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

**Authors:** Tatiana A. Michtchenko, Douglas A. Barros  
**arXiv:** [2308.14305](https://arxiv.org/abs/2308.14305)  
**Date:** 2023-08-28  
**Summary page:** https://www.summarizepaper.com/en/paper/2308.14305v1/

## Key points

- Gaia third Data Release provides information on kinematics of stars
- Study investigates motion regimes of stars in an axisymmetric Galactic potential model
- Model consists of axisymmetric disk, central spheroidal bulge, and spherical halo of dark matter
- Observational kinematic constraints used to determine physical and structural parameters
- Various methods used to study phase space of the model
- Nearly-circular and low-altitude stellar behavior consists of radial and vertical motions
- Vertical oscillation amplitudes increase with Galactocentric distances
- Planar eccentricities and altitudes lead to new regimes of stellar motion called e-z resonances
- Resonant motion leads to changes in amplitude, bifurcations in dynamical spectra, and stable motion in phase space
- Results contribute to understanding 3D distribution of stars around the Sun and 3D stellar dynamics within an axisymmetric Galactic potential model.

## Summary

The Gaia third Data Release has provided a wealth of information on the kinematics of a large number of stars, leading to an increased demand for a better understanding of 3D stellar dynamics. In this study, the authors investigate the possible motion regimes of stars in an axisymmetric Galactic potential model. The model consists of three components: an axisymmetric disk, a central spheroidal bulge, and a spherical halo of dark matter. The axisymmetric disk is further divided into stellar and gaseous subcomponents, each modeled by three Miyamoto-Nagai profiles. To determine the physical and structural parameters of the Galaxy components, observational kinematic constraints are taken into account. The phase space of the two-degrees-of-freedom model is then studied using various methods including Poincaré and dynamical mapping, dynamical spectrum analysis, and direct numerical integrations of the Hamiltonian equations of motion. For the chosen physical parameters, it is found that nearly-circular and low-altitude stellar behavior consists of two weakly coupled simple oscillations: radial and vertical motions. The amplitudes of these vertical oscillations gradually increase with growing Galactocentric distances in accordance with assumed exponential mass decay. However, as planar eccentricities and altitudes over the equatorial disk increase, new regimes of stellar motion emerge due to beating between radial and vertical oscillation frequencies. These regimes are referred to as e-z resonances. The corresponding resonant motion leads to sudden increases or decreases in the amplitude of vertical oscillation, bifurcations in dynamical spectra, and chains of islands representing stable motion in phase space. The results obtained from this study can be valuable for understanding and interpreting features observed in the 3D distribution of stars around the Sun. Additionally, they contribute to our overall understanding of 3D stellar dynamics within an axisymmetric Galactic potential model.