Resonances in Nonaxisymmetric Gravitational Potentials
Abstract
We study sectoral resonances of the form jκ = m(n - Ω) around a nonaxisymmetric body with spin rate Ω, where κ and n are the epicyclic frequency and mean motion of a particle, respectively, where j > 0 and m (<0 or >0) are integers, j being the order of the resonance. This describes n/Ω ∼ m/(m - j) resonances inside and outside the corotation radius, as well as prograde and retrograde resonances. Results are as follows: (1) the kinematics of a periodic orbit depends only on (m', j'), the irreducible (relatively prime) version of (m, j). In a rotating frame, the periodic orbit has j' braids, $| m^{\prime} | $ identical sectors, and $| m^{\prime} | (j^{\prime} -1)$ self-crossing points; (2) thus, Lindblad resonances (with j = 1) are free of self-crossing points; (3) resonances with the same j' and opposite m' have the same kinematics, and are called twins; (4) the order of a resonance at a given n/Ω depends on the symmetry of the potential. A potential that is invariant under a 2π/k-rotation creates only resonances with m multiple of k; (5) resonances with the same j and opposite m have the same kinematics and same dynamics, and are called true twins; (6) A retrograde resonance (n/Ω < 0) is always of higher order than its prograde counterpart (n/Ω > 0); (7) the resonance strengths can be calculated in a compact form with the classical operators used in the case of a perturbing satellite. Applications to Chariklo and Haumea are made.
- Publication:
-
The Astronomical Journal
- Pub Date:
- March 2020
- DOI:
- 10.3847/1538-3881/ab6d06
- arXiv:
- arXiv:2001.06382
- Bibcode:
- 2020AJ....159..102S
- Keywords:
-
- Galaxy disks;
- Orbital resonances;
- Planetary rings;
- None;
- Centaur group;
- Trans-Neptunian objects;
- Gravitational interaction;
- 589;
- 1181;
- 1254;
- 1065;
- 215;
- 1705;
- 669;
- Astrophysics - Earth and Planetary Astrophysics
- E-Print:
- 20 pages, 2 figures