MNRAS 000,1–17 (2021) Preprint 17 June 2021 Compiled using MNRAS LATEX style file v3.0 Peculiar orbits and asymmetries in extreme trans-Neptunian space C. de la Fuente Marcos1? and R. de la Fuente Marcos2 1Universidad Complutense de Madrid, Ciudad Universitaria, E-28040 Madrid, Spain 2AEGORA Research Group, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Ciudad Universitaria, E-28040 Madrid, Spain Accepted 2021 June 12. Received 2021 June 10; in original form 2021 January 5 ABSTRACT It is still an open question how the Solar system is structured beyond 100 au from the Sun. Our understanding of this vast region remains very limited and only recently we have become aware of the existence there of a group of enigmatic bodies known as the extreme trans- Neptunian objects (ETNOs) that have large orbits with perihelia beyond the orbit of Neptune. Four ETNOs —Sedna, Leleakuhonua, 2012 VP113, and 2013 SY99— have perihelia beyond 50 au. The study of the ETNOs may provide much needed information on how this remote region is organized. Here, we apply machine-learning techniques to the sample of 40 known ETNOs to identify statistically significant clusters that may signal the presence of true dynam- ical groupings and study the distribution of the mutual nodal distances of the known ETNOs that measure how close two orbits can get to each other. Machine-learning techniques show that the known ETNOs may belong to four different populations. Results from the analysis of the distribution of nodal distances show that 41 per cent of the known ETNOs have at least one mutual nodal distance smaller than 1.45 au (1st percentile of the distribution), perhaps hinting at past interactions. In this context, the peculiar pair of ETNOs made of 505478 (2013 UT15) and 2016 SG58 has a mutual ascending nodal distance of 1.35 au at 339 au from the Sun. In addition, the known ETNOs exhibit a highly statistically significant asymmetry between the distributions of object pairs with small ascending and descending nodal distances that might be indicative of a response to external perturbations. Key words: methods: statistical – celestial mechanics – minor planets, asteroids: general – Kuiper belt: general – Oort Cloud. 1 INTRODUCTION recognized (see e.g. Gladman et al. 2002; Kenyon & Bromley 2004; Morbidelli & Levison 2004; Stern 2005), the origin and evolution Our degree of understanding of the structure of the Solar system of this population (or populations) is far from well established. beyond 100 au from the Sun remains very limited. In order for this Here, we adopt the naming convention featured in Trujillo & situation to change, we have to find and study objects with orbits Sheppard(2014): extreme (outer) Solar system bodies have per- not only much larger than those of typical members of the trans- ihelion distances, q > 30 au and semimajor axes, a > 150 au. Neptunian or Kuiper belt, but also with perihelia increasingly far- These boundaries in q and a are dynamically motivated: q > 30 au ther from Neptune so their trajectories are only weakly affected by implies that the ETNOs cannot experience close encounters with the gravitational pull of the giant planets. The first object fitting Neptune and a > 150 au makes a resonant engagement with Nep- into these rather general requirements, 148209 (2000 CR ), was 105 tune unlikely (see e.g. Clement & Sheppard 2021). Such a group arXiv:2106.08369v1 [astro-ph.EP] 15 Jun 2021 discovered in February 2000 at Lowell Observatory during a sur- of minor bodies was designated as exterior trans-Neptunian objects vey of the trans-Neptunian belt (Millis et al. 2000; Gladman et al. or ETNOs by Rickman et al.(2004) and extreme trans-Neptunian 2001), signalling the presence of an extended scattered structure objects (also ETNOs) by de la Fuente Marcos & de la Fuente Mar- well beyond Pluto. cos(2014). In the following, we will use the term ‘extreme trans- A trickle of related discoveries has continued throughout the Neptunian objects’ (ETNOs) to refer to Trujillo and Sheppard’s 21st century, in spite of this being an intrinsically challenging task. extreme outer Solar system bodies (those with a > 150 au and Major milestones in this continuing effort have been the discover- q > 30 au). ies of 90377 Sedna (2003 VB12) in 2003 (Brown, Trujillo & Ra- The ETNOs are unlikely to be captured in distant 1:N mean- binowitz 2004) and of 2012 VP113 in 2012 (Trujillo & Sheppard 2014). Although the distinctive nature of this group of objects rel- motion resonances with Neptune: the farthest ones with known ob- ative to that of the already well-understood scattered disc was soon jects in them are 1:9 at a∼130 au with 2007 TC434 and 2015 KE172 (Volk et al. 2018), and probably 1:10 at a∼140 au with 533563 (2014 JW80) and 1:11 