The current observational sample consists of about 2000 KBOs. Their orbital parameters are displayed in Fig. 2. This orbital distribution is subject to heavy observational biases because a KBO’s on-sky rate of motion and brightness both decrease rapidly with heliocentric distance, which makes the more distant and smaller objects less detectable. Most discovered objects are larger than ~ 100 km in size, and are closer than 50 au heliocentric distance. Still, with the measured orbital parameters, we can recognize several dynamical classes (e.g., Gladman et al. 2008).
Classical KBOs
These are the non-resonant objects, most concentrated in the semimajor axis range 42–47 au. The inner boundary of this range is near the ν8 apsidal secular resonance which renders circular orbits unstable (Knezevic et al. 1991), and the outer boundary is near Neptune’s 2/1 MMR. Despite the observational selection bias against the discovery of more distant objects, the edge of the classical Kuiper belt near ~ 50 au appears to be quite real (Allen et al. 2001). Two sub-classes are also recognized within the classical KBOs: the cold classicals (those with low-eccentricity e ≲ 0.1, and low inclination, i ≲ 5°), and the hot classicals (those with higher eccentricities and inclinations). The cold classicals are thought to be the most undisturbed remnants of the primordial Kuiper belt whose orbits have been mildly excited by means of long-term diffusive chaos (Zhou et al. 2007).
Resonant KBOs
These objects are found in Neptune’s MMRs, most strikingly in the 3/2 resonance (the Plutinos); smaller populations in the 1/1, 2/1, 5/3, 7/4, 5/2, and several other MMRs have been identified. In the semimajor axis–eccentricity plane, the resonant populations present as a vertical concentration over a range of eccentricities with an upper bound corresponding to perihelion distance q ≈ 26 au; this upper bound is understood to be owed to the destabilizing effects of Uranus.
Scattered disk objects
The “scattered disk” is the prominent structure visible in the semimajor axis-eccentricity plane as a curved wing along perihelion distances concentrated in the narrow range 30 au ≲ q ≲ 38 au and semimajor axes 30 au ≲ a ≲ 1000 au. Although most of the known scattered disk objects (SDOs) have heliocentric distance currently closer than ~ 50 au, we infer from their orbital parameters that a vast population exists over heliocentric distances to ~ 2000 au. Their total population appears to be comparable to or even exceeding the total population of the resonant and classical KBOs.
Scattering objects
These are the very high eccentricity non-resonant objects which have perihelion distances below ~ 26 au and semimajor axes above 30 au. They are so-named because their orbits are unstable on timescales less than 1 megayear as they have close encounters with Neptune. These are a transitional population between the Kuiper belt and the Centaurs/Jupiter family short-period comets.
Detached objects
These are the relatively small number of known objects which have semimajor axes a ≳ 50 au and perihelion distance q ≳ 40 au. They are so-named because they are thought to originate from the gravitationally scattered population but have been detached from that population by some mechanism that raised their perihelion distance beyond the limits of the scattered disk. Possible mechanisms include: the action of close stellar encounters or tidal torques in the stellar cluster in which the Sun formed (Fernandez and Brunini 2000), the action of massive planetary embryos in the young Kuiper belt (Silsbee and Tremaine 2018), eccentricity-inclination cycles in sweeping MMRs (Gomes et al. 2005) or slow chaotic diffusion in MMRs over gigayear long timescales (Lykawka and Mukai 2007).
It is apparent from Fig. 2 that the resonant populations are quite prominent, as is the population of SDOs and the non-resonant population of the classical KBOs. Overall, the resonant KBOs are roughly one-third of the observational sample. Significant resonant populations have been measured in the following MMRs of Neptune (listed in order of increasing semimajor axis): 1/1, 4/3, 3/2, 5/3, 7/4, 2/1, 5/2, 3/1, 4/1. The most prominent is the Plutinos in the 3/2 MMR, with more than 300 objects known. For sizes ≳ 100 km (absolute magnitude ≾ 8.7), the intrinsic (de-biased) population of the Plutinos is estimated to be about 8000 (Volk et al. 2016). Accounting for the slow erosion of this population over gigayear timescales leads to the conclusion that ~ 4 gigayears ago it may have exceeded ~ 27,000. Similar backward-in-time extrapolations can be applied for each resonance.
For the currently known observational sample, the relative intrinsic (de-biased) populations in some of the resonances are displayed in Fig. 3; it should be noted that the uncertainties of these de-biased estimates are typically ~ 50% (Volk et al. 2016). We observe that the intrinsic Plutinos/Twotinos population ratio at present is about ~ 2. Accounting for the slow differential erosion of these populations over ~ 4 gigayears implies that their populations ~ 4 gigayears ago would have been of comparable size. This is marginally consistent with the predictions of adiabatic resonance capture which yields the largest capture efficiencies in the 2/1 MMR followed by the 3/2 MMR (Malhotra 1995).
The case of the 5/2 MMR (at a ≈ 55 au) presents a puzzle. Its presently known population is only 34, but given its greater distance, its intrinsic (de-biased) population is estimated to be 8500, comparable to the Plutino population (Volk et al. 2016). If confirmed, this is inconsistent with adiabatic resonance capture from an initially cold planetesimal disk (Chiang et al. 2003). Moreover, this population has a peculiar eccentricity distribution, with a strong concentration near e ≈ 0.4. Stimulated by these puzzling observations, we recently investigated the phase space structure of the 5/2 MMR which had not previously been explored in detail (Malhotra et al. 2018). We discovered that the narrow resonance width of the 5/2 MMR at low eccentricities widens dramatically at higher eccentricities, reaching a maximum near 0 ≈ 0.4, then narrows again; at eccentricities exceeding e ≈ 0.5, the perihelion distance is small enough that perturbations from Uranus have a destabilizing effect. Thus, the likely explanation for the peculiar eccentricity distribution of the observed 5/2 resonant KBOs is that the resonance zone is filled in proportion to the width of the stable libration zone as a function of eccentricity.
We also found that the size of the stable libration zone of the 5/2 MMR is comparable to that of the 3/2 MMR and of the 2/1 MMR. This suggests that the similarity of the intrinsic populations in these resonances is related to the sizes of their stable resonance libration zones. This conjecture can be tested in the future as the observational sample size increases and we can measure more reliably the populations of many more MMRs.
However, unlike the case for the 2/1 and 3/2 MMRs, adiabatic resonance sweeping does not provide a compelling mechanism for populating the 5/2 MMR because this third-order resonance has a very narrow neck at low eccentricities which limits the capture probability. Whether direct gravitational scattering can populate this resonance to the observed level remains to be investigated in detail.
An important observation is that the population of non-resonant objects (the classical KBOs) appears to be comparable to or even exceeds the resonant population. This also indicates that the adiabatic resonance sweeping is not the whole story. The other parts of the story are not well constrained yet; they include the following possibilities (see, e.g., Nesvorny 2018, for a review): Neptune’s planetesimal-driven outward migration was not smooth, either because the giant planets encountered MMRs with each other or because the scattered planetesimals included significant numbers of large bodies, perhaps even super-Earth-mass planets; the effects of self-stirring and self-gravity of the primordial planetesimal disk; perturbations from planetary-mass objects beyond Neptune that existed at early times, one or more of which may still remain bound in the distant solar system yet-to-be-discovered; external perturbations, such as rare close encounters with passing stars.