Dynamical classification of trans-neptunian objects: Probing their origin, evolution, and interrelation
Introduction
Trans-neptunian objects (TNOs) represent the remnants of the primordial planetesimal disk that formed the planets (Edgeworth, 1949, Kuiper, 1951). These minor bodies are believed to be the least processed Solar System members, and thus their study can offer precious information about the origin and evolution of our system (Luu and Jewitt, 2002). Currently more than 1000 TNOs have been observed so far thanks mainly to dedicated surveys (e.g., Jewitt et al., 1996, Gladman et al., 2001, Larsen et al., 2001, Trujillo et al., 2001, Allen et al., 2002, Elliot et al., 2005, Petit et al., 2006), and their orbital elements are available in public domain databases (e.g., Lowell Observatory—ftp://ftp.lowell.edu/pub/elgb/astorb.html). TNOs orbit mainly in two reservoirs: the trans-neptunian belt (or Edgeworth–Kuiper belt), at typical semimajor axes , and the scattered disk, at (Duncan and Levison, 1997, Luu et al., 1997). Members of the trans-neptunian belt show low to moderate eccentricities e, while TNOs in the scattered disk typically show large eccentricities. Both populations share the same range of inclinations, i (up to ∼48°). Several TNOs are also currently locked in resonances with Neptune.1 In particular, the 3:2 (), 5:3 (), 7:4 (), 2:1 (), and 5:2 () resonances are the most populated.
Tentative classification schemes have been suggested as the number of discoveries increased in the trans-neptunian reservoirs. The main purpose of a classification system is to provide clues on the origin and evolution of its members, and consequently a better understanding of the history of the outer Solar System. TNOs properly classified (avoiding misclassification) can also be used in statistical analyses to provide more precise results, which may yield new trends, correlations and insights (e.g., see Delsanti et al., 2006 and references therein). Combined with physical properties, one might obtain a more robust classification scheme. However, only a very small fraction of TNOs have their basic physical properties known. The exceptions are photometric colors and absolute magnitudes H, which have been taken into account recently (de Sanctis et al., 2006, Gulbis et al., 2006).
The common challenge of dynamical classification schemes is that populations appear to mix smoothly so that no boundaries are clearly known. For this reason, arbitrary values are often assumed. For instance, classical TNOs2 are traditionally set between an inner edge at 40–42 AU and an outer edge at 48–50 AU (e.g., Jewitt et al., 1998), but the inner and outer boundaries are difficult to establish. Moreover, a TNO inside this region is not necessarily a genuine classical TNO because of the presence of resonances (e.g., 5:3, 7:4, 2:1, etc.) and possible close encounters with Neptune at perihelion distances , which may indicate a scattered disk member (Kuchner et al., 2002, Lykawka and Mukai, 2005b). Scattered disk objects are often defined as those TNOs with and , but as we pointed out above, a few members can be found in the trans-neptunian belt (<48 AU) (see also Morbidelli and Brown, 2004). Furthermore, the existence of long-term resonant TNOs and detached bodies3 in the scattered disk complicates the situation even more (Hahn and Malhotra, 2005, Lykawka and Mukai, 2007). Another source of uncertainty is that osculating orbital elements change quickly with time. For example, the osculating semimajor axis can vary 0.5–1.5 AU after a short integration into the future of typical trans-neptunian orbits (35–50 AU). Such variation can reach a few to several AU in the scattered disk. Thus, the osculating semimajor axis does not provide enough information to tell if a TNO currently near a resonance location is in resonance or not.
We briefly comment on two recent dynamical classification systems: the one described in Morbidelli and Brown (2004), and that used by the Deep Ecliptic Survey (DES) team (Elliot et al., 2005, Chiang et al., 2007). Based on previous works on dynamics, Morbidelli and Brown (2004) introduced four classes: resonant, scattered, extended scattered (detached), and classical TNOs. In Morbidelli and Brown's (2004) scheme, only the 4:3, 3:2, and 2:1 resonances were considered. However, the resonance identification method is missing. Bodies that suffered close encounters with Neptune at least once over the age of the Solar System were classified as scattered TNOs. Morbidelli and Brown (2004) also set an arbitrary threshold at 50 AU to divide extended scattered () and classical TNOs (). Except the “stability” criterion of adopted for the latter, no other boundaries in phase space were given in Morbidelli and Brown (2004). The DES classification system is based on orbital numerical integration and consists of five classes: resonant, scattered-near, scattered-extended and classical TNOs, and the centaurs (objects crossing the orbits of any of the giant planets). Resonance identification is limited to order 4 (e.g., ), and valid only in the region between the 6:5 and 5:1 resonances (34–88 AU). The ‘scattered-near’ and ‘scattered-extended’ classes resemble the scattered and detached TNOs discussed previously. Lastly, two arbitrary averaged thresholds were used to define scattered-near (), scattered-extended (, ) and classical TNOs (, ), where T and e are the Tisserand parameter and object's eccentricity. In summary, although both Morbidelli and Brown (2004) and DES schemes introduced important physical criteria leading to classification improvements, they use arbitrary thresholds, provide incomplete resonance identification, and fail to distinguish more clearly the non-resonant populations.
