Escape dynamics and fractal basin boundaries in Seyfert galaxies

Abstract

The escape dynamics in a simple analytical gravitational model which describes the motion of stars in a Seyfert galaxy is investigated in detail. 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 physical (x, y) and in the phase (x,ẋ) 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. It was also observed, that for energy levels close to the critical escape energy the escape rates of orbits are large, while for much higher values of energy most of the orbits have low escape periods or they escape immediately to infinity. We also present evidence obtained through numerical simulations that our model can describe the formation and the evolution of the observed spiral structure in Seyfert galaxies. We hope our outcomes to be useful for a further understanding of the escape mechanism in galaxies with active nuclei.

Basin entropy: a new tool to analyze uncertainty in dynamical systems

“…For instance, escape basins are widely used in astronomy, as shown in recent studies on the Pluto-Charon system 27 . In these investigations it is commonly argued that basins close to the escape energy present a higher degree of fractalization 28 29 . Here we have shown an example of an open Hamiltonian system used in galactic dynamics, namely the Hénon-Heiles potential, and we have been able to quantify its uncertainty for different values of the energy.…”

Dynamical configurations of celestial systems comprised of multiple irregular bodies

“…Nonlinear dynamical behaviors in space science have been analyzed theoretically and numerically in previous studies, which include behaviors such as periodic orbits in three-dimensional (3D) potentials (Zotos and Caranicolas 2012), escape dynamics in galaxies (Zotos 2015), equilibria in binary-asteroid systems (Vera 2009a;Jacobson and Scheeres 2011) or the three body problem (Vera 2009b), stability of planetary rings (Salo and Schmidt 2010), and the instability regions of moonlets for the 2 triple-body system 87 Sylvia (Frouard et al 2012). However, most of the multiple asteroid systems in the Solar system are comprised of irregular minor bodies (Lagerros 1997;Beauvalet and Marchis 2014).…”