Fugitive stars in active galaxies

Abstract: We investigate in detail the escape dynamics in an analytical gravitational model which describes the motion of stars in a quasar galaxy with a disk and a massive nucleus. We conduct a thorough numerical analysis distinguishing between regular and chaotic orbits as well as between trapped and escaping orbits, considering only unbounded motion for several energy levels. In order to distinguish safely and with certainty between ordered and chaotic motion we apply the Smaller ALingment Index (SALI) method. It is of particular interest to locate the escape basins through the openings around the collinear Lagrangian points $L_1$ and $L_2$ and relate them with the corresponding spatial distribution of the escape times of the orbits. Our exploration takes place both in the configuration $(x,y)$ and in the phase $(x,\dot{x})$ space in order to elucidate the escape process as well as the overall orbital properties of the galactic system. Our numerical analysis reveals the strong dependence of the properties of the considered escape basins with the total orbital energy, with a remarkable presence of fractal basin boundaries along all the escape regimes. We hope our outcomes to be useful for a further understanding of the escape mechanism in active galaxy models.