Conditions for the occurrence of mean-motion resonances in a low mass planetary system

TL;DR

This paper investigates how different migration rates in low-mass planetary systems influence the formation of mean-motion resonances, identifying conditions under which various resonances can occur and persist.

Contribution

It provides a combined numerical and analytical study of resonance formation conditions for migrating low-mass planets, highlighting the impact of migration speed and planetary mass ratios.

Findings

Slow migration favors 2:1 resonance formation.

Fast migration can produce high-degree resonances like 8:7 or 11:10.

Multiple resonances can form sequentially during large-scale migration.

Abstract

The dynamical interactions that occur in newly formed planetary systems may reflect the conditions occurring in the protoplanetary disk out of which they formed. With this in mind, we explore the attainment and maintenance of orbital resonances by migrating planets in the terrestrial mass range. Migration time scales varying between millions of years and thousands of years are considered. In the former case, for which the migration time is comparable to the lifetime of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter, relatively rapid migration regime commensurabilities of high degree such as 8:7 or 11:10 may be formed. However, in any one large-scale migration several different commensurabilities may be formed sequentially, each being associated with significant orbital evolution. We also use a simple analytic theory to develop conditions for first order commensurabilities to be formed. These depend on the degree of the commensurability, the imposed migration and circularization rates, and the planet mass ratios. These conditions are found to be consistent with the results of our simulations.