In order to overcome those difficulties, we propose a new and more reliable dynamical classification based on numerical simulation of currently observed TNOs and fictitious objects over timescales up to 5 Gyr (Section 4). Our classification scheme confirms the traditional five classes: centaurs, resonant, scattered, detached, and classical TNOs, and also has important improvements: (a) identification of resonant TNOs of order at 4; (b) tentative boundaries for all non-resonant classes (based on comprehensive simulations over 4–5 Gyr); (c) identification of detached TNOs. Moreover, the new features are: (a) identification of Kozai resonant (KR) TNOs; (b) determination of “proper elements” for all TNOs; (c) determination of amplitude of the resonant angles (A and ), libration types, and libration centers for both resonant and KR TNOs; (d) amplitudes and periods of the osculating coupled KR oscillations; (e) possible identification of a new subclass of TNOs (those with approximately ). Lastly, we compare our identified resonant and KR TNOs with the outcome of migration models and the (un)stable regions of resonances. A discussion about the origin and evolution of identified dynamical classes and their interrelationship is presented too (Section 5). In light of the usefulness and purposes of a classification system, such discussions and comparisons (missing in past work) should be valuable.
Section snippets
Methods
We investigated the current dynamical state of TNOs by performing numerical simulations using the EVORB package (Brunini and Melita, 2002, Fernández et al., 2002). We selected 687 outer Solar System bodies in long-arc orbits5 as available on 12 September
Results
We found 622 TNOs and 65 non-resonant objects (centaurs) whose orbits evolved to giant planet crossing orbits within 1 Myr (see Section 4.5). Henceforth we will focus on TNOs and refer to their orbital elements as those averaged over the best-fit orbit + 10 clones for 10 Myr of simulation. Considering that the equations of motion are time reversible, these averaged values can be interpreted as the “proper” orbital elements of TNOs over the last 10 Myr. In Fig. 1 it is possible to identify
Resonant TNOs
Any TNO that showed libration of the resonant angle for a specific resonance within a certain dynamical timescale (minimum ∼0.2 Myr) was classified as a resonant TNO (Murray and Dermott, 1999). We securely identified 196 TNOs trapped in resonances, namely the 1:1 (4), 5:4 (5), 4:3 (6), 11:8 (1), 3:2 (100), 18:11 (1), 5:3 (11), 12:7 (1), 19:11 (1), 7:4 (22), 9:5 (2), 11:6 (1), 2:1 (14), 9:4 (3), 16:7 (1), 7:3 (3), 12:5 (2), 5:2 (12), 8:3 (1), 3:1 (2), 4:1 (1), 11:2 (1), and 27:4 (1), with the
Origin, dynamical evolution, and interrelationship among defined classes
The current existence of distinct classes in the trans-neptunian region suggests several dynamical mechanisms could have operated in the early Solar System. At least two of them have been active until today: the gravitational sculpting of Neptune and resonance dynamics. One should also recall that all TNOs were part of the same primordial planetesimal disk ∼4.5 Gyr ago in nearly circular and low-i orbits (Kenyon and Luu, 1999, Luu and Jewitt, 2002, Kenyon and Bromley, 2004). Several questions
Summary
We performed numerical integrations of long-arc orbits of 687 outer Solar System bodies (622 TNOs and 65 centaurs) + 10 clones over 10 Myr to identify their current dynamical state. In some cases long-term dynamical behavior (4–5 Gyr) of objects of interest was followed using 10–100 clones. Additional simulations were conducted to investigate stability in certain resonances, better define dynamical boundaries, and improve the results of particular investigations. Finally, comparison between TNO
Acknowledgements
We thank B. Gladman for a dedicated review with helpful comments and suggestions. Many thanks also to an anonymous reviewer whose critical comments importantly improved this paper. We are also grateful to A. Toigo for carefully reading the manuscript. This research was supported by “The 21st Century COE Program of Origin and Evolution of Planetary Systems” of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
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