S2D2: Small-scale Significant substructure DBSCAN Detection: I. NESTs detection in 2D star-forming regions

International audienceContext. The spatial and dynamical structure of star-forming regions can offer insights into stellar formation patterns. The amount of data from current and upcoming surveys calls for robust and objective procedures for detecting structures in order to statistically analyse the various regions and compare them.Aims. We aim to provide the community with a tool capable of detecting, above random expectations, the small-scale significant structure in star-forming regions that could serve as an imprint of the stellar formation process. The tool makes use of the one-point correlation function to determine an appropriate length scale for ϵ and uses nearest-neighbour statistics to determine a minimum number of points Nmin for the DBSCAN algorithm in the neighbourhood of ϵ.Methods. We implemented the procedure and applied it to synthetic star-forming regions of different nature and characteristics to obtain its applicability range. We also applied the method to observed star-forming regions to demonstrate its performance in realistic circumstances and to analyse its results.Results. The procedure successfully detects significant small-scale substructures in heterogeneous regions, fulfilling the goals it was designed for and providing very reliable structures. The analysis of regions close to complete spatial randomness (Q ∈ [0.7, 0.87]) shows that even when some structure is present and recovered, it is hardly distinguishable from spurious detection in homogeneous regions due to projection effects. Thus, any interpretation should be done with care. For concentrated regions, we detect a main structure surrounded by smaller ones, corresponding to the core plus some Poisson fluctuations around it. We argue that these structures do not correspond to the small compact regions we are looking for. In some realistic cases, a more complete hierarchical, multi-scale analysis would be needed to capture the complexity of the region.Conclusions. We carried out implementations of our procedure and devised a catalogue of the Nested Elementary STructures (NESTs) detected as a result in four star-forming regions (Taurus, IC 348, Upper Scorpius, and Carina). This catalogue is being made publicly available to the community. Implementations of the 3D versionsof the procedure, as well as up to 6D versions, including proper movements, are in progress and will be provided in a future work