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)
