Tidal effect of rings on central figures of equilibrium

The effect of a gravitating ring or torus on the central figure of relative equilibrium of a rotating liquid or gaseous mass is studied in the tidal approximation. A formula is derived for the increment in the square of the angular velocity of the central figure. Three models for wide rings are examined and one, for circular tori. The effects of rings on the oblateness of the planet Saturn or on the figure of the sun lie beyond the limits of modern measurements; however, the effect of a gravitating torus is already comparable to the effect of the star’s rotation in the case of the red supergiant WOH G64 in the LMC. The method is modified for galaxies; it then describes the effect of rings both on the stellar subsystem and, separately, on the diffuse subsystem. The well known NGC 4594 “Sombrero” galaxy is introduced as an example. This method may also be useful for estimating the dark mass surrounding giant E-galaxies.