Dynamics and stability of resonant rings in galaxies

Abstract

We have developed a model for a spheroidal, ring-shaped galaxy. The stars move in a ring with an elliptical cross section at the 1: 1 frequency resonance. The shape of the cross section of the equilibrium ring depends on the oblateness of the galaxy itself, so that the ellipse of the ring cross section is radially extended when the oblateness of the galaxy is small. If the oblateness of galaxy exceeds some critical value, the ellipse cross section is extended along the Ox3 axis. The shape of the ring cross section is circular for a galaxy with critical eccentricity. The stability of the ring over a wide range of perturbations is studied. A fundamental bicubic dispersion equation for the frequencies of small oscillations of a perturbed ring is derived. Application of the model to the ring galaxy NGC 7020 shows that its ring cross section should be approximately circular. Analysis of the dispersion equation demonstrates that stellar orbits in the arm are unstable (but the instability increment is small). We conclude that stars in the ring of this galaxy should drift from the 1: 1 resonance, and the ring itself should evolve.