It is shown that based on the concept of a toroidal self-gravitating ring vortex with a swirl (with an orbital motion along the torus generatrix), it is possible to explain all the main morphological features of the famous Hoag ring galaxy, including the still unexplained rotation of the central elliptical galaxy. The astronomical observations can be used, thus, to study complex vortex motions [The article based on the authors’ reports Bannikova et al., XIII International Conference to 100 years of Illia Mikhailovich Lifshitz, Kharkiv, KhNU (2017) and Kontorovich et al., XIV International Science Conference “Physical phenomena in solids”, Kharkiv, KhNU (2019) at the Conferences on condensed matter physics at Kharkiv National University, the first of which was dedicated to the 100th anniversary of the birth of Ilya Mikhailovich Lifshitz, a teacher and friend of Mark Azbel.].