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

I. Method and application to the Pleiades cluster^⋆

¹ Dpto. de Inteligencia Artificial, ETSI Informática, UNED, Juan del Rosal, 16 28040 Madrid Spain
e-mail: lsb@dia.uned.es
² Centro de Astrobiología, depto. de Astrofísica, INTA-CSIC, PO BOX 78, ESAC Campus 28691, Villanueva de la Cañada, Madrid, Spain
³ Dpt. Statistics and Operations Research, University of Cádiz, Campus Universitario Río San Pedro s/n, 11510 Puerto Real, Cádiz, Spain
⁴ Institut d’Astrophysique de Paris, CNRS UMR 7095 and UPMC, 98bis bd Arago, 75014 Paris, France
⁵ UJF-Grenoble 1/CNRS-INSU, Institut de Planétologie et d’Astrophysique de Grenoble (IPAG), UMR 5274, 38041 Grenoble, France
⁶ Canada-France-Hawaii Telescope Corporation, 65-1238 Mamalahoa Highway, Kamuela, HI96743, USA

Received: 31 July 2013
Accepted: 21 January 2014

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.