Secular dynamics of a test particle perturbed by a Miyamoto-Nagai disc

We study the secular behaviour of a test particle orbiting a dominant central body and perturbed by a Miyamoto-Nagai (MN) disc eta We derive a quadrupole-level secular Hamiltonian of this system, which involves a dimensionless parameter. that is used to characterize the flattening of MN disc eta (The smaller., the flatter disc; and eta = 0 gives the infinitely thin Kuzmin disc.) We find that, in the quadrupole approximation, the perturbation of the MN disc can give rise to the von Zeipel-Lidov-Kozai (ZLK)-like dynamics and depending on the value of. the dynamics has two different manifestations: (i) when eta < 1/3, the test particle's behaviour is similar to that described in the classical ZLK problem. In particular, as eta increases from 0 to 1/3, the critical inclination for the large eccentricity oscillations decreases from 26 degrees, 56 to 0 degrees; (ii) when eta > 1/3, the orbital evolution of the test particle and the phase-space morphology are opposite to the classical ZLK case. This leads to a striking result that the test particle cannot remain on a near-coplanar orbit if its eccentricity is sufficiently large. However, as eta increases further the ZLK-like dynamics would be gradually suppressed by the spherical term in the Hamiltonian. We also survey the global secular dynamics numerically in which the quadrupole approximation is no longer valid.

Automated summary

The study reveals that the perturbation of the MN disc can lead to von Zeipel-Lidov-Kozai (ZLK)-like dynamics, with two different manifestations depending on the value of eta. When eta < 1/3, the behavior of the test particle is similar to that of the classical ZLK problem, while when eta > 1/3, the orbital evolution and phase-space morphology are opposite to the classical ZLK case.