  The dissipation of turbulent gas motions is one of the likely mechanisms that
has been proposed to heat the intracluster medium (ICM) in the cores of
clusters and groups of galaxies. We consider the impact of gas motions on the
width of the most prominent X-ray emission lines. For heavy elements (like
iron) the expected linewidth is much larger than the width due to pure thermal
broadening and the contribution due to turbulent gas motions should be easily
detected with the new generation of X-ray micro-calorimeters, such as the
Spektr-RG calorimeter (SXC). For instance in the Perseus cluster the turbulent
velocity required to balance radiative cooling (as derived by Rebusco et al.
2006), would imply a width of the 6.7 keV Fe line of 10-20 eV, while the pure
thermal broadening is ~4 eV. The radial dependence of the linewidth is
sensitive to i) the radial dependence of the velocity amplitude and ii) the
"directionality" of the stochastic motions (e.g. isotropic turbulence or
predominantly radial gas motions). If the width of several lines,
characteristic for different gas temperatures, can be measured, then it should
be possible to probe both the "directionality" and the amplitude of the gas
motions. Moreover a measurement of the width would put a lower limit on the
amount of the kinetic energy available for dissipation, giving a constraint on
the ICM models.
