The Effect of Massive Trans-Neptunian Objects in the Long-term Evolution and Leaking Rates of Neptune's 3:2 and 2:1 Mean Motion Resonances

TL;DR

This work investigates how massive trans-Neptunian objects influence the long-term evolution and leakage rates of Neptune's main resonances, the 3:2 Plutino and the 2:1 Twotino. Using both SBDB observations and the L7 debiased Kuiper belt model as initial populations, the authors run extensive N-body simulations (via REBOUND/MERCURIUS) with and without the ten most massive resonant TNOs, including Pluto, to quantify leakage over 4 Gyr. They find that resonance decay follows an exponential form with a nonzero offset, and that Pluto — along with the other massive Plutinos/Twotinos — significantly enhances leakage, particularly in the 2:1 resonance, while the 3:2 resonance is more sensitive to Pluto’s perturbations. The results imply rapid dynamical erosion driven by massive inner-resonant bodies, challenging purely migration-based constraints and emphasizing Pluto’s critical role in shaping the current resonant population and its evolution. Overall, the study provides a quantified framework for how massive TNOs modulate Neptune’s resonant populations over the Solar System’s age, with implications for outer-Solar-System dynamics and inclination–eccentricity evolution.

Abstract

The current populations trapped in Neptune's main mean motion resonances in the Kuiper belt, Plutinos in the 3:2 and Twotinos in the 2:1, contain some of the best-characterized minor objects in the Solar System, given their dynamical importance. In particular, Twotinos may hide evidence of Neptune's early migration. However, these populations vary in time, declining at a rate that has not been previously clearly established. In this work, we use numerical simulations to study the long-term evolution of the Plutino and Twotino populations. We use two data sources: the most up-to-date observations and the theoretical debiased model of the Kuiper belt known as L7. In addition to studying the giant planets' effect on these populations over 4 Gyr, we analyze the additional impact produced by the ten most massive trans-Neptunian objects (TNOs) trapped in these resonances, as well as the effect of Pluto on the 2:1 population. We find that the decay rate in each resonance can be modeled as a stochastic process well described by an exponential decay with an offset determined by an underlying long-term stable population. The most massive TNOs, particularly Pluto, influence this decay rate significantly, as expected for the 3:2 resonance. Remarkably, Pluto also strongly influences the 2:1 resonance's evolution.

Figures (9)

• Figure 1: Initial orbital parameters of retrieved objects in the 3:2 (left panels) and 2:1 (right panels) MMRs. The top panels show the distribution in semimajor axis vs. eccentricity, while the lower panels show semimajor axis vs inclination. Gray dots show the sample obtained from the L7 model; blue dots show the observational sample obtained from JPL's SBDB. An initial statistical characterization is shown in dashed lines, which represent the median values of semimajor axis (vertical dashed lines) and eccentricity and inclination (horizontal dashed lines) for the L7 and SBDB populations, color-coded in the same way as the dots.
• Figure 2: Orbital parameter distribution of resonant particles in our samples after a short-term, 10 Myr integration under perturbations from the Sun and the four giant planets only. As in Fig. \ref{['fig:aei_0']}, top panels show $a$ vs. $e$, and lower panels $a$ vs. $i$ distributions; also, left panels correspond to the 3:2 resonant populations and right panels to the 2:1 populations. As in Fig. \ref{['fig:aei_0']} L7 objects are plotted in gray, SBDB objects, however, are now divided into two groups where most of the objects are plotted in blue, but the ten most massive objects in each resonance are plotted in red; we will use these ten objects as massive perturbers in some of our long-term simulations, see text. Finally, dashed horizontal and vertical lines show median values of each element, color-coded as the dots, as in Fig. \ref{['fig:aei_0']}. All the panels show significant sculpting of the resonant populations, but this is especially evident in the $a$-$e$ plane.
• Figure 3: Same as Fig. \ref{['fig:aei_10']}, but for the orbital parameter distribution of resonant particles after a long-term, 4 Gyr integration under perturbations from the Sun and the four giant planets only.
• Figure 4: Initial (at 10 Myr, top panels) and final (at 4 Gyr, bottom panels) conditions for SBDB and L7 libration centers and libration amplitudes. The angles were calculated from the short-term integrations at the beginning and end of the 4 Gyr runs.
• Figure 5: Distributions of libration centers and libration amplitudes of SBDB and L7 populations against their semimajor axes, at the end of long-term integrations. As in previous Figures, blue and gray dots indicate particles from the SBDB and the L7 models, respectively. The left column corresponds to the 3:2 resonant population, while the right column corresponds to the 2:1 population.