The spatial evolution of young massive clusters. I. A new tool to quantitatively trace stellar clustering

Context. There are a number of methods that identify stellar sub-structure in star forming regions, but these do not quantify the degree of association of individual stars - something which is required if we are to better understand the mechanisms and physical processes that dictate structure.
Aims: We present the new novel statistical clustering tool "INDICATE" which assesses and quantifies the degree of spatial clustering of each object in a dataset, discuss its applications as a tracer of morphological stellar features in star forming regions, and to look for these features in the Carina Nebula (NGC 3372).
Methods: We employ a nearest neighbour approach to quantitatively compare the spatial distribution in the local neighbourhood of an object with that expected in an evenly spaced uniform (i.e. definitively non-clustered) field. Each object is assigned a clustering index ("I") value, which is a quantitative measure of its clustering tendency. We have calibrated our tool against random distributions to aid interpretation and identification of significant I values.
Results: Using INDICATE we successfully recover known stellar structure of the Carina Nebula, including the young Trumpler 14-16, Treasure Chest and Bochum 11 clusters. Four sub-clusters contain no, or very few, stars with a degree of association above random which suggests these sub-clusters may be fluctuations in the field rather than real clusters. In addition we find: (1) Stars in the NW and SE regions have significantly different clustering tendencies, which is reflective of differences in the apparent star formation activity in these regions. Further study is required to ascertain the physical origin of the difference; (2) The different clustering properties between the NW and SE regions are also seen for OB stars and are even more pronounced; (3) There are no signatures of classical mass segregation present in the SE region - massive stars here are not spatially concentrated together above random; (4) Stellar concentrations are more frequent around massive stars than typical for the general population, particularly in the Tr14 cluster; (5) There is a relation between the concentration of OB stars and the concentration of (lower mass) stars around OB stars in the centrally concentrated Tr14 and Tr15, but no such relation exists in Tr16. We conclude this is due to the highly sub-structured nature of Tr16.
Conclusions: INDICATE is a powerful new tool employing a novel approach to quantify the clustering tendencies of individual objects in a dataset within a user-defined parameter space. As such it can be used in a wide array of data analysis applications. In this paper we have discussed and demonstrated its application to trace morphological features of young massive clusters.