The structure and stability of orbits in Hoag-like ring systems
  Ring galaxies are amazing objects exemplified by the famous case of the
Hoag's Object. Here the mass of the central galaxy may be comparable to the
mass of the ring, making it a difficult case to model mechanically. In a
previous paper, it was shown that the outer potential of a torus (ring) can be
represented with good accuracy by the potential of a massive circle with the
same mass. This approach allows us to simplify the problem of the particle
motion in the gravitational field of a torus associated with a central mass by
replacing the torus with a massive circle. In such a system there is a circle
of unstable equilibrium that we call "Lagrangian circle" (LC). Stable circular
orbits exist only in some region limited by the last possible circular orbit
related to the disappearance of the extrema of the effective potential. We call
this orbit "the outermost stable circular orbit" (OSCO) by analogy with the
innermost stable circular orbit (ISCO) in the relativistic case of a black
hole. Under these conditions, there is a region between OSCO and LC where the
circular motion is not possible due to the competition between the
gravitational forces by the central mass and the ring. As a result, a gap in
the matter distribution can form in Hoag-like system with massive rings.
