Disc and halo kinematic populations from HIPPARCOS and Geneva-Copenhagen surveys of the solar neighbourhood

Discontinuities in the local velocity distribution associated with stellar populations are studied using the Maximum Entropy of the Mixture Probability from HIerarchical Segregation (MEMPHIS) improved statistical method, by combining a sampling parameter, an optimisation of the mixture approach, and a maximisation of the partition entropy for the constituent populations of the stellar sample. The sampling parameter is associated with isolating integrals of the stellar motion and is used to build a hierarchical family of subsamples. We provide an accurate characterisation of the entropy graph, in which a local maximum of entropy takes place simultaneously with a local minimum of the $\chi^2$ error. By analysing different sampling parameters, the method is applied to samples from the HIPPARCOS and Geneva-Copenhagen survey (GCS) to determine the kinematic parameters and the stellar population mixture of the thin disc, thick disc, and halo. The sampling parameter P=|(U,V,W)|, which is the absolute heliocentric velocity, allows us to build an optimal subsample containing both thin and thick disc stars, omitting most of the halo population. The sampling parameter P=|W|, which is absolute perpendicular velocity, allows us to create an optimal subsample of all disc and halo stars, although it does not allow an optimal differentiation of thin and thick discs. Other sampling parameters, such as P=|(U,W)| or P=|V|, are found to provide less information about the populations. By comparing both samples, HIPPARCOS provides more accurate estimates for the thick disc and halo, and GCS for the total disc. In particular, the radial velocity dispersion of the halo fits perfectly into the empirical Titius-Bode-like law $\sigma_{U} = 6.6 \, (\frac43)^{3n+2}$, previously proposed for discrete kinematical components, where the values n=0,1,2,3 represent early-type stars, thin disc, thick disc, and halo populations, respectively. The kinematic parameters are used to segregate thin disc, thick disc, and halo stars, and to obtain a more accurate Bayesian estimation of the population fractions. To check the reliability of our results, an alternative segregation approach is used. GCS stars are classified into different kinematical populations in terms of their orbital parameters. The population fractions and velocity moments obtained by both methods are in excellent agreement.