The Spatial Evolution of Young Massive Clusters II. Looking for Imprints
  of Star Formation in NGC 2264 with Gaia DR2
  Aims. To demonstrate that `INDICATE' is a powerful spatial analysis tool
which when combined with kinematic data from Gaia DR2 can be used to robustly
probe star formation history.
  Methods. We compared the dynamic & 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 & 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 0.05deg 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 robustly study the star formation history of a cluster.
