Dynamical classification of trans-neptunian objects: Probing their origin, evolution, and interrelation

The orbital structure of trans-neptunian objects (TNOs) in the trans-neptunian belt (Edgeworth-Kuiper belt) and scattered disk provides important clues to understand the origin and evolution of the Solar System. To better characterize these populations, we performed computer simulations of currently observed objects using long-arc orbits and several thousands of clones. Our preliminary analysis identified 622 TNOs, and 65 non-resonant objects whose orbits penetrate that of at least one of the giant planets within 1 Myr (the centaurs). In addition, we identified 196 TNOs locked in resonances with Neptune, which, sorted by distance from the Sun, are 1:1 (Neptune trojans), 5:4, 4:3, 11:8, 3:2, 18:11, 5:3, 12:7, 19:11, 7:4, 9:5, 11:6, 2:1, 9:4, 16:7, 7:3, 12:5, 5:2, 8:3, 3:1, 4:1, 11:2, and 27:4. Kozai resonant TNOs are found inside the 3:2, 5:3, 7:4, and 2:1 resonances. We present detailed general features for the resonant populations (i.e., libration amplitude angles, libration centers, Kozai libration amplitudes, etc.). Taking together the simulations of Lykawka and Mukai [Lykawka, P.S., Mukai, T., 2007. Icarus 186, 331-341], an improved classification scheme is presented revealing five main classes: centaurs, resonant, scattered, detached and classical TNOs. Scattered and detached TNOs (non-resonant) have q (perihelion distance) <37 AU and q>40 AU, respectively. TNOs with 37 AU<q<40 AU occupy an intermediate region where both classes coexist. Thus, there are no clear boundaries between the scattered and detached regions. We also securely identified a total of 9 detached TNOs by using 4-5 Gyr orbital integrations. Classical objects are non-resonant TNOs usually divided into cold and hot populations. Their boundaries are as follows: cold classical TNOs (i?5°) are located at 37 AU<a<40 AU (q>37 AU) and 42 AU<a<47.5 AU (q>38 AU), and hot classical TNOs (i>5°) occupy orbits with 37 AU<a<47.5 AU (q>37 AU). However, a more firm classification is found with i>10° for hot classical TNOs. Lastly, we discuss some implications of our classification scheme comparing all TNOs with our model and other past models.     

Long term dynamical evolution and classification of classical TNOs

Classical trans-Neptunian objects (TNOs) are believed to represent the most dynamically pristine population in the trans-Neptunian belt (TNB) offering unprecedented clues about the formation of our Solar System. The long term dynamical evolution of classical TNOs was investigated using extensive simulations. We followed the evolution of more than 17000 particles with a wide range of initial conditions taking into account the perturbations from the four giant planets for 4 Gyr. The evolution of objects in the classical region is dependent on both their inclination and semimajor axes, with the inner (a<45 AU) and outer regions (a>45 AU) evolving differently. The reason is the influence of overlapping secular resonances with Uranus and Neptune (40–42 AU) and the 5:3 (a∼ ∼42.3 AU), 7:4 (a∼ ∼43.7 AU), 9:5 (a∼ ∼44.5 AU) and 11:6 (a∼ ∼ 45.0 AU) mean motion resonances strongly sculpting the inner region, while in the outer region only the 2:1 mean motion resonance (a∼ ∼47.7 AU) causes important perturbations. In particular, we found: (a) A substantial erosion of low-i bodies (i<10°) in the inner region caused by the secular resonances, except those objects that remained protected inside mean motion resonances which survived for billion of years; (b) An optimal stable region located at 45 AU<a<47 AU, q>40 AU and i>5° free of major perturbations; (c) Better defined boundaries for the classical region: 42–47.5 AU (q>38 AU) for cold classical TNOs and 40–47.5 AU (q>35 AU) for hot ones, with i=4.5° as the best threshold to distinguish between both populations; (d) The high inclination TNOs seen in the 40–42 AU region reflect their initial conditions. Therefore they should be classified as hot classical TNOs. Lastly, we report a good match between our results and observations, indicating that the former can provide explanations and predictions for the orbital structure in the classical region.     

Origin of scattered disk resonant TNOs: Evidence for an ancient excited Kuiper belt of 50 AU radius

Resonance occupation of trans-neptunian objects (TNOs) in the scattered disk (>48 AU) was investigated by integrating the orbits of 85 observed members for 4 Gyr. Twenty seven TNOs were locked in the 9:4, 16:7, 7:3, 12:5, 5:2, 8:3, 3:1, 4:1, 11:2, and 27:4 resonances. We then explored mechanisms for the origin of the resonant structure in the scattered disk, in particular the long-term 9:4, 5:2, and 8:3 resonant TNOs (median 4 Gyr), by performing large scale simulations involving Neptune scattering and planetary migration over an initially excited planetesimals disk (wide range of eccentricities and inclinations). To explain the formation of Gyr-resident populations in such distant resonances, our results suggest the existence of a primordial planetesimal disk of at least 45-50 AU radius that suffered a dynamical perturbation leading to 0.1-0.3 or greater eccentricities and a range of inclinations up to ∼20° during early stages of the Solar System history, before planetary migration.     

