Elena Bannikova | Searcharxiv

arXiv2026

Global m=1 slow mode in near-Keplerian self-gravitating torus: applications to stellar nuclear disks and AGN molecular tori

Global m=1 asymmetries are observed in many self-gravitating astrophysical systems and are often interpreted as large-scale slow modes in near-Keplerian potentials. Prominent examples include eccentric nuclear disks in galactic centres, such as the double nucleus of M31. However, the origin and long-term stability of such modes remain unclear. We investigate the evolution and stability of a collisionless, self-gravitating torus orbiting a dominant central mass, aiming to determine whether a slow non-axisymmetric (m=1) mode can arise spontaneously. We perform direct N-body simulations exploring different torus-to-central mass ratios and initial conditions. The calculations use the high-order Hermite GPU integrator (ϕ-GPU), allowing us to follow long-term evolution with many particles. We find that a global slow m=1 mode forms spontaneously from initially axisymmetric configurations. The lopsided structure is sustained by coherent apsidal alignment and persists over secular timescales. Its maintenance requires nonlinear coupling of low-order modes, including the m=3 component, as well as a sufficient vertical thickness of the torus. As a result of the long-lived overdensity, the central mass is displaced from the system barycenter. These results provide a framework for understanding eccentric nuclear disks, such as those in M31 and NGC4486B, as well as molecular tori in AGNs, and suggest that such asymmetries may produce observable offsets of the central supermassive black hole.

astro-ph.GA↗

arXiv2025

The outer gravitational potential of an inhomogeneous torus with an elliptical cross-section

Toroidal structures are a common feature in a wide variety of astrophysical objects, including dusty tori in AGNs, rings in galaxies, protoplanetary disks, and others. The matter distribution in such structures is not homogeneous and can be flattened by self-gravity or become elongated in the vertical direction, as is the case with obscuring tori in AGNs. This led us to consider the more general case of the gravitational potential of an inhomogeneous torus with an elliptical cross-section. We begin by showing that the outer potential of a homogeneous elliptical torus can be effectively approximated with less than 1\% error by the potentials of two infinitely thin rings with a minor correction term. These two rings have masses each equal to half the total mass of the torus. The most notable feature is that each such infinitely thin ring is positioned at precisely the halfway point between the center and the focus of the elliptical cross-section, regardless of the torus' other parameters. The result, which holds for both oblate and prolate geometries, allows us to find a new expression to handle the outer potential of an inhomogeneous torus with an elliptical cross-section. The confocal density distribution is a special case. We have found that the outer potential of such a torus is only weakly dependent of the density distribution law. Consequently, even for the confocal inhomogeneous case, the outer potential is well represented by two infinitely thin rings. This approach can simplify problems of dynamics for the systems consisting of toroidal structures. We have also derived the expressions for the external force components exerted by a homogeneous torus with an elliptical cross-section, both for the exact form of the potential and for our approximation by two infinitely thin rings. Comparison of the two shows that our model fits the true trend of the force well.

astro-ph.GA↗