Precession of Stellar Rings in the Center of Galaxy

The dynamics of two interacting concentric wide star rings located around a supermassive black hole in the central parsec of the Galaxy is investigated. The most massive of them, the ring with the retrograde motion of stars (known in the literature as a ‘‘clockwise’’ disk) is modeled as R-disk with a small cutout in the center. Another ring with a direct motion of stars (‘‘counter-clockwise’’ disk) is represented by a thin circular ring with an inclination \(\alpha\approx 62^{\circ}\) to the plane of the R-disk. The masses of these rings \(M_{1}\), \(M_{2}\) \(\left(M_{1}/M_{2}\approx 60\right)\), their geometric parameters and spatial orientation are known from observations. The mutual gravitational energy \(W_{\textrm{mut}}\) and the angular moment of force \(\mathbf{M}\) between the rings have been found, and graphs of these quantities depending on the angle of inclination have been constructed. The angular momenta of the rings \(L^{(1)}\) and \(L^{(2)}\), whose ratio \(L^{(1)}/L^{(2)}\approx 23.4\) have also been calculated. For the system of rings, the Laplace plane and the angles of its orientation are determined. It has been established that the mutual perturbation of the rotating rings leads to precession of the nodes with a period of \(T_{\Omega}\approx 3.53\times 10^{5}\) years. The lines of the nodes of both rings in the Laplace plane move with the same angular velocity but in opposite directions. This explains the large angle of divergence of the lines of nodes known from observations.