Measuring turbulence and gas motions in galaxy clusters via synthetic Athena X-IFU observations

The X-ray Integral Field Unit (X-IFU) that will be on board the Athena telescope will provide an unprecedented view of the intracluster medium (ICM) kinematics through the observation of gas velocity, $v$, and velocity dispersion, $w$, via centroid-shift and broadening of emission lines, respectively. The improvement of data quality and quantity requires an assessment of the systematics associated with this new data analysis, namely biases, statistical and systematic errors, and possible correlations between the different measured quantities. We have developed an end-to-end X-IFU simulator that mimics a full X-ray spectral fitting analysis on a set of mock event lists, obtained using SIXTE. We have applied it to three hydrodynamical simulations of a Coma-like cluster that include the injection of turbulence. This allowed us to assess the ability of X-IFU to map five physical quantities in the cluster core: emission measure, temperature, metal abundance, velocity and velocity dispersion. Finally, starting from our measurements maps, we computed the 2D structure function (SF) of emission measure fluctuations, $v$ and $w$ and compared them with those derived directly from the simulations. All quantities match with the input projected values without bias; the systematic errors were below 5%, except for velocity dispersion whose error reaches about 15%. Moreover, all measurements prove to be statistically independent, indicating the robustness of the fitting method. Most importantly, we recover the slope of the SFs in the inertial regime with excellent accuracy, but we observe a systematic excess in the normalization of both SF$_v$ and SF$_w$ ascribed to the simplistic assumption of uniform and (bi-)Gaussian measurement errors. Our work highlights the excellent capabilities of Athena X-IFU in probing the thermodynamic and kinematic properties of the ICM. (abridged)