A dynamical model of the inner Galaxy

An extension of Schwarzschild's galaxy-building technique is presented that enables one to build Schwarzschild models with known distribution function s (DFs). The new extension makes it possible to combine a DF that depends o nly on classical integrals with orbits that respect non-classical integrals . With such a combination, Schwarzschild's orbits are used only to represen t 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 22 168 regular orbits. The model aims to reproduce the three-dimensional mass density of Binney, Gerhard & Spergel, which was obtained through deprojection of the COBE surf ace photometry, and to reproduce the observed kinematics in three windows - namely Baade's Window with (l,b)=(1 degrees,-4 degrees) and two off-axis f ields at (8 degrees, 7 degrees) and (12 degrees, 3 degrees). The viewing an gle is assumed to be 20 degrees to the long axis of the bar and the pattern speed is taken to be 60 km s(-1) kpc(-1). The model fits essentially all the available data within the innermost 3 kp c. The axial ratio and the morphology of the projected density contours of the COBE bar are recovered to excellent accuracy within corotation. The kin ematic quantities - the line-of-sight streaming velocity and velocity dispe rsion, as well as the proper motions when available - are recovered, not me rely for the fitted fields at (1 degrees, -4 degrees) and (8 degrees, 7 deg rees), but also for three new fields at (84, -6 degrees), (121, -167) and ( -114, 181). The dynamical model deviates most from the input density close to the Galactic plane just outside corotation, where the deprojection of th e surface photometry is suspect. The dynamical model does not reproduce the kinematics at the most distant window, (12 degrees, 3 degrees), where disc contamination of the data may be severe. Maps of microlensing optical depth are presented both for randomly chosen s tars and for stars that belong to individual components within the model. W hile the optical depth to a randomly chosen star in Baade's Window is half what measurements imply, the optical depth to stars in a particular compone nt can be as high as the measured values. The contributions to the optical depth towards randomly chosen stars from lenses in different components are also given.