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

¹ Universidade de São Paulo, IAG, Rua do Matão 1226, Cidade Universitária, 05508-090 São Paulo, Brazil
e-mail: tatiana.michtchenko@iag.usp.br
² Rua Sessenta e Três 125, Olinda, 53090-393 Recife, Pernambuco, Brazil
e-mail: douglas.barros@alumni.usp.br

Received: 18 June 2023
Accepted: 27 August 2023

Abstract

Context. The full phase-space information on the kinematics of a huge number of stars provided by Gaia Data Release 3 increases the demand for a better understanding of the 3D stellar dynamics.

Aims. In this paper, we investigate the possible regimes of motion of stars in the axisymmetric approximation of the Galactic potential, applying a 3D observation-based model developed elsewhere. The model consists of three components: the axisymmetric disc, the central spheroidal bulge, and the spherical halo of dark matter. The axisymmetric disc model is divided into thin and thick stellar discs and H I and H₂ gaseous disc subcomponents, by combining three Miyamoto-Nagai disc profiles of any model order (1, 2, or 3) for each disc subcomponent, to reproduce a radially exponential mass distribution. The physical and structural parameters of the Galaxy components are adjusted by observational kinematic constraints.

Methods. The phase space of the two-degrees-of-freedom model was studied by means of the Poincaré and dynamical mapping, the dynamical spectrum method, and the direct numerical integrations of the Hamiltonian equations of motion.

Results. For the chosen physical parameters, the nearly circular (close to the rotation curve) 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 gradually increase with the growing Galactocentric distances, in concordance with the exponential mass decay assumed. However, for increasing planar eccentricities, e, and the altitudes over the equatorial disc, z, 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 the characteristic sudden increase or decrease in the amplitude of the vertical oscillation, bifurcations in the dynamical spectra, and the chains of islands of stable motion in the phase space.

Conclusions. The results obtained can be useful in understanding and interpreting the features observed in the stellar 3D distribution around the Sun.