The outer realm of the Solar System, known either as the trans-Neptunian space or the Kuiper belt, is of great interest among celestial mechanical studies. Its dynamical structure is shaped to a large extent by the mean-motion resonances (MMRs) occurring between the trans-Neptunian objects (TNOs) and (mainly) the Neptune.
In a recent research, we carried out a large-scale survey of the TNOs, with a sample containing more than 4100 small bodies. By applying the FAIR method (Forgács-Dajka, Sándor, and Érdi, 2018), we identified the most important MMRs, and distinguished between the so-called short- and long-term resonances: TNOs in the former category are only temporarily captured in a given MMR, while those of the latter remain resonant throughout the (sufficiently long) integration time. We explored the dynamical properties of such intriguing MMRs through the quantification of the chaotic diffusion. For this purpose, we adopted both classical methods (as the one e.g. based on the computation of the time evolution of the variance of an action variable) and a more recent one (based on the computation of the time derivative of the Shannon entropy).
Apart from investigating the individual TNOs of our sample, we constructed dynamical maps of fictitious test particles, too. This approach enabled us to analyze the structure of the phase space in the vicinity of the resonances.
Our findings indicate that a notable percentage of the examined TNOs are engaged in MMRs with Neptune, and that however chaotic the phase space appears to be, the diffusion timescales are remarkably long.
As for the technical realization of the research, we adopted a barycentric model of the Solar System - containing the four giant planets and either a massless TNO or a test particle -, and integrated the equations of motion on a timescale of million years. Our codes were optimized for GPU computations in order to deal with the significant computational costs of integrating several hundreds of thousands of initial conditions (i.e. test particles).