Structure of the velocity distribution of the Galactic disc. A maximum entropy statistical approach - Part I

The maximum entropy approach is proposed to describe the local structures of the velocity distribution, which are collected through its sample moments. The method is used with several samples from the HIPPARCOS and Geneva-Copenhagen survey catalogues. For the large-scale distribution, the phase density function may be obtained by fitting moments up to sixth order as a product of two exponential functions, one giving a background ellipsoidal shape of the distribution and the other accounting for the skewness and for the slight shift in the ellipsoidal isocontours in terms of the rotation velocity. The small-scale distribution can be deduced from truncated distributions, such as velocity-bounded samples with |V| ≤ 51 km s, which contain a complex mixture of early-type and young disc stars. By fitting up to ten-order moments, the maximum entropy approach gives a realistic portrait of actual asymmetries, showing a clear bimodal pattern: (i) around the Hyades-Pleiades stream, with negative radial mean velocity and (ii) around the Sirius-UMa stream, with slightly positive radial mean velocity. The “U-anomaly” along the radial direction is estimated straightforwardly 30− 35 km s from the contour plots.