Abstract
We present a new technique designed to take full advantage of the high dimensionality (photometric, astrometric, temporal) of the DANCe survey to derive self-consistent and robust membership probabilities of the Pleiades cluster. 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. 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. 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 $\approx$ 1000 sources, 4 to 5 times more than obtained in the most recent astro-photometric studies of the cluster. 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.
Highlights
The analysis of stellar clusters is one of the stepping stones for understanding galactic and stellar formation and evolution
We explore probabilistic models for the estimation of membership probabilities in a multidimensional data set composed of proper motions and apparent magnitudes of sources in the Pleiades cluster sky region
We modelled the distribution of examples of both members and non-members in several representation spaces discussed below
Summary
The analysis of stellar clusters is one of the stepping stones for understanding galactic and stellar formation and evolution. Kozhurina-Platais et al (1995) combined celestial coordinates with proper motions assuming conditional independency to refine their membership probabilities They followed the conceptual framework set up by the earlier works cited in the previous paragraph, based on the posterior probability density distribution of a bi-variate Gaussian mixture model. The methodologies presented far do not extend the probabilistic treatment first put forward by Vasilevskis et al (1958) and Sanders (1971) for the VPD, to extended data sets with photometric or spectrometric measurements An exception to this is the recent work by Malo et al (2013) in young stellar kinematic groups, where the authors treat the astrometric and photometric data consistently in a probabilistic framework, albeit assuming that all measurements included in the inference of membership probabilities are independent and uncorrelated.
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