Limiting curves in an axially symmetric galaxy

Abstract

The aim of this article is to reveal the geometry of the windows through which stars escape from a potential modeling the central part of a galaxy with axial symmetry and presenting one exit channel. This study has been performed by analyzing the ingoing and outgoing asymptotic orbits to the Lyapunov orbit located at the opening of the potential in a suitable surface of section.

Dependence of the escape from an axially symmetric galaxy on the energy

“…We analyze the motion of a particle in the ( r , z ) meridian plane near the central part of an axially symmetric galaxy modeled by a galactic type potential of the form which is made up of perturbed harmonic oscillators with frequency along the r and z axis, where r and z are cylindrical coordinates, is the perturbation strength and and are parameters 13 , 19 . The potential ( 1 ) can be derived by expanding global galactic potentials near the central stable equilibrium point of the system, located at the center of the galaxy.…”

“…Throughout this paper, we have taken the following values for the parameters: , , , and . Then, the energy of escape is given by 13 . In Fig.…”

“…For the computation of the initial part of these asymptotic curves, we follow the method suggested by Deprit and Henrard 21 . The selection of the initial conditions of these curves have been determined by following the procedure described by Navarro 13 . We have computed and integrated backward a set of initial conditions taken in the ingoing asymptotic orbits to the Lyapunov orbit, until they intersect the surface of section ( ), where is an adequate constant value.…”

“…To this end, we study the escape from a galactic model with axial symmetry. This type of galactic system has been previously studied by Zotos 19 and Navarro 12 , 13 . In a companion paper, Navarro 13 investigates the geometry of the curves that delimite the escape domains by determining the intersection of the ingoing and outgoing asymptotic trajectories to the Lyapunov orbit with an apropiate surface of section, for a fixed value of the energy.…”

“…This type of galactic system has been previously studied by Zotos 19 and Navarro 12 , 13 . In a companion paper, Navarro 13 investigates the geometry of the curves that delimite the escape domains by determining the intersection of the ingoing and outgoing asymptotic trajectories to the Lyapunov orbit with an apropiate surface of section, for a fixed value of the energy. In this paper, we describe how these limiting curves evolve as the energy of the system varies, showing that the intersection between the ingoing and outgoing asymptotic trajectories to the Lyapunov orbit takes place in a way that relies on the energy of the system.…”