How the presence of a gas giant affects the formation of mean-motion resonances between two low-mass planets in a locally isothermal gaseous disc

In this paper we investigate the possibility of a migration-induced resonance locking in systems containing three planets, namely an Earth analogue (1 M⊕), a super-Earth (4 M⊕) and a gas giant (one Jupiter mass). The planets have been listed in order of increasing orbital periods. All three bodies are embedded in a locally isothermal gaseous disc and orbit around a solar mass star. We are interested in answering the following questions: will the low-mass planets form the same resonant structures with each other in the vicinity of the gas giant as in the case when the gas giant is absent? More in general, how will the presence of the gas giant affect the evolution of the two low-mass planets? When there is no gas giant in the system, it has been already shown that if the two low-mass planets undergo a convergent differential migration, they will capture each other in a mean-motion resonance. For the choices of disc parameters and planet masses made in this paper, the formation of the 5:4 resonance in the absence of the Jupiter has been observed in a previous investigation and confirmed here. In this work we add a gas giant on the most external orbit of the system in such a way that its differential migration is convergent with the low-mass planets. We show that the result of this set-up is the speeding up of the migration of the super-Earth and, after that, all three planets become locked in a triple mean-motion resonance. However, this resonance is not maintained due to the low-mass planet eccentricity excitation, a fact that leads to close encounters between planets and eventually to the ejection from the internal orbits of one or both low-mass planets. We have observed that the ejected low-mass planets can leave the system, fall into a star or become the external planet relative to the gas giant. In our simulