Nonlinear Effects in Models of the Galaxy. I. Midplane Stellar Orbits in the Presence of Three-dimensional Spiral Arms

With the aim of studying the nonlinear stellar and gaseous response to the gravitational potential of a galaxy such as the Milky Way, we have modeled three-dimensional Galactic spiral arms as a superposition of inhomogeneous oblate spheroids and added their contribution to an axisymmetric model of the Galactic mass distribution. Three spiral loci are proposed here, based in different sets of observations. A comparison of our model with a tight-winding approximation shows important differences in the middle and outer Galactic regions. A preliminary self-consistency analysis taking (omega)p = 15 and 20 km s^-1 kpc^-1 for the angular speed of the spiral pattern seems to favor the value (omega)p = 20 km s^-1 kpc^-1. As a first step to the full threedimensional calculations for which the model is suitable, we have explored the stellar orbital structure in the midplane of the Galaxy. We present the standard analysis in the pattern rotating frame and complement this analysis with orbital information from the Galactic inertial frame. Prograde and retrograde orbits are defined unambiguously in the inertial frame, then labeled as such in the Poincaré diagrams of the noninertial frame. In this manner, we found a sharp separatrix between the two classes of orbits. Chaos is restricted to the prograde orbits, and its onset occurs for the higher spiral perturbation considered plausible in our Galaxy. An unrealistically high spiral perturbation tends to destroy the separatrix and make chaos pervasive. This might be relevant in other spiral galaxies.