The seven sisters DANCe

IV. Bayesian hierarchical model^⋆

¹ Departamento de Inteligencia Artificial, UNED, Juan del Rosal 16, 28040 Madrid, Spain
e-mail: lsb@dia.uned.es
² Université Grenoble-Alpes, CNRS, IPAG, 38000 Grenoble, France
³ Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Allée Geoffroy Saint-Hilaire, 33615 Pessac, France
⁴ Dpt. Statistics and Operations Research, University of Cádiz, Campus Universitario Río San Pedro s/n., 11510 Puerto Real, Cádiz, Spain
⁵ Departamento Astrofísica, Centro de Astrobiología (INTA-CSIC), ESAC campus, PO Box 78, 28691 Villanueva de la Cañada, Spain
⁶ Institut d’Astrophysique de Paris, CNRS UMR 7095 and UPMC, 98bis Bd Arago, 75014 Paris, France
⁷ Instituto de Astronomia, Geofísica e Ciências Atmosféricas, Universidade de São Paulo, Rua do Matão, 1226, Cidade Universitária, 05508-900, São Paulo, Brazil

Received: 11 April 2017
Accepted: 23 April 2018

Abstract

Context. The photometric and astrometric measurements of the Pleiades DANCe DR2 survey provide an excellent test case for the benchmarking of statistical tools aiming at the disentanglement and characterisation of nearby young open cluster (NYOC) stellar populations.

Aims. We aim to develop, test, and characterise of a new statistical tool (intelligent system) for the sifting and analysis of NYOC populations.

Methods. Using a Bayesian formalism, with this statistical tool we were able to obtain the posterior distributions of parameters governing the cluster model. It also used hierarchical bayesian models to establish weakly informative priors, and incorporates the treatment of missing values and non-homogeneous (heteroscedastic) observational uncertainties.

Results. From simulations, we estimated that this statistical tool renders kinematic (proper motion) and photometric (luminosity) distributions of the cluster population with a contamination rate of 5.8 ± 0.2%. The luminosity distributions and present day mass function agree with the ones found in a recent study, on the completeness interval of the survey. At the probability threshold of maximum accuracy, the classifier recovers ≈90% of the recently published candidate members and finds 10% of new ones.

Conclusions. A new statistical tool for the analysis of NYOC is introduced, tested, and characterised. Its comprehensive modelling of the data properties allows it to get rid of the biases present in previous works. In particular, those resulting from the use of only completely observed (non-missing) data and the assumption of homoskedastic uncertainties. Also, its Bayesian framework allows it to properly propagate observational uncertainties into membership probabilities and cluster velocity and luminosity distributions. Our results are in a general agreement with those from the literature, although we provide the most up-to-date and extended list of candidate members of the Pleiades cluster.