostatic mass bias correlates as strongly The scatters after correcting derived trends 6-7$ cent. These predictions can be verified existing SZ observations combined forthcoming measurements microcalorimeters.