Exploring the 7:4 mean motion resonance—I: Dynamical evolution of classical transneptunian objects

Abstract

In the transneptunian classical region ( 42 AU < a < 48 AU ), an unexpected orbital excitation in eccentricity and inclination, dynamically distinct populations and the presence of chaotic regions are observed. For instance, the 7:4 mean motion resonance ( a ∼ 43.7 AU ) appears to have been causing unique dynamical excitation according to observational evidences, namely, an apparent shallow gap in number density and anomalies in the colour distribution, both features enhanced near the 7:4 mean motion resonance location. In order to investigate the resonance dynamics, we present extensive computer simulation results totalizing almost 10,000 test particles under the effect of the four giant planets for the age of the solar system. A chaotic diffusion experiment was also performed to follow tracks in phase space over 4–5 Gyr. The 7:4 mean motion resonance is weakly chaotic causing irregular eccentricity and inclination evolution for billions of years. Most 7:4 resonant particles suffered significant eccentricities and/or inclinations excitation, an outcome shared even by those located in the vicinity of the resonance. Particles in stable resonance locking are rare and usually had 0.25 < e < 0.3 . For other regions, 7:4 resonants had quite large mobility in phase space typically leaving the resonance (and being scattered) after reaching a critical e ∼ 0.2 . The escape happened in 10 8–10 9 yr time scales. Concerning the inclination dependence for 7:4 resonants, we found strong instability islands for approximately i > 10 ° . Taking into account those particles still locked in the resonance at the end of the simulations, we determined a retainability of 12–15% for real 7:4 resonant transneptunian objects (TNOs). Lastly, our results demonstrate that classical TNOs associated with the 7:4 mean motion resonance have been evolving continuously until present with non-negligible mixing of populations.