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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2007.11.035 Byline: Harold F. Levison (a), Alessandro Morbidelli (b), Christa VanLaerhoven (c), Rodney Gomes (d), Kleomenis Tsiganis (e) Keywords: Origin; Solar System; Kuiper belt; Trans-neptunian objects; Planets; migration; Celestial mechanics Abstract: We explore the origin and orbital evolution of the Kuiper belt in the framework of a recent model of the dynamical evolution of the giant planets, sometimes known as the Nice model. This model is characterized by a short, but violent, instability phase, during which the planets were on large eccentricity orbits. It successfully explains, for the first time, the current orbital architecture of the giant planets [Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F., 2005. Nature 435, 459-461], the existence of the Trojans populations of Jupiter and Neptune [Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R., 2005. Nature 435, 462-465], and the origin of the late heavy bombardment of the terrestrial planets [Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A., 2005. Nature 435, 466-469]. One characteristic of this model is that the proto-planetary disk must have been truncated at roughly 30 to 35AU so that Neptune would stop migrating at its currently observed location. As a result, the Kuiper belt would have initially been empty. In this paper we present a new dynamical mechanism which can deliver objects from the region interior to [approximately equal to]35AU to the Kuiper belt without excessive inclination excitation. In particular, we show that during the phase when Neptune's eccentricity is large, the region interior to its 1:2 mean motion resonance becomes unstable and disk particles can diffuse into this area. In addition, we perform numerical simulations where the planets are forced to evolve using fictitious analytic forces, in a way consistent with the direct N-body simulations of the Nice model. Assuming that the last encounter with Uranus delivered Neptune onto a low-inclination orbit with a semi-major axis of [approximately equal to]27AU and an eccentricity of [approximately equal to]0.3, and that subsequently Neptune's eccentricity damped in [approximately equal to]1 My, our simulations reproduce the main observed properties of the Kuiper belt at an unprecedented level. In particular, our results explain, at least qualitatively: (1) the co-existence of resonant and non-resonant populations, (2) the eccentricity-inclination distribution of the Plutinos, (3) the peculiar semi-major axis -- eccentricity distribution in the classical belt, (4) the outer edge at the 1:2 mean motion resonance with Neptune, (5) the bi-modal inclination distribution of the classical population, (6) the correlations between inclination and physical properties in the classical Kuiper belt, and (7) the existence of the so-called extended scattered disk. Nevertheless, we observe in the simulations a deficit of nearly-circular objects in the classical Kuiper belt. Author Affiliation: (a) Southwest Research Institute, Department of Space Studies, 1050 Walnut Street, Suite 400, Boulder, CO 80302, USA (b) Observatoire de la CA[acute accent]te d' Azur, BP 4229, 06304 Nice Cedex 4, France (c) Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver BC, V6T 1Z1, Canada (d) Observatorio Nacional/MCT, Rua General Jose Cristino 77, 20921-400 Rio de Janeiro, RJ, Brazil (e) Section of Astrophysics, Astronomy & Mechanics, Department of Phyiscs, Aristotle University of Thessaloniki, GR 54 124 Thessaloniki, Greece Article History: Received 30 December 2006; Revised 13 November 2007

