A new model for gravitational potential perturbations in disks of spiral galaxies. An application to our Galaxy

Abstract: We propose a new, more realistic, description of the perturbed gravitational potential of spiral galaxies, with spiral arms having Gaussian-shaped groove profiles. We investigate the stable stellar orbits in galactic disks, using the new perturbed potential. The influence of the bulge mass on the stellar orbits in the inner regions of a disk is also investigated. The new description offers the advantage of easy control of the parameters of the Gaussian profile of its potential. We find a range of values for the perturbation amplitude from 400 to 800 km^2 s^{-2} kpc^{-1} which implies a maximum ratio of the tangential force to the axisymmetric force between 3% and 6%, approximately. Good self-consistency of arm shapes is obtained between the Inner Lindblad resonance (ILR) and the 4:1 resonance. Near the 4:1 resonance the response density starts to deviate from the imposed logarithmic spiral form. This creates bifurcations that appear as short arms. Therefore the deviation from a perfect logarithmic spiral in galaxies can be understood as a natural effect of the 4:1 resonance. Beyond the 4:1 resonance we find closed orbits which have similarities with the arms observed in our Galaxy. In regions near the center, in the presence of a massive bulge, elongated stellar orbits appear naturally, without imposing any bar-shaped potential, but only extending the spiral perturbation a little inward of the ILR. This suggests that a bar is formed with a half-size around 3 kpc by a mechanism similar to that of the spiral arms. The potential energy perturbation that we adopted represents an important step in the direction of self-consistency, compared to previous sine function descriptions of the potential. Our model produces a realistic description of the spiral structure, able to explain several details that were not yet understood.