Assessing membership projection errors in star forming regions
  Young stellar clusters harbour complex spatial structures emerging from the
star formation process. Identifying stellar over-densities is a key step to
constrain better how these structures are formed. The high accuracy of
distances derived from Gaia DR2 parallaxes yet do not allow to locate with
certainty individual stars within clusters of size $\approx 1\, \rm{pc}$. In
this work, we explore how such uncertainty in distance estimates can lead to
the misidentification of membership of sub-clusters selected by the minimum
spanning tree (MST) algorithm. Our goal is to assess how this impacts their
estimated properties. Using N-body simulations, we build Gravity-Driven
Fragmentation (GDF) models that reproduce self-consistently the early stellar
configurations of a star forming region. Stellar groups are then identified
both in 3- and 2-dimensions by the MST algorithm, representing respectively an
ideal and an inaccurate identification. We compare the properties derived of
these resulting groups, to assess the systematic bias introduced by projection
and incompleteness. We show that in such fragmented configurations, the
dynamical mass of groups identified in projection is systematically
underestimated compared to those of groups identified in 3D. This systematic
error is statistically of $50\%$ for more than half of the groups and reach
$100\%$ in a quarter of them. Adding incompleteness further increases this
bias. These results challenge our ability to identify accurately sub-clusters
in most nearby star forming regions where distance estimate uncertainties are
comparable to the size of the region. New clump finding methods have to tackle
this issue in order to define better the dynamical state of these
substructures.
