# The structure and stability of orbits in Hoag-like ring systems

## TL;DR

This paper models the gravitational dynamics of Hoag-like ring systems by simplifying the ring as a massive circle, revealing regions of stable and unstable orbits that can explain observed matter gaps.

## Contribution

It introduces a simplified potential model for ring systems and identifies key orbital regions, including the Lagrangian circle and outermost stable orbit, in Hoag-like galaxies.

## Key findings

- Existence of a Lagrangian circle (LC) of unstable equilibrium.
- Identification of the outermost stable circular orbit (OSCO).
- Prediction of matter gaps in Hoag-like systems due to orbital stability regions.

## Abstract

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.