On the Super-Earths locked in the 3:2 mean-motion resonance

Abstract

The first study of migration-induced resonances in a pair of Earth-like planets has been performed by Papaloizou & Szuszkiewicz (2005). They concluded that in the case of disparate masses embedded in a disc with the surface density expected for a minimum mass solar nebula at 5.2 au, the most likely resonances are ratios of large integers, such as 8:7. For equal masses, planets tend to enter into the 2:1 or 3:2 resonance. In Papaloizou & Szuszkiewicz (2005) the two low-mass planets have masses equal to 4 Earth masses, chosen to mimic the very well known example of two pulsar planets which are close to the 3:2 resonance. That study has stimulated quite a few interesting questions. One of them is considered here, namely how the behaviour of the planets close to the mean-motion resonance depends on the actual values of the masses of the planets. We have chosen a 3:2 commensurability and investigated the outcome of an orbital migration in the vicinity of this resonance in the case of a pair of equal mass super-Earths, whose mass is either 5 or 8 Earth masses.