What Do the Hitomi Observations Tell Us About the Turbulent Velocities in the Perseus Cluster? Probing the Velocity Field with Mock Observations

Hitomi made the first direct measurements of galaxy cluster gas motions in the Perseus cluster, which implied that its core is fairly "quiescent", with velocities less than $\sim$200 km s$^{-1}$, despite the presence of an active galactic nucleus and sloshing cold fronts. Building on previous work, we use synthetic Hitomi/SXS observations of the hot plasma of a simulated cluster with sloshing gas motions and varying viscosity to analyze its velocity structure in a similar fashion. We find that sloshing motions can produce line shifts and widths similar to those measured by Hitomi. We find these measurements are unaffected by the value of the gas viscosity, since its effects are only manifested clearly on angular scales smaller than the SXS $\sim$1' PSF. The PSF biases the line shift of regions near the core as much as $\sim 40-50$ km s$^{-1}$, so it is crucial to model this effect carefully. We also infer that if sloshing motions dominate the observed velocity gradient, Perseus must be observed from a line of sight which is somewhat inclined from the plane of these motions, but one that still allows the spiral pattern to be visible. Finally, we find that assuming isotropy of motions can underestimate the total velocity and kinetic energy of the core in our simulation by as much as $\sim$60%. However, the total kinetic energy in our simulated cluster core is still less than 10% of the thermal energy in the core, in agreement with the Hitomi observations.