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Abstract The detached trans-Neptunian objects (TNOs) are those with semimajor axes beyond the 2:1 resonance with Neptune that are neither resonant nor scattering. Using the detached sample from the Outer Solar System Origins Survey (OSSOS) telescopic survey, we produce the first studies of their orbital distribution based on matching the orbits and numbers of the known TNOs after accounting for survey biases. We show that the detached TNO perihelion ( q ) distribution cannot be uniform but is instead better matched by two uniform components with a break near q ≈ 40 au. We produce parametric two-component models that are not rejectable by the OSSOS data set and estimate that there are 36,000 − 9000 + 12 , 000 detached TNOs with absolute magnitudes H r < 8.66 ( D ≳ 100 km) and semimajor axes 48 au < a < 250 au (95% confidence limits). Although we believe that these heuristic two-parameter models yield a correct population estimate, we then use the same methods to show that the perihelion distribution of a detached disk created by a simulated rogue planet matches the q distribution even better, suggesting that the temporary presence of other planets in the early solar system is a promising model to create today’s large semimajor axis TNO population. This cosmogonic simulation results in a detached TNO population estimate of 48,000 − 12 , 000 + 15 , 000 . Because this illustrates how difficult-to-detect q > 50 au objects are likely present, we conclude that there are (5 ± 2) × 10 4 dynamically detached TNOs, roughly twice as many as in the entire trans-Neptunian hot main belt. 

ABSTRACT We explore a simplified model of the outcome of an early outer Solar System gravitational upheaval during which objects were captured into Neptune’s 3:2 mean-motion resonance via scattering rather than smooth planetary migration. We use N-body simulations containing the sun, the four giant planets, and test particles in the 3:2 resonance to determine whether long-term stability sculpting over 4.5 Gyr can reproduce the observed 3:2 resonant population from an initially randomly scattered 3:2 population. After passing our simulated 3:2 resonant objects through a survey simulator, we find that the semimajor axis (a) and eccentricity (e) distributions are consistent with the observational data (assuming an absolute magnitude distribution constrained by prior studies), suggesting that these could be a result of stability sculpting. However, the inclination (i) distribution cannot be produced by stability sculpting and thus must result from a distinct process that excited the inclinations. Our simulations modestly under-predict the number of objects with high-libration amplitudes (Aϕ), possibly because we do not model transient sticking. Finally, our model under-populates the Kozai subresonance compared to both observations and to smooth migration models. Future work is needed to determine whether smooth migration occurring as Neptune’s eccentricity damped to its current value can resolve this discrepancy. 

Abstract The orientations of orbital planes of minor planets are directional random variables. Their free inclination is the deviation of the orbit plane from the plane forced by the major planets. We construct a model of the distribution of free inclinations of classical Kuiper Belt objects (CKBOs) based on the von Mises–Fisher (vMF) distribution function, the analog of the normal distribution for directional statistics. The CKBOs are known to have a “cold” component of orbit planes concentrated near the forced plane and a more widely dispersed “hot” component. Adopting a model with a linear combination of two vMF functions, we find that the cold and hot components account for 57% and 43%, characterized by widths of 1.°7 and 12.°9, respectively. This model improves upon previous models based on smaller observational samples and empirical choices of functional forms for inclination distributions. 

Abstract The Vera C. Rubin Observatory is expected to start the Legacy Survey of Space and Time (LSST) in early to mid-2025. This multiband wide-field synoptic survey will transform our view of the solar system, with the discovery and monitoring of over five million small bodies. The final survey strategy chosen for LSST has direct implications on the discoverability and characterization of solar system minor planets and passing interstellar objects. Creating an inventory of the solar system is one of the four main LSST science drivers. The LSST observing cadence is a complex optimization problem that must balance the priorities and needs of all the key LSST science areas. To design the best LSST survey strategy, a series of operation simulations using the Rubin Observatory scheduler have been generated to explore the various options for tuning observing parameters and prioritizations. We explore the impact of the various simulated LSST observing strategies on studying the solar system’s small body reservoirs. We examine what are the best observing scenarios and review what are the important considerations for maximizing LSST solar system science. In general, most of the LSST cadence simulations produce ±5% or less variations in our chosen key metrics, but a subset of the simulations significantly hinder science returns with much larger losses in the discovery and light-curve metrics. 

Abstract Mean plane measurements of the Kuiper Belt from observational data are of interest for their potential to test dynamical models of the solar system. Recent measurements have yielded inconsistent results. Here we report a measurement of the Kuiper Belt’s mean plane with a sample size more than twice as large as in previous measurements. The sample of interest is the nonresonant Kuiper Belt objects, which we identify by using machine learning on the observed Kuiper Belt population whose orbits are well determined. We estimate the measurement error with a Monte Carlo procedure. We find that the overall mean plane of the nonresonant Kuiper Belt (semimajor axis range of 35–150 au) and also that of the classical Kuiper Belt (semimajor axis range of 42–48 au) are both close to (within ∼0.°7) but distinguishable from the invariable plane of the solar system to greater than 99.7% confidence. When binning the sample into smaller semimajor axis bins, we find the measured mean plane is mostly consistent with both the invariable plane and the theoretically expected Laplace surface forced by the known planets. Statistically significant discrepancies are found only in the semimajor axis ranges 40.3–42 au and 45–50 au; these ranges are in proximity to the ν 8 secular resonance and Neptune’s 2:1 mean motion resonance where the theory for the Laplace surface is likely to be inaccurate. These results do not support a previously reported anomalous warp at semimajor axes above 50 au. 

