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Resonant Trapping in the Galactic Disc and Halo and its Relation with Moving Groups

With the use of a detailed Milky Way nonaxisymmetric potential, observationally and dynamically constrained, the effects of the bar and the spiral arms in the Galaxy are studied in the disc and in the stellar halo. Especially the trapping of stars in the disc and Galactic halo by resonances on the Galactic plane, induced by the Galactic bar, has been analysed in detail. To this purpose, a new method is presented to delineate the trapping regions using empirical diagrams of some orbital properties obtained in the Galactic potential. In these diagrams we plot in the inertial Galactic frame a characteristic orbital energy versus a characteristic orbital angular momentum, or versus the orbital Jacobi constant in the reference frame of the bar, when this is the only nonaxisymmetric component in the Galactic potential. With these diagrams some trapping regions are obtained in the disc and halo using a sample of disc stars and halo stars in the solar neighbourhood. We compute several families of periodic orbits on the Galactic plane, some associated with this resonant trapping. In particular, we find that the trapping effect of these resonances on the Galactic plane can extend several kpc from this plane, trapping stars in the Galactic halo. The purpose of our analysis is to investigate if the trapping regions contain some known moving groups in our Galaxy. We have applied our method to the Kapteyn group, a moving group in the halo, and we have found that this group appears not to be associated with a particular resonance on the Galactic plane.