at a∼150 au with 543735 (2014 OS394) as ? E-mail: [email protected] pointed out by Clement & Sheppard(2021). Resonant objects in © 2021 The Authors 2 C. de la Fuente Marcos and R. de la Fuente Marcos the 1:12 mean-motion resonance with Neptune at a∼157 au and be- al. 2014; Bannister et al. 2018; Khain et al. 2020). Whether or yond may not exist although Clement & Sheppard(2021) showed not there is a plausible single population of ETNOs remains an reasonable numbers of captures as far out as the 1:14, see also the open question and here we explore possible answers by applying discussion in Gallardo(2006) regarding the 1:18, 1:19 and 1:20 machine-learning techniques to the sample of 40 known ETNOs to mean-motion resonances with Neptune.1;2 The topic of Neptune’s study how are they arranged in orbital parameter space. This paper resonances in the scattered disc has already been extensively stud- is organized as follows. In Section 2, we discuss data and methods. ied and it is relatively well understood within the context of the Machine-learning techniques, in the form of the k-means++ algo- known Solar system (see e.g. Lykawka & Mukai 2007; Kaib & rithm implemented in the Python library Scikit-learn, are applied Sheppard 2016; Nesvorný, Vokrouhlický & Roig 2016; Saillenfest in Section 3 to three-dimensional datasets to evaluate the presence et al. 2017a; Lan & Malhotra 2019; Gallardo 2020). However, the of any significant clustering in the sample. Our findings are tested issue of capture of small bodies in distant mean-motion resonances against the distribution of their mutual nodal distances that mea- with Neptune remains an open question. Volk, Malhotra, & Graham sures how close two orbits can get to each other in Section 4. Poles (2021) have recently explored the 1:N, 2:N and 3:N mean-motion and perihelia that define the orientation of the orbits in space are resonances with Neptune out to a=550 au at a wide range of peri- studied in Section 5. Our results are discussed in Section 6 and our helion distances (q=33–60 au) within the context of the restricted conclusions are summarized in Section 7. three-body problem to find out that at large a, the surviving libra- tion zones of Neptune’s strongest resonances are generally wider for larger q due to less crowding from weaker neighbouring reso- nances, although the sticking times tend to be shorter as one moves 2 DATA AND METHODS further out (see e.g. Gallardo 2006). Here, we work with publicly available data from Jet Propulsion The ETNOs discovered so far (see Table1) move in rather Laboratory’s (JPL) Small-Body Database (SBDB)3 and HORI- elongated orbits and have perihelion distances beyond 30 au; these ZONS on-line solar system data and ephemeris computation unusual properties make them particularly hard to find. In fact, the service,4 both provided by the Solar System Dynamics Group ETNOs have only been found at perihelion or very near it, lead- (Giorgini 2011, 2015). The HORIZONS ephemeris system has re- ing to a very distinctive pattern regarding how orbital properties cently been updated to replace the DE430/431 planetary ephemeris, relate to discovery locations: their equatorial coordinates at discov- used since 2013, with the new DE440/441 solution (Park et al. ery time strongly constraint the orientations of their orbits in space. 2021) and sixteen most massive small-body perturbers. The new Orbits are defined by the values of semimajor axis (that controls DE440/441 general-purpose planetary solution includes seven ad- orbital size), eccentricity, e (that controls shape), and those of the ditional years of ground and space-based astrometric data, data cal- angular elements —inclination, i, longitude of the ascending node, ibrations, and dynamical model improvements, most significantly Ω, and argument of perihelion, !— that control the orientation of involving Jupiter, Saturn, Pluto, and the Kuiper Belt (Park et al. the orbit in space. 2021). DE440 covers the years 1550–2650 while DE441 is tuned Figure 1 in de la Fuente Marcos & de la Fuente Marcos(2014) to cover a time range of −13,200 to +17,191 years (Park et al. shows that the sizes and shapes of the orbits of the ETNOs (panels 2021). The most visible change with this update may be in the B and C in the figure) do not depend on the position of the object at ephemerides expressed with respect to the Solar system barycen- discovery, but i, Ω and ! (panels D, E and F) do. This means that tre. There is a time-varying shift of ∼100 km in DE441’s barycen- the way observations have been conducted (i.e. where the discover- tre relative to DE431 due to the inclusion of 30 new Kuiper-belt ies are being made) affects the observed distributions of the angular masses, and the Kuiper Belt ring mass (Park et al.