The spatial evolution of young massive clusters II. Looking for imprints of star formation in NGC 2264 with Gaia DR2

Context. Better understanding of star formation in clusters with high-mass stars requires rigorous dynamical and spatial analyses of star-forming regions. Aims. We seek to demonstrate that "INDICATE" is a powerful spatial analysis tool which when combined with kinematic data from Gaia DR2 can be used to probe star formation history in a robust way. Methods. We compared the dynamic and spatial distributions of young stellar objects (YSOs) at various evolutionary stages in NGC 2264 using Gaia DR2 proper motion data and INDICATE. Results. The dynamic and spatial behaviours of YSOs at different evolutionary stages are distinct. Dynamically, Class II YSOs predominately have non-random trajectories that are consistent with known substructures, whereas Class III YSOs have random trajectories with no clear expansion or contraction patterns. Spatially, there is a correlation between the evolutionary stage and source concentration: 69.4% of Class 0/I, 27.9% of Class II, and 7.7% of Class III objects are found to be clustered. The proportion of YSOs clustered with objects of the same class also follows this trend. Class 0/I objects are both found to be more tightly clustered with the general populous/objects of the same class than Class IIs and IIIs by a factor of 1.2/4.1 and 1.9/6.6, respectively. An exception to these findings is within 0.05 degrees of S Mon where Class III objects mimic the behaviours of Class II sources across the wider cluster region. Our results suggest (i) current YSOs distributions are a result of dynamical evolution, (ii) prolonged star formation has been occurring sequentially, and (iii) stellar feedback from S Mon is causing YSOs to appear as more evolved sources. Conclusions. Designed to provide a quantitative measure of clustering behaviours, INDICATE is a powerful tool with which to perform rigorous spatial analyses. Our findings are consistent with what is known about NGC 2264, effectively demonstrating that when combined with kinematic data from Gaia DR2 INDICATE can be used to study the star formation history of a cluster in a robust way.