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Abstract:

An extension of Schwarzschild's galaxy-building technique is presented that, for the first time, enables one to build Schwarzschild models with known distribution functions (DFs). The new extension makes it possible to combine a DF that depends only on classical integrals with orbits that respect non-classical integrals. With such a combination, Schwarzschild's orbits are used only to represent the difference between the true galaxy DF and an approximating classical DF. The new method is used to construct a dynamical model of the inner Galaxy. The model is based on an orbit library that contains 22168 regular orbits. The model aims to reproduce the three-dimensional mass density of Binney, Gerhard & Spergel (1997), which was obtained through deprojection of the COBE surface photometry, and to reproduce the observed kinematics in three windows - namely Baade's Window and two off-axis fields. The model fits essentially all the available data within the innermost 3 kpc. The axis ratio and the morphology of the projected density contours of the COBE bar are recovered to good accuracy within corotation. The kinematic quantities - the line-of-sight streaming velocity and velocity dispersion, as well as the proper motions when available - are recovered, not merely for the fitted fields, but also for three new fields. The dynamical model deviates most from the input density close to the Galactic plane just outside corotation, where the deprojection of the surface photometry is suspect. The dynamical model does not reproduce the kinematics at the most distant window, where disk contamination may be severe.

Abstract:

The Hipparcos mission has prompted a thorough reanalysis of the kinematics of the Solar neighborhood. Reliable proper motions are now available for a photometrically complete sample of similar to 10(6) stars, but the largest complete sample of stars with good parallaxes contains only similar to 10(4) stars. The latter sample yields precise values for the first and second moments of near main-sequence stars as a function of color. The effects of the secular increase in velocity dispersion are very evident. From these moments one can redetermine the velocity of the LSR and the age of the Solar neighborhood rather precisely. One can also determine how the density of stars in velocity space varies in the neighborhood of the LSR. This density distribution proves to be significantly more complex than the Schwarzschild distribution and may be affected by the Galactic bar. The larger sample for which only proper motions can be obtained allows one to probe gradients in the large-scale streaming motions that the Oort constants aim to describe. Here again the data imply a significantly more complex situation than has been considered previously. It is probable that these complexities are in part caused by spiral arms and/or the central Galactic bar.