Migration of planets embedded in a circumstellar disk

TL;DR

This paper investigates planetary migration within planetesimal disks using analytic and numerical methods, revealing that large planets do not migrate significantly when multiple planets stir the disk, impacting theories of planet formation.

Contribution

It combines analytic derivations with N-body simulations to analyze migration rates and shows that multiple planets halt large-scale migration in planetesimal disks.

Findings

Migration rates scale inversely with planet mass and eccentricity.

Large-scale migration ceases when multiple planets stir the disk.

Migration has limited impact on terrestrial planet formation.

Abstract

Planetary migration poses a serious challenge to theories of planet formation. In gaseous and planetesimal disks, migration can remove planets as quickly as they form. To explore migration in a planetesimal disk, we combine analytic and numerical approaches. After deriving general analytic migration rates for isolated planets, we use N-body simulations to confirm these results for fast and slow migration modes. Migration rates scale as 1/m (for massive planets) and 1/(1+(e_H/3)^3), where m is the mass of a planet and e_H is the eccentricity of the background planetesimals in Hill units. When multiple planets stir the disk, our simulations yield the new result that large-scale migration ceases. Thus, growing planets do not migrate through planetesimal disks. To extend these results to migration in gaseous disks, we compare physical interactions and rates. Although migration through a gaseous disk is an important issue for the formation of gas giants, we conclude that migration has little impact on the formation of terrestrial planets.