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2006.05.026 Byline: Rodney S. Gomes (a), John J. Matese (b), Jack J. Lissauer (c) Keywords: Trans-neptunian belt; Comets; dynamics Abstract: Most known trans-neptunian objects (TNO's) are either on low eccentricity orbits or could have been perturbed to their current trajectories via gravitational interactions with known bodies. However, one or two recently-discovered TNO's are distant detached objects (DDO's) (perihelion, q40AU and semimajor axis, a50AU) whose origins are not as easily understood. We investigate the parameter space of a hypothetical distant planetary-mass solar companion which could detach the perihelion of a Neptune-dominated TNO into a DDO orbit. Perturbations of the giant planets are also included. The problem is analyzed using two models. In the first model, we start with a distribution of undetached, low-inclination TNO's having a wide range of semimajor axes. The planetary perturbations and the companion perturbation are treated in the adiabatic, secularly averaged tidal approximation. This provides a starting point for a more detailed analysis by providing insights as to the companion parameter space likely to create DDO's. The second model includes the companion and the planets and numerically integrates perturbations on a sampling that is based on the real population of scattered disk objects (SDO's). A single calculation is performed including the mutual interactions and migration of the planets. By comparing these models, we distinguish the distant detached population that can be attributable to the secular interaction from those that require additional planetary perturbations. We find that a DDO can be produced by a hypothetical Neptune-mass companion having semiminor axis, b.sub.ca[c]1/22000AU or a Jupiter-mass companion with b.sub.ca[c]1/25000AU. DDO's produced by such a companion are likely to have small inclinations to the ecliptic only if the companion's orbit is significantly inclined. We also discuss the possibility that the tilt of the planets' invariable plane relative to the solar equatorial plane has been produced by such a hypothetical distant planetary-mass companion. Perturbations of a companion on Oort cloud comets are also considered. Author Affiliation: (a) Observatorio Nacional, Rua General Jose Cristino, 77, 20921-400 Rio de Janeiro, RJ, Brazil (b) Department of Physics, University of Louisiana at Lafayette, Lafayette, LA 70504-4210, USA (c) Space Science and Astrobiology Division, MS 245-3, NASA Ames Research Center, Moffett Field, CA 94035, USA Article History: Received 16 December 2005; Revised 18 May 2006

We study planetary migration in a gas-free disk of planetesimals. In the case of our Solar System we show that Neptune could have had either a damped migration, limited to a few AUs, or a forced migration up to the disk's edge, depending on the disk's mass density. We also study the possibility of runaway migration of isolated planets in very massive disk, which might be relevant for extra-solar systems. We investigate the problem of the mass depletion of the Kuiper belt in the light of planetary migration and conclude that the belt lost its pristine mass well before that Neptune reached its current position. Therefore, Neptune effectively hit the outer edge of the proto-planetary disk. We also investigate the dynamics of massive planetary embryos embedded in the planetesimal disk. We conclude that the elimination of Earth-mass or Mars-mass embryos originally placed outside the initial location of Neptune also requires the existence of a disk edge near 30 AU. Keywords: Kuiper belt Resonance; Solar System formation

I simulate the orbital evolution of the four major planets and a massive primordial planetesimal disk composed of [10.sup.4] objects, which perturb the planets but not themselves. As Neptune migrates by energy and angular momentum exchange with the planetesimals, a large number of primordial Neptune-scattered objects are formed. These objects may experience secular, Kozai, and mean motion resonances that induce temporary decrease of their eccentricities. Because planets are migrating, some planetesimals can escape those resonances while in a low-eccentricity incursion, thus avoiding the return path to Neptune close encounter dynamics. In the end, this mechanism produces stable orbits with high inclination and moderate eccentricities. The population so formed together with the objects coming from the classical resonance sweeping process, originates a bimodal distribution for the Kuiper Belt orbits. The inclinations obtained by the simulations can attain values above 30[degrees] and their distribution resembles a debiased distribution for the high-inclination population coming from the real classical Kuiper Belt. Keywords: Kuiper Belt; resonance; Solar System formation

Abstract: Numerical integrations of the equations of motion of the giant planets and scattering particles show that there is a possible orbital itinerary that a particle may follow from a scattering mode up to a stable position near the orbit of 2004 XR190. This orbital evolution requires that the particle gets trapped in a mean motion resonance with Neptune coupled with the Kozai resonance. Imposing migration on Neptune while a particle is experiencing both resonances can entail an escape from resonance at a low particle’s eccentricity. This eccentricity and the associated inclination are always similar to those of 2004 XR190. I conclude that 2004 XR190 was most likely a scattered object that went through those resonance processes and was eventually deposited at its current position. By the same argument, it is expected that there must exist several other objects with similar semimajor axis, eccentricity and inclination as those of 2004 XR190. [Copyright &y& Elsevier]