On the migration of two planets in a disc and the formation of mean motion resonances

TL;DR

This paper investigates how two super-Earths migrate within a protoplanetary disc, showing that their interactions often lead to resonant configurations, with migration direction depending on disc parameters and initial conditions.

Contribution

It introduces a simple irradiated viscous disc model and uses analytical prescriptions to study planet migration, revealing the conditions for convergent or divergent migration and resonance formation.

Findings

Most simulated systems end in resonant configurations.

Migration can be inward or outward depending on disc parameters.

Resonant systems are typically periodic configurations.

Abstract

We study the dynamics of a system of two super-Earths embedded in a protoplanetary disc. We build a simple model of an irradiated viscous disc and use analytical prescriptions for the planet-disc interactions which lead to migration. We show that depending on the disc parameters, planets' masses and their positions in the disc, the migration of each planet can be inward or outward and the migration of a two-planet system can be convergent (which may lead to formation of a first order mean motion resonance, MMR) or divergent (a system moves away from MMR). We performed $3500$ simulations of the migration of two-planet systems with various masses and initial orbits. Almost all of them end up as resonant configurations, although the period ratios may be very distant from the nominal values of a given MMR. We found that almost all the systems resulting from the migration are periodic configurations.