3D stellar motion in the axisymmetric Galactic potential and the e-z resonances

Résumé : The full phase space information on the kinematics of a huge number of stars provided by the Gaia third Data Release raises the demand for a better understanding of the 3D stellar dynamics. In this paper, we investigate the possible regimes of motion of stars in the axisymmetric approximation of a Galactic potential model. The model consists of three components: the axisymmetric disk, the central spheroidal bulge and the spherical halo of dark matter. The axisymmetric disk is divided into stellar and gaseous disk subcomponents, each one modeled by three Miyamoto-Nagai profiles. The physical and structural parameters of the Galaxy components are adjusted by observational kinematic constraints. The phase space of the two-degrees-of-freedom model is studied by means of the Poincar\'e and dynamical mapping, the dynamical spectrum method and the direct numerical integrations of the Hamiltonian equations of motion. For the chosen physical parameters, the nearly-circular and low-altitude stellar behaviour is composed of two weakly coupled simple oscillations, radial and vertical motions. The amplitudes of the vertical oscillations of these orbits are gradually increasing with the growing Galactocentric distances, in concordance with the exponential mass decay assumed. However, for increasing planar eccentricities and the altitudes over the equatorial disk, new regimes of stellar motion emerge as a result of the beating between the radial and vertical oscillation frequencies, which we refer to as e-z resonances. The corresponding resonant motion produces characteristic sudden increase or decrease of the amplitude of the vertical oscillation, bifurcations in the dynamical spectra and the chains of islands of stable motion in the phase space. The results obtained can be useful in the understanding and interpretation of the features observed in the stellar 3D distribution around the Sun.