Resonant Chains of Exoplanets: Libration Centers for Three-body Angles
Abstract
Resonant planetary systems contain at least one planet pair with orbital periods librating at a near-integer ratio (2/1, 3/2, 4/3, etc.) and are a natural outcome of standard planetary formation theories. Systems with multiple adjacent resonant pairs are known as resonant chains and can exhibit three-body resonances—characterized by a critical three-body angle. Here we study three-body angles as a diagnostic of resonant chains through tidally damped N-body integrations. For each combination of the 2:1, 3:2, 4:3, and 5:4 mean motion resonances (the most common resonances in the known resonant chains), we characterize the three-body angle equilibria for several mass schemes, migration timescales, and initial separations. We find that under our formulation of the three-body angle, which does not reduce coefficients, 180° is the preferred libration center, and libration centers shifted away from 180° are associated with nonadjacent resonances. We then relate these angles to observables, by applying our general results to two transiting systems: Kepler-60 and Kepler-223. For these systems, we compare N-body models of the three-body angle to the zeroth order in e approximation accessible via transit phases, used in previous publications. In both cases, we find the three-body angle during the Kepler observing window is not necessarily indicative of the long-term oscillations and stress the role of dynamical models in investigating three-body angles. We anticipate our results will provide a useful diagnostic in the analysis of resonant chains.
- Publication:
-
The Astronomical Journal
- Pub Date:
- June 2021
- DOI:
- 10.3847/1538-3881/abf8a6
- arXiv:
- arXiv:2104.14665
- Bibcode:
- 2021AJ....161..290S
- Keywords:
-
- Exoplanets;
- Exoplanet evolution;
- Exoplanet dynamics;
- Exoplanet tides;
- 498;
- 491;
- 490;
- 497;
- Astrophysics - Earth and Planetary Astrophysics
- E-Print:
- Accepted for publication in Astronomical Journal