A study of the high-inclination population in the Kuiper belt -- V. Mean motion resonances beyond 50 AU

TL;DR

This study extends the analysis of Neptune’s mean-motion resonances into the distant Kuiper belt (50–100 AU) to map resonance occupancy and stability for hundreds of RKBOs. It combines a data-driven identification of resonant objects with long-term numerical integrations (10 Myr clones and 4 Gyr evolutions) to quantify which m:n resonances can host bodies, how resonance width and centre depend on eccentricity and inclination, and how stability varies across resonance order. A key finding is the number-reversal phenomenon, where higher-order, weaker resonances (e.g., 3:8) can host more stable resonators than lower-order neighbors (e.g., 3:7) due to larger perihelion distances and e-dependent stability; this has implications for primordial KBO eccentricity distributions and Neptune’s migration history. The results indicate that RKBOs beyond 50 AU could populate nearly all resonances from 1:$n$ to 7:$n$ up to 100 AU, though high-order resonances beyond order ~20 are rare, and observational biases strongly affect the detected distributions. Overall, the work provides a comprehensive dynamical framework and a predictive database for future surveys (e.g., LSST) to test the outer Kuiper belt structure and Planetary migration scenarios.

Abstract

In this paper, we present the most comprehensive study to date on Neptune's mean-motion resonances (MMRs) in the distant Kuiper belt from 50 to 100 AU. Over 200 resonant Kuiper belt objects (KBOs) have been identified in this region, spanning resonances from the 2nd-order 1:3 MMR to the 22nd-order 7:29 MMR, with inclinations $i<40^\circ$. Building on these diverse distributions, we first analyse the dynamical features of numerous $m$:$n$ MMRs, providing an informative database that includes the possible eccentricity ($e$) range, resonance widths, resonance centres, and permissible $(e,i)$ distributions. We then conduct numerical simulations to explore the long-term stability of these MMRs. Our results show that: (1) resonators can occupy all 1:$n$ to 7:$n$ MMRs, with nearly any $n$ corresponding to the 50-100 AU region, including the farthest-out MMRs of 5:29 (24th-order), 6:35 (29th-order), and 7:40 (33rd-order). This suggests that KBOs could potentially exist in even higher-order MMRs than those currently observed. (2) For each set of $m$:$n$ resonances with the same $m$, resonators consistently exhibit inclinations up to $40^\circ$, while eccentricities remain strictly restricted below 0.7. (3) For the 1:3 and 1:4 MMRs, the leading population is less stable than the trailing population. Most interestingly, we discover a novel phenomenon of number reversal, where the higher-order, weaker 3:8 MMR (at semimajor axis $a\approx57.9$ AU) hosts more resonators, rather than fewer as expected, compared to the lower-order, stronger 3:7 MMR (at $a\approx53.0$ AU). Future observations, whether confirming or challenging this phenomenon, will offer valuable insight into the eccentricity and inclination distributions of primordial KBOs.

Figures (13)

• Figure 1: Time evolution of the resonant angle for candidate RKBOs in extremely high-order resonances from the 1 Myr integration. The upper, middle, and lower panels correspond to the 13:51, 14:33, and 15:41 resonances, respectively. All three cases are associated with eccentricity-type resonances, with resonant angles $\sigma_{m:n}$ as defined in equation (\ref{['anglemn']}).
• Figure 2: Time evolution of a candidate RKBO associated with the 2:5 resonance: (upper panel) the inclination-related resonant angle $\sigma^{(-1)}=5\lambda-2\lambda_N-\varpi-2\Omega$; (middle panel) the eccentricity-type resonant angle $\sigma^{(0)}=5\lambda-2\lambda_N-3\varpi$; (lower panel) the argument of perihelion $\omega$.
• Figure 3: Orbital distributions of the currently observed RKBOs beyond 50 AU. The original data is obtained from the MPC as of April 29, 2024, including only objects with multiple-opposition observation arcs. These RKBOs are distributed across the 1:$n$ (red), 2:$n$ (green), 3:$n$ (green), 4:$n$ (orange), 5:$n$ (purple), 6:$n$ (Magenta), and 7:$n$ (black) resonances; and the sole 7:$n$ RKBO, 2021 RW237 in the 7:29 resonance, is specifically marked in panel (a). For clarity, the semimajor axes, eccentricities and inclinations are taken to be the average values over the 10 Myr integration. The filled circles stand for secure RKBOs, the open circles denote probable RKBOs, while the star indicates an insecure RKBO (2021 LS43 in the 3:16 resonance). For reference, a solid line is plotted at a perihelion distance of $q = 45$ AU, above which all the MPC RKBOs reside (i.e. with $q > 45$ AU).
• Figure 4: Two typical scenarios illustrating the time evolution of the resonant angle for two KBOs associated with resonances higher than the 20th-order. (Panel a) The object 2005 PT21 initially experiences the 13:51 resonance (38th-order) but eventually transitions to a circulation state. (Panel b) The object 2021 RW237, trapped in the 7:29 resonance (22nd-order), exhibits stable libration over 10 Myr and is thus identified as an RKBO.
• Figure 5: Libration zones as a function of semimajor axis ($a$) and eccentricity ($e$) for a selection of Neptune’s MMRs in the distant Kuiper belt extending from 50 to 100 AU, based on the planar CR3BP model. For each MMR, the libration zone is bounded by two curves of a specific colour, which represent the sunward and anti-sunward resonance separatrices. The resonance width is defined as the range of $a$ variation between these separatrices. To better visualise the relative widths of the resonances, the aspect ratios of panels (a) and (b) are adjusted to ensure that both have the same scale of $a$. For reference, three curves of constant perihelion distance are plotted: the solid curve represents orbits with perihelion distances equal to Neptune's aphelion ($\sim30.3$ AU), the dashed curve represents orbits with perihelion distances equal to Uranus's aphelion ($\sim20.1$ AU), and the dotted curve represents orbits with perihelion distances of 45 AU.