Cluster membership probabilities from proper motions and multi-wavelength photometric catalogues

Abstract

Context. With the advent of deep wide surveys, large photometric and astrometric catalogues of literally all nearby clusters and associations have been produced. The unprecedented accuracy and sensitivity of these data sets and their broad spatial, temporal and wavelength coverage make obsolete the classical membership selection methods that were based on a handful of colours and luminosities. We present a new technique designed to take full advantage of the high dimensionality (photometric, astrometric, temporal) of such a survey to derive self-consistent and robust membership probabilities of the Pleiades cluster. Aims. We aim at developing a methodology to infer membership probabilities to the Pleiades cluster from the DANCe multidimensional astro-photometric data set in a consistent way throughout the entire derivation. The determination of the membership probabilities has to be applicable to censored data and must incorporate the measurement uncertainties into the inference procedure. Methods. We use Bayes' theorem and a curvilinear forward model for the likelihood of the measurements of cluster members in the colour-magnitude space, to infer posterior membership probabilities. The distribution of the cluster members proper motions and the distribution of contaminants in the full multidimensional astro-photometric space is modelled with a mixture-of-Gaussians likelihood. Results. We analyse several representation spaces composed of the proper motions plus a subset of the available magnitudes and colour indices. We select two prominent representation spaces composed of variables selected using feature relevance determination techniques based in Random Forests, and analyse the resulting samples of high probability candidates. We consistently find lists of high probability (p > 0.9975) candidates with ≈1000 sources, 4 to 5 times more than obtained in the most recent astro-photometric studies of the cluster. Conclusions. Multidimensional data sets require statistically sound multivariate analysis techniques to fully exploit their scientific information content. Proper motions in particular are, as expected, critical for the correct separation of contaminants. The methodology presented here is ready for application in data sets that include more dimensions, such as radial and/or rotational velocities, spectral indices, and variability.

ASteCA: Automated Stellar Cluster Analysis

“…Techniques making use of PMs go back to the Vasilevskis-Sanders (V-S) method (Vasilevskis et al 1958;Sanders 1971), which modeled cluster and field stars as a bi-variate Gaussian distributions in the vector point diagram (VPD) solving iteratively the resulting likelihood equation. The original method has been largely improved since and is present in numerous works (Stetson 1980;Zhao & He 1990;Kozhurina-Platais et al 1995;Wu et al 2002;Balaguer-Nunez et al 2004;Javakhishvili et al 2006;Frinchaboy & Majewski 2008;Krone-Martins et al 2010;Sarro et al 2014).…”

Orion revisited

“…In this study, we selected members using a novel multidimensional probabilistic analysis using carefully selected color-magnitude diagrams and luminosities. The method is described in detail in Sarro et al (2014). Briefly, an initial training set is obtained through the following steps.…”

Messier 35 (NGC 2168) DANCe

“…We use the method described in Sarro et al (2014) to derive membership probabilities of all the sources. Briefly, the method uses a training set -in this case the sample of candidate members from Barrado y Navascués et al (2001) -to identify the features that most efficiently separate the cluster's population from the field and background population among all combinations of proper motion, luminosities and colors available.…”