The Spatial Evolution of Young Massive Clusters III. Effect of the Gaia
  Filter on 2D Spatial Distribution Studies
  [Context.] Gaia is limited in the optical down to G~21 mag so it is essential
to understand the biases introduced by a magnitude-limited sample on spatial
distribution studies. [Aims.] We ascertain how sample incompleteness in Gaia
observations of young clusters affects the local spatial analysis tool INDICATE
and subsequently the perceived spatial properties of these clusters. [Methods.]
We created a mock Gaia cluster catalogue from a synthetic dataset using the
observation generating tool MYOSOTIS. The effect of cluster distance, uniform
and variable extinction, binary fraction, population masking by the point
spread function wings of high-mass members, and contrast sensitivity limits on
the trends identified by INDICATE are explored. A comparison of the typical
index values derived by INDICATE for members of the synthetic dataset and their
corresponding mock Gaia catalogue observations is made to identify any
significant changes. [Results.] We typically find only small variations in the
pre- and post-observation index values of cluster populations, which can
increase as a function of incompleteness percentage and binarity. No
significant strengthening, or false signatures, of stellar concentrations are
found but real signatures may be diluted. Conclusions drawn about the spatial
behaviour of Gaia-observed cluster populations that are, and are not,
associated with their natal nebulosity are reliable for most clusters but the
perceived behaviours of individual members can change so INDICATE should be
used as a measure of spatial behaviours between members as a function of their
intrinsic properties (e.g. mass, age, object type), rather than to draw
conclusions about any specific observed member. [Conclusions.] INDICATE is a
robust spatial analysis tool to reliably study Gaia-observed young cluster
populations within 1 kpc, up to a sample incompleteness of 83.3% and binarity
of 50%.
