On the migration of three planets in a protoplanetary disc and the formation of chains of mean motion resonances

Abstract

We study the migration of three-planet systems in an irradiated 1+1D $\alpha$-disc with photoevaporation. We performed $2700$ simulations with various planets' masses and initial orbits. We found that most of the systems which ended up as compact configurations form chains of mean motion resonances (MMRs) of the first and higher orders. Most of the systems involved in chains of MMRs are periodic configurations. The period ratios of such system, though, are not necessarily close to exact commensurability. If a given system resides in a divergent migration zone in the disc, the period ratios increase and evolve along resonant divergent migration paths at ($P_2/P_1, P_3/P_2)$-diagram, where $P_1, P_2, P_3$ are the orbital periods of the first, second and third planet, respectively. The observed systems, though, do not lie on those paths. We show that an agreement between the synthetic and the observed systems distributions could be achieved if the orbital circularization was slower than it results from models of the planet-disc interactions. Therefore, we conclude that most of those systems unlikely formed as a result of divergent migration out of nominal chains of MMRs.