UPMASK: unsupervised photometric membership assignment in stellar clusters

Abstract: We develop a method for membership assignment in stellar clusters using only photometry and positions. The method, UPMASK, is aimed to be unsupervised, data driven, model free, and to rely on as few assumptions as possible. It is based on an iterative process, principal component analysis, clustering algorithm, and kernel density estimations. Moreover, it is able to take into account arbitrary error models. An implementation in R was tested on simulated clusters that covered a broad range of ages, masses, distances, reddenings, and also on real data of cluster fields. Running UPMASK on simulations showed that it effectively separates cluster and field populations. The overall spatial structure and distribution of cluster member stars in the colour-magnitude diagram were recovered under a broad variety of conditions. For a set of 360 simulations, the resulting true positive rates (a measurement of purity) and member recovery rates (a measurement of completeness) at the 90% membership probability level reached high values for a range of open cluster ages ($10^{7.1}-10^{9.5}$ yr), initial masses ($0.5-10\times10^3$M$_{\sun}$) and heliocentric distances ($0.5-4.0$ kpc). UPMASK was also tested on real data from the fields of the open cluster Haffner~16 and of the closely projected clusters Haffner~10 and Czernik~29. These tests showed that even for moderate variable extinction and cluster superposition, the method yielded useful cluster membership probabilities and provided some insight into their stellar contents. The UPMASK implementation will be available at the CRAN archive.