Windows for escaping particles in quartic galactic potentials

Abstract

We investigate the shape of the windows through which stars may escape from a galaxy modeled by a bi–symmetrical potential made up of a two–dimensional harmonic oscillator with quartic perturbing terms. The escape from the potential well is governed by the unstable periodic orbits in the openings of the potential. The unstable and stable manifolds to these periodic orbits reveal the way test particles escape from the potential well. Our main objective is to compute accurately these manifolds to analyze the shapes and sizes of the windows of escape, founding that they consist of a “main window” and of a hierarchy of secondary spiral windows. We have also found that the shape and the way this hierarchy is constructed depend on the energy of the system. This study is performed through the analysis of intersections of stable and unstable manifolds in the x −˙x Poincaré phase plane.