Two triaxial induction tools: sensitivity to radial invasion profile‡

I study the responses of two different triaxial induction tools to invaded dipping anisotropic formations. I show that the triaxial measurements have generally higher sensitivity to the radial invasion profile, compared to the conventional induction measurements. This enables accurate interpretation of both the anisotropic formation properties and the invasion parameters. Multi‐spacing and single‐spacing multi‐frequency triaxial induction tools can both be used for this purpose. Failure to take the invasion properties into account may lead to misinterpretation of the vertical formation resistivity. Symmetrization of the apparent conductivity matrix opens ways for a visual interpretation of triaxial induction logs for the formation and the invasion zone properties. This technique enables simpler and faster inversion algorithms. I study how the effect of a conductive annulus forming around the invasion zone couples with effects of the dipping anisotropy and the dipping boundaries and show when these effects are additive. Thus, a visual detection of log parts affected by a conductive annulus becomes possible. The key tool for interpretation in complex 3D scenarios is efficient modelling software. I use a 3D finite‐difference modelling approach to simulate responses of induction logging tools of the new generation. Its high efficiency enables simultaneous multi‐spacing and multi‐frequency computing of the tool responses to arbitrary 3D anisotropic formations that made the study possible.     

Variations in multiscale curvature distribution and signatures of LiDAR DTM errors

The development of high resolution LiDAR digital terrain models (DTMs) has enabled the exploration of the statistical signature of morphology on curvature distributions. This work analyzes Minimum Curvature distributions to identify the statistical signature of two types of LiDAR‐DTM errors (outliers and striping artifacts) in the derived estimates, rather than morphology itself. The analysis shows the importance of modeling these errors correctly, in relation to the scale of analysis and DTM resolution, in order to have reliable curvature estimates. Nine DTMs of different morphological areas are considered, and grouped into a training dataset (without errors) and a test dataset (with errors). In the training dataset, the original DTMs are considered as true values; errors are then applied to these data. Minimum Curvature is computed at multiple scales from each DTM: changes in curvature distributions due only to morphology and scale are characterized from the original data; error effects are then identified from the datasets with simulated errors, and validated against the test dataset. The analysis shows that outliers and striping artifacts can be realistically simulated by heavily left tailed distributions. For DTMs without errors, the scale‐dependent change in curvature distribution is primarily controlled by real morphology. When DTMs include errors, curvature distributions become controlled by these errors, whose propagation depends on error distribution, error spatial correlation, and the scale of analysis. This study shows that the curvature distributions are impacted upon differently by striping artifacts and outliers, and that these are clearly distinguishable from the signal of morphological features: a scale‐dependent change in curvature distribution can therefore be interpreted as the signature of these specific errors, rather than morphology. Copyright © 2012 John Wiley & Sons, Ltd.     

High‐resolution mapping of Manawatu palaeochannels

New remote sensing techniques, such as airborne laser scanning (LiDAR), have led to a dramatic increase in terrain information, providing new opportunities for landform analysis. A major advance in using LiDAR‐derived high‐resolution topography (HRT) is the capability to provide an accurate and detailed terrain morphology. This study aims to use LiDAR HRT to identify palaeochannels of the Manawatu River (New Zealand) using an automated procedure based on the statistical analysis of landform curvature. The approach can provide rapid assessment and classification of floodplain topography. The proposed analysis is crucial, especially for intensively used floodplains requiring effective flood management and mitigation.     

Doppler-shift approximations of encountered wave statistics

In this paper the joint density of waveheight and half-wavelength is considered for waves observed at a fixed time point and encountering waves that are overtaking a ship from behind. The densities for these two cases are related by a Doppler shift, expressed in terms of the relative velocity of the waves and the ship. Based on this observation, an approximation of the encountered density is proposed. This approximation is then investigated for a Gaussian sea having a Pierson–Moskowitz spectrum.     

High‐resolution topography and anthropogenic feature extraction: testing geomorphometric parameters in floodplains

In floodplains, anthropogenic features such as levees or road scarps, control and influence flows. An up‐to‐date and accurate digital data about these features are deeply needed for irrigation and flood mitigation purposes. Nowadays, LiDAR Digital Terrain Models (DTMs) covering large areas are available for public authorities, and there is a widespread interest in the application of such models for the automatic or semiautomatic recognition of features. The automatic recognition of levees and road scarps from these models can offer a quick and accurate method to improve topographic databases for large‐scale applications. In mountainous contexts, geomorphometric indicators derived from DTMs have been proven to be reliable for feasible applications, and the use of statistical operators as thresholds showed a high reliability to identify features. The goal of this research is to test if similar approaches can be feasible also in floodplains. Three different parameters are tested at different scales on LiDAR DTM. The boxplot is applied to identify an objective threshold for feature extraction, and a filtering procedure is proposed to improve the quality of the extractions. This analysis, in line with other works for different environments, underlined (1) how statistical parameters can offer an objective threshold to identify features with varying shapes, size and height; (2) that the effectiveness of topographic parameters to identify anthropogenic features is related to the dimension of the investigated areas. The analysis also showed that the shape of the investigated area has not much influence on the quality of the results. While the effectiveness of residual topography had already been proven, the proposed study underlined how the use of entropy can anyway provide good extractions, with an overall quality comparable to the one offered by residual topography, and with the only limitation that the extracted features are slightly wider than the investigated one. Copyright © 2013 John Wiley & Sons, Ltd.