Disk populations from HIPPARCOS kinematic data

Discontinuities in the local velocity distribution

Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, 08034-Barcelona, Catalonia, Spain e-mail: rcubarsi@mat.upc.es

Received: 3 June 2005
Accepted: 26 July 2005

Abstract

The full space motions – including radial velocities – of a stellar sample drawn from HIPPARCOS catalogue are used to discriminate differentiated statistical behaviours that are associated with stellar populations in the solar neighbourhood. 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 resulting method has been named MEMPHIS, Maximum Entropy of the Mixture Probability from HIerarchical Segregation. 
In addition to both main kinematic components, thin and thick disk, with respective velocity dispersions and  km s^-1, two discrete non-Gaussian subcomponents are detected within the thin disk. These populations are identified with early-type and young disk stars. Moreover, a continuous old disk population is mixed with the foregoing subcomponents composing all together the thin disk. Older thin disk stars have a velocity dispersion overlapping a wing of the thick disk. Although they could appear like 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. Almost the same qualitative results, but with less accuracy, are obtained whether MEMPHIS is applied to subsamples from the Third Catalogue of Nearby Stars (CNS3). 
A dynamic model according to Chandrasekhar's approximation, under particular symmetry hypotheses, allows to interpret the results. The non-vanishing vertex deviation – lower for older stars – of all Galactic components is suggesting that, at least, point-axial symmetry is required in order to explain the local kinematic behaviour. According to this model, the oldest thick disk population, with no net radial movement, can be extrapolated, having heliocentric velocities of  km s^-1 in rotation, and  km s^-1 in the radial direction. Early-type stars show a worthy local singularity, nearly with no net radial motion, similarly to the oldest thick disk stars. Older populations – half of the thin disk and the whole thick disk – share a common differential galactic movement, suggesting a common dynamical origin for the rupture of the axial symmetry.
The relationship between the maximum stellar velocity of a sample and its average age τ is discussed, finding an approximate relation . Local stellar populations can be described from a Titius-Bode-like law for the radial velocity dispersion, , so that for natural values it determines average energy levels of discrete populations, while for continuous intervals and it describes the velocity-age evolution of thin and thick disk components, according to .