Order and Chaos in a Three-dimensional Binary System of Interacting
  Galaxies
  In the present article, we present a galactic gravitational model of three
degrees of freedom, in order to investigate and reveal the behavior of orbits
in a binary quasar system. The two quasars are hosted in a pair of interacting
disk galaxies. We study in detail the regular or chaotic character of motion,
in two different cases: the time independent model in both 2D and 3D dynamical
systems and the evolving 3D model. Our numerical calculations, indicate that a
large fraction of orbits in the 2D system are chaotic in the time independent
case. A careful analysis suggest that several Lindblad resonances are also
responsible for the chaotic motion of stars in both hosts galaxies. In the time
dependent system, we follow the evolution of 3D orbits in our dynamical model,
as the two interacting host galaxies develop dense and massive quasars in their
cores, by mass transportation from the disks to their nuclei. In this
interesting case, there are orbits that change their orbital character from
regular to chaotic and vise versa and also orbits that maintain their character
during the galactic evolution. These results strongly indicate that the ordered
or chaotic nature of 3D orbits depends, not only in the galactic interaction
but also in the presence of the quasars in the galactic cores of the host
galaxies. The outcomes derived from our dynamical model are compared with
observational data. Some theoretical arguments to support the numerically
derived outcomes are presented, both in 2D and 3D systems, while a comparison
with similar earlier work is also made.