ABSTRACT Small Solar system bodies have widely dispersed orbital poles, posing challenges to dynamical models of Solar system origin and evolution. To characterize the orbit pole distribution of dynamical groups of small bodies it helps to have a functional form for a model of the distribution function. Previous studies have used the small-inclination approximation and adopted variations of the normal distribution to model orbital inclination dispersions. Because the orbital pole is a directional variable, its distribution can be more appropriately modelled with directional statistics. We describe the von Mises–Fisher (vMF) distribution on the surface of the unit sphere for application to small bodies’ orbital poles. We apply it to the orbit pole distribution of the observed Plutinos. We find a mean pole located at inclination i0 = 3.57° and longitude of ascending node Ω0 = 124.38° (in the J2000 reference frame), with a 99.7 per cent confidence cone of half-angle 1.68°. We also estimate a debiased mean pole located 4.6° away, at i0 = 2.26°, Ω0 = 292.69°, of similar-size confidence cone. The vMF concentration parameter of Plutino inclinations (relative to either mean pole estimate) is κ = 31.6. This resembles a Rayleigh distribution function, with width parameter σ = 10.2°. Unlike previous models, the vMF model naturally accommodates all physical inclinations (and no others), whereas Rayleigh or Gaussian models must be truncated to the physical inclination range 0–180°. Further work is needed to produce a theory for the mean pole of the Plutinos against which to compare the observational results. 

ABSTRACT Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel properties in the low-eccentricity regime for interior mean motion resonances of Jupiter in the fundamental model of the circular planar restricted three-body model. Here, we extend the non-perturbative investigation to exterior mean motion resonances in the low-eccentricity regime (up to about 0.1) and for perturber mass in the range of ∼5 × 10−5 to 1 × 10−3 (in units of the central mass). Our results demonstrate that first-order exterior resonances have two branches at low eccentricity as well as low-eccentricity bridges connecting neighbouring first-order resonances. With increasing perturber mass, higher order resonances dissolve into chaos, whereas low-order resonances persist with larger widths in their radial extent but smaller azimuthal widths. For low-order resonances, we also detect secondary resonances arising from small-integer commensurabilities between resonant librations and the synodic frequency. These secondary resonances contribute significantly to generating the chaotic sea that typically occurs near mean motion resonances of higher mass perturbers. 

Abstract We investigate different conditions, including the orbital and size–frequency distribution (SFD) of the early Kuiper Belt, that can trigger catastrophic planetesimal destruction. The goal of this study is to test if there is evidence for collisional grinding in the Kuiper Belt that has occurred since its formation. This analysis has important implications for whether the present-day SFD of the cold classical trans-Neptunian objects (TNOs) is a result of collisional equilibrium or if it reflects the primordial stage of planetesimal accretion. As an input to our modeling, we use the most up-to-date debiased OSSOS++ ensemble sample of the TNO population and orbital model based on the present-day architecture of the Kuiper Belt. We calculate the specific impact energies between impactor–target pairs from different TNO groups and compare our computed energies to catastrophic disruption results from smoothed particle hydrodynamics simulations. We explore different scenarios by considering different total primordial Kuiper Belt masses and power slopes of the SFD and allowing collisions to take place over different timescales. The collisional evolution of the Kuiper Belt is a strong function of the unknown initial mass in the trans-Neptunian region, where collisional grinding of planetesimals requires a total primordial Kuiper Belt mass of M > 5 M ⊕ , collision speeds as high as 3 km s −1 , and collisions over at least 0.5 Gyr. We conclude that presently, most of the collisions in the trans-Neptunian region are in the cratering rather than disruption regime. Given the low collision rates among the cold classical Kuiper Belt objects, their SFD most likely represents the primordial planetesimal accretion. 

Abstract The most distant known trans-Neptunian objects (TNOs), those with perihelion distance above 38 au and semimajor axis above 150 au, are of interest for their potential to reveal past, external, or present but unseen perturbers. Realizing this potential requires understanding how the known planets influence their orbital dynamics. We use a recently developed Poincaré mapping approach for orbital phase space studies of the circular planar restricted three-body problem, which we have extended to the case of the 3D restricted problem with N planetary perturbers. With this approach, we explore the dynamical landscape of the 23 most distant TNOs under the perturbations of the known giant planets. We find that, counter to common expectations, almost none of these TNOs are far removed from Neptune’s resonances. Nearly half (11) of these TNOs have orbits consistent with stable libration in Neptune’s resonances; in particular, the orbits of TNOs 148209 and 474640 overlap with Neptune’s 20:1 and 36:1 resonances, respectively. Five objects can be ruled currently nonresonant, despite their large orbital uncertainties, because our mapping approach determines the resonance boundaries in angular phase space in addition to semimajor axis. Only three objects are in orbital regions not appreciably affected by resonances: Sedna, 2012 VP113 and 2015 KG163. Our analysis also demonstrates that Neptune’s resonances impart a modest (few percent) nonuniformity in the longitude of perihelion distribution of the currently observable distant TNOs. While not large enough to explain the observed clustering, this small dynamical sculpting of the perihelion longitudes could become relevant for future, larger TNO data sets. 

Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called ``low-eccentricity resonant bridges" connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some -- though not necessarily entire -- resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.