A self-consistent model of the spiral structure of the galaxy

We investigate the stable orbits of stars in the disc of the Galaxy, using a gravitational potential based on a model of mass distribution which fits the rotation curve and agrees with recent star count models. In order to verify the stability of the spiral pattern, we look for self-consistent solutions; we impose a spiral perturbation to the potential, and then we examine the resulting perturbation in the density distribution. We find that a superposition of a 2- and of a 4-arms component, with a pitch angle of about 14 degrees, is a self-consistent solution. This model is consistent with the observed directions of maximum density of spiral arm tracers, interpreted as directions tangential to the spiral arms. We discuss observational evidence that the rotation speed of the spiral pattern is about 20 km s(-1) kpc(-1), close to the rotation speed of the bulge, recently determined by Ibata & Gilmore. As a consequence, the corotation radius is about 9 kpc and the 4/1 resonance at 6 kpc (the adopted solar radius is 7.9 kpc). With the adopted pattern rotation speed, the model predicts a range of Galactic radii for the spiral structure, between the internal and the external Lindblad resonances, at 2.8 and 12.8 kpc respectively, similar to the observed range. The model predicts the existence of negative radial velocities of the same order as the observed ones in directions close to the Galactic Centre, and is able to reproduce a number of features of the rotation curve. The 'stable-orbits' approach that we use seems promising to explain the existence of short arms like the local arm (or Orion 'spur'), and of bifurcations. According to our model, the Milky Way looks like the 4-arms galaxy M101.