http://arxiv.org/abs/2203.03349
Many exoplanets evolving in (or close) to MMRs and resonant chains have been discovered by space missions. Oftentimes, the published data possess very large uncertainties, due to observational limitations, which deem the system chaotic in short or large timescales. We propose a study of the dynamics of such systems by exploring particular regions in phase space. We exemplify our method by studying the long-term orbital stability of the three-planet system Kepler-51 and either favor or constrain its data. It is a dual process which breaks down in two steps: the computation of the families of periodic orbits in the 1:2:3 resonant chain and the visualization of the phase space through maps of dynamical stability. We present novel results in the General 4-Body Problem. Stable periodic orbits were found only in the low-eccentricity regime. We demonstrate three possible scenarios safeguarding Kepler-51, each followed by constraints. Firstly, the 2/1 and 3/2 two-body MMRs, in which $e_b<0.02$, so that such two-body MMRs last for long-time spans. Secondly, the 1:2:3 three-body Laplace-like resonance, in which $e_c<0.016$ and $e_d<0.006$ for such a chain to be viable. Thirdly, the combination comprising an 1/1 secondary resonance inside 2/1 MMR for the inner pair of planets and an apsidal difference oscillation for the outer pair of planets in which the observational eccentricities $e_b$ and $e_c$ are favored as long as $e_d\approx 0$. Aiming to the optimum deduction of the orbital elements, this study showcases the need for dynamical analyses based on periodic orbits being performed in parallel to the fitting processes.
K. Antoniadou and G. Voyatzis
Tue, 8 Mar 22
56/100
Comments: Accepted for publication in A&A
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