Exploring the nature of orbits in a galactic model with a massive
  nucleus
  In the present article, we use an axially symmetric galactic gravitational
model with a disk-halo and a spherical nucleus, in order to investigate the
transition from regular to chaotic motion for stars moving in the meridian
(r,z) plane. We study in detail the transition from regular to chaotic motion,
in two different cases: the time independent model and the time evolving model.
In the time dependent model, we follow the evolution of orbits as the galaxy
develops a dense and massive nucleus in its core, as mass is transported
exponentially from the disk to the galactic center. In addition, we construct
some numerical diagrams in which we present the correlations between the main
parameters of our galactic model. Our numerical calculations indicate, that
stars with values of angular momentum Lz less than or equal to a critical value
Lzc, moving near to the galactic plane, are scattered to the halo upon
encountering the nuclear region and subsequently display chaotic motion. A
linear relationship exists between the critical value of the angular momentum
Lzc and the mass of the nucleus Mn. Furthermore, the extent of the chaotic
region increases as the value of the mass of the nucleus increases. Moreover,
our simulations indicate that the degree of chaos increases linearly, as the
mass of the nucleus increases. These results strongly indicate that the ordered
or chaotic nature of orbits, depends on the presence of massive objects in the
galactic cores of the galaxies. Our results suggest, that for disk galaxies
with massive and prominent nuclei, the low angular momentum stars in the
associated central regions of the galaxy, must be in predominantly chaotic
orbits. Some theoretical arguments to support the numerically derived outcomes
are presented. Comparison with similar previous works is also made.
