Dynamical Classifications of Multi-opposition TNOs as of 2023 December

Transneptunian objects (TNOs) display a wide variety of dynamical behavior, and understanding their different dynamical sub-populations is critical to constraining the dynamical history of the outer solar system (see, e.g., Gladman & Volk 2021). Gladman et al. (2008) defined a classification scheme for objects with barycentric semimajor axes a beyond Jupiter (a > 5.2 au) and interior to the Oort cloud (a < 2000 au) as follows:

• 1.  
  Jupiter-coupled (JC) objects: bodies with perihelia q < 7.35 au and Tisserand parameters with respect to Jupiter T_J < 3.05
• 2.  
  Centaurs: bodies with semimajor axes interior to Neptune (a < 30.06 au) that are not Jupiter-coupled
• 3.  
  Resonant TNOs: objects that librate in one of Neptune's external mean motion resonances (MMRs) for more than half of a 10 Myr integration of their present-day orbit
• 4.  
  Scattering TNOs: non-resonant objects that undergo a barycentric semimajor axis change Δa > 1.5 au within 10 Myr
• 5.  
  Detached TNOs: non-resonant, non-scattering, high eccentricity (e > 0.24) objects
• 6.  
  Classical TNOs: non-resonant, non-scattering, low eccentricity (e ≤ 0.24) objects; these are further divided into inner (i) classicals with a interior to Neptune's 3:2 MMR (a < 39.4 au), main (m) classicals with a between Neptune's 3:2 and 2:1 MMRs (39.4 < a < 47.8 au), and outer (o) classicals with a exterior to Neptune's 2:1 MMR (a > 47.8 au).

To separate observed TNOs into the above categories, we: (1) Initialize a numerical simulation based on three clones of a TNO's orbit: the best-fit orbit and a minimum-a and maximum-a variation of the orbit. (2) Integrate the clones forward for 10 Myr under the gravitational influence of the Sun and the giant planets (with the mass of the terrestrial planets added to the Sun). (3) Evaluate the behavior of each clone to place it in a dynamical class. (4) Label that classification secure if all three clones agree. If there is disagreement, the classification defaults to the best-fit orbit's classification or the most common classification and is labeled insecure.

On 2023 December 6, we downloaded the Minor Planet Center (MPC) lists of Centaurs and Scattered Disk Objects and TNOs ⁴ and used the astroquery package (Ginsburg et al. 2019) to retrieve the astrometric measurements of each object. ⁵ We discarded objects with observational arcs shorter than one year as those orbits are too poorly determined (a few additional objects with 1–3 yr arcs were also discarded for poorly determined orbits). For objects with arcs shorter than seven years, we followed the exact procedure from Gladman et al. (2008) to generate clones; we used the Bernstein & Khushalani (2000) orbit-fitting code to find the best-fit and minimum/maximum-a orbits directly from the astrometry and integrated them using SWIFT (Levison & Duncan 1994). For longer-arc objects, that orbit-fitting procedure is no longer valid, so we relied on the orbit fits and covariance matrices in JPL's small body database. ⁶ We used the Small Body Dynamics Tool (SBDynT) ⁷ to initialize integrations with best-fit and minimum/maximum-a clones (found by randomly sampling the covariance matrix 1000 times); the orbits were integrated using rebound's mercurius integrator (Rein & Liu 2012; Rein & Spiegel 2015; Rein & Tamayo 2015). Note that unlike the minimum/maximum-a clones generated using the Gladman et al. (2008) procedure, the clones of these longer-arc TNOs do not account for potential systematic errors in the measured astrometry.

The integration outputs were passed through a classification pipeline and then examined by eye to ensure accurate classifications. Visual examination is particularly important for resonant classifications as libration is often messy; when a human judgment call was required to classify an object, the secure or insecure flag is noted as "SH" or "IH." We made a few modifications from Gladman et al. (2008) for assigning classifications: (1) For insecure objects, if the best-fit orbit is resonant, we assign that object as insecurely resonant even if the other two clones have matching classifications. (2) We soften the Δa = 1.5 au requirement for a scattering classification when visual inspection reveals clearly scattering-induced changes in a that fall just short of that somewhat arbitrary threshold (smaller-a orbits require a larger energy change to induce Δa = 1.5 au). (3) We label objects that have a uncertainties large enough for MMRs to fall entirely between the three clones (σ_a  ≳ 1–3 au;  several typical resonance widths) as insecure, even if all three clones show the same behavior.

The resulting classifications of the 3357 objects are presented in Table 1. Plots of the 10 Myr classification integrations for the TNOs are also available on GitHub:https://github.com/katvolk/TNO-classifications and in Zenodo at doi:10.5281/zenodo.10558440 .

We note that the most distant secure resonant TNO remains the 9:1 TNO 2007 TC434 discovered by OSSOS (Bannister et al. 2018) and detailed in Volk et al. (2018). The most distant insecure resonant TNO is 2016 SD106, whose best-fit orbit is in Neptune's 40:1 MMR (a ≈ 350 au); see Volk & Malhotra (2022) for a detailed examination of MMRs near distant TNOs. We also examined previously identified retrograde MMRs. The second retrograde TNO discovered, 471325 (Chen et al. 2016), was initially identified as being in Neptune's 7:9 retrograde MMR for timescales of several Myr by Morais & Namouni (2017). Its since-updated best-fit and minimum-a orbits show only short-term (∼0.5 Myr) libration; its maximum-a orbit is still classified as resonant. Morais & Namouni (2017) also identified TNO 528219 as potentially retrograde resonant. Its status remains unclear with the best-fit and maximum-a clones showing some intermittent libration in the retrograde 13:8 MMR and the maximum-a orbit librating on longer timescales.

K.V. acknowledges support for this work from NASA grant 80NSSC23K0886.

Software: rebound, astroquery, SBDynT.