The spatial evolution of young massive clusters III. Effect of the Gaia filter on 2D spatial distribution studies

Context. With the third release of the high-precision optical-wavelength Gaia survey, we are in a better position than ever before to study young clusters. However, Gaia is limited in the optical down to G ∼ 21 mag, and therefore 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%