Scattered Disk Dynamics: The Mapping Approach

We derive, and discuss the properties of, a symplectic map for the dynamics of bodies on nearly parabolic orbits. The orbits are perturbed by a planet on a circular, coplanar orbit interior to the pericenter of the parabolic orbit. The map shows excellent agreement with direct numerical integrations and elucidates how the dynamics depends on perturber mass and pericenter distance. We also use the map to explore the onset of chaos, statistical descriptions of chaotic transport, and sticking in mean-motion resonances. We discuss implications of our mapping model for the dynamical evolution of the solar system's scattered disk and other highly eccentric trans-Neptunian objects.Comment: submitted to MNRA

Intra-system uniformity: a natural outcome of dynamical sculpting

There is evidence that exoplanet systems display intra-system uniformity in mass, radius, and orbital spacing (like "peas in a pod") when compared with the system-to-system variations of planetary systems. This has been interpreted as the outcome of the early stages of planet formation, indicative of a picture in which planets form at characteristic mass scales with uniform separations. In this paper, we argue instead that intra-system uniformity in planet sizes and orbital spacings likely arose from the long-term dynamical sculpting of initially-overly-packed planetary systems (in other words, the giant impact phase). With a suite of $N$-body simulations, we demonstrate that systems with random initial masses and compact planet spacings naturally develop intra-system uniformity, in quantitative agreement with observations, due to collisions between planets. Our results suggest that the pre-giant impact planet mass distribution is fairly wide and provide evidence for the prevalence of dynamical sculpting in shaping the observed population of exoplanets.Comment: 5 pages, 5 figures. Submitted to MNRAS Letter