Dynamical characterization of galaxies up to $z \sim 7$
  The characterization of the dynamical state of galaxies up to z~7 is crucial
for constraining the mechanisms driving the mass assembly in the early
Universe. However, it is unclear whether the data quality of current and future
observations is sufficient to perform a solid dynamical analysis. This paper
defines the angular resolution and S/N required for a robust characterization
of the dynamical state of galaxies up to the EoR. The final aim is to help
design spatially-resolved surveys targeting emission lines of primeval
galaxies. We investigate the [CII]-158um emission from z~6-7 LBGs from the
SERRA cosmological simulation, covering a range of dynamical states: from disks
to major mergers. We create ALMA mock observations with various data quality
and apply the kinematic classification methods used in the literature. These
tests allow us to quantify the performances of such methods as a function of
angular resolution and S/N. We find that barely-resolved observations do not
allow the correct dynamical characterization of a galaxy, resulting in the
misclassification of all disks in our sample. However, even when using
spatially-resolved observations with data quality typical of high-z galaxies,
the standard kinematic classification methods, based on the analysis of the
moment maps, fail to distinguish a merger from a disk. The high angular
resolution and S/N needed to apply these standard methods successfully can be
achieved with current data only for a handful of bright galaxies. We propose a
new classification method, called PVsplit, that quantifies the asymmetries and
morphological features in position-velocity diagrams using three empirical
parameters. We test PVsplit on our mock data concluding that it can predict
whether a galaxy is a disk or a merger provided that S/N $\gtrsim10$, and the
major axis is covered by $\gtrsim3$ independent resolution elements.
