Revealing the character of orbits in a binary system consisting of a
  primary galaxy and a satellite companion
  In this article, we present a galactic gravitational model of three degrees
of freedom (3D), in order to study and reveal the character of the orbits of
the stars, in a binary stellar system composed of a primary quiet or active
galaxy and a small satellite companion galaxy. Our main dynamical analysis will
be focused on the behavior of the primary galaxy. We investigate in detail the
regular or chaotic nature of motion, in two different cases: (i) the
time-independent model in both 2D and 3D dynamical systems and (ii) the
time-evolving 3D model. Our numerical calculations indicate that the percentage
of the chaotic orbits increases when the primary galaxy has a dense and massive
nucleus. The presence of the dense galactic core also increases the stellar
velocities near the center of the galaxy. Moreover, for small values of the
distance R between the two bodies, low-energy stars display chaotic motion,
near the central region of the galaxy, while for larger values of the distance
R, the motion in active galaxies is entirely regular for low-energy stars. Our
simulations suggest that in galaxies with a satellite companion, the chaotic
nature of motion is not only a result of the galactic interaction between the
primary galaxy and its companion, but also a result caused by the presence of
the dense nucleus in the core of the primary galaxy. Theoretical arguments are
presented in order to support and interpret the numerically derived outcomes.
Furthermore, we follow the 3D evolution of the primary galaxy, when mass is
transported adiabatically from the disk to the nucleus. Our numerical results
are in satisfactory agreement with observational data obtained from the
M51-type binary stellar systems. A comparison between the present research and
similar and earlier work is also made.
