Entropy of The Mixture Probability as Indicator of Population Discontinuities: MEMPHIS Algorithm

The full space motions of a stellar sample obtained from Hipparcos catalogue are used to discriminate statistical behaviours that are associated with local stellar populations. A sampling parameter is used to build a hierarchical set of nested samples, where a discontinuous pattern, based in a partition introduced by two normal distributions, scans the subsamples. Two quantities inform whether any subsample fits properly into the discontinuous model. A test measures the gaussianity of both components, and the entropy of the mixture probability gives account of how informative the resulting segregation is. The less informative partition is the one with maximum population entropy, which provides most representative kinematic parameters. Each new population merged to the cumulative subsample produces a discontinuity in the plot entropy versus sampling parameter, that allows to determine the number of populations contained in the whole sample. The algorithm has been named Maximum Entropy of the Mixture Probability from HIerarchical Segregation (MEMPHIS). The entropy variations and the behaviour of the segregation algorithm are illustrated through synthetic samples from Monte Carlo simulations. For Hipparcos sample, two main gaussian kinematic components are detected, thin and thick disk, with respective velocity dispersions (28 ± 1, 16 ± 2, 13 ± 1) and (65 ± 2, 39 ± 9, 41 ± 2) Km/s. The core of the thin disk is composed of two discrete non-gaussian subcomponents, early-type and young disk stars, as well as a continuous old disk population that is mixed with the foregoing subcomponents. Older thin disk stars have a velocity dispersion overlapping a wing of the thick disk. Although they could appear as an intermediate continuous population, nested subsamples distributions allow us to conclude that they definitively belong to the thin disk, and that a clear discontinuity detaches thick from thin disk.