S2D2: Small-scale Significant substructure DBSCAN Detection II. Tracing episodes and gradients of star formation activity

We provide the community with a homogeneous catalogue of small, significant substructures (henceforth NESTs) extracted from the spatial distribution of Young Stellar Objects (YSOs) in a large, consistent sample of star-forming regions. The catalog allows us to explore the relevance of small scale spatial substructure and discuss the interpretation of NESTs as tracers of star formation activity and remnants of the star formation process. We apply our procedure to consistent catalogues of YSOs to obtain NESTs in a sample of star-forming regions. We apply a photometric classification scheme to obtain the evolutionary stage of YSOs and statistically explore the distribution of class 0/I objects as a proxy of recent star formation activity. The region sample is diverse (in distance, size, structure, and global evolutionary stage), and we consequently find different structural properties and star formation histories. Most NESTs in regions with high recent star formation activity show even higher levels of activity. Moreover, the proportion of NESTs with higher activity than the region average increases with the global level of activity of the region. In approximately half of the regions we also find significant spans in the evolutionary stages of the NESTs, consistent with gradients and episodes of star formation. The combination of NESTs with a statistical exploration of the star formation history within each region provides robust and powerful insights into the star formation process. Our results support the role of NESTs as pristine remnants of star formation in highly active regions,stressing the role of fragmentation. The combination of small structures with large scale spatio-evolutionary patterns suggests hyerarchical, prolonged, dynamic, and complex star formation scenarios.