A SELF-CONSISTENT MODEL OF THE SPIRAL STRUCTURE OF THE GALAXY

We investigate the stable orbits of stars in the disc of the Galaxy, u sing a gravitational potential based on a model of mass distribution w hich fits the rotation curve and agrees with recent star count models. In order to verify the stability of the spiral pattern, we look for s elf-consistent solutions; we impose a spiral perturbation to the poten tial, and then we examine the resulting perturbation in the density di stribution. We find that a superposition of a 2- and of a 4-arms compo nent, with a pitch angle of about 14 degrees, is a self-consistent sol ution. This model is consistent with the observed directions of maximu m density of spiral arm tracers, interpreted as directions tangential to the spiral arms. We discuss observational evidence that the rotatio n speed of the spiral pattern is about 20 km s(-1) kpc(-1), close to t he rotation speed of the bulge, recently determined by Ibata & Gilmore . As a consequence, the corotation radius is about 9 kpc and the 4/1 r esonance at 6 kpc (the adopted solar radius is 7.9 kpc). With the adop ted pattern rotation speed, the model predicts a range of Galactic rad ii for the spiral structure, between the internal and the external Lin dblad resonances, at 2.8 and 12.8 kpc respectively, similar to the obs erved range. The model predicts the existence of negative radial veloc ities of the same order as the observed ones in directions close to th e Galactic Centre, and is able to reproduce a number of features of th e rotation curve. The 'stable-orbits' approach that we use seems promi sing to explain the existence of short arms like the local arm (or Ori on 'spur'), and of bifurcations. According to our model, the Milky Way looks like the 4-arms galaxy M101.