Constraints on Migration Scenarios of Neptune Due to Stochasticity

Observational signatures of outer solar system dynamics that require comparisons across several mean motion resonances (MMRs) in the trans-Neptunian population have been difficult to evaluate in the past due to observational limits. Well-characterized surveys such as the Outer Solar System Origins Survey (OSSOS) and the upcoming LSST provide an opportunity to look across the resonances and improve our understanding of the dynamical history of our solar system, making this an excellent time to be studying cross-MMR signatures. All standard scenarios of Neptune’s outward migration have a planetesimal-driven component at the end. Even a gravitational upheaval scenario will experience a planetesimal-driven migration component after some eccentricity damping. During this migration, “graininess” due to the finite sizes of planetesimals leads to imperfect retention of objects in MMRs. We explore how the stochasticity of the planetesimal-driven process limits the possible time spent in this phase of Neptune’s dynamical evolution. While noise has been considered in several models, the current literature is missing up-to-date constraints for how long and how far Neptune could have migrated before losing objects in resonance due to stochasticity, as well as constraints on the size distribution of planetesimals present during migration. Understanding the planetesimal-driven component provides a constraint on a unified model that explains MMR occupation over the full range of resonances. In this study, we identify the relative impact of noisy migration on resonance retention for all resonances up to fourth-order lying between the 3:2 and the 3:1, including the 5:2 which hosts a surprisingly large population of objects. Weaker resonances have not been taken into strong consideration in past studies. For a given size distribution of planetesimals, stochasticity is dominated by those with maximum Nm² where N is the number of planetesimals and m is the mass of the individual planetesimal, implying that the largest planetesimals primarily drive stochastic loss. We know that the residual planetesimal disk mass is significantly lower than it was before migration, but it is still uncertain what physical processes caused such a substantial depletion of material. We approach this question by finding a maximum constraint on the amount of mass in large (r ~ 800 km) objects during Neptune’s era of planetesimal-driven migration and drawing conclusions about the primordial size distribution of planetesimals. Our results provide constraints on the complicated migration scenarios needed to explain the Kuiper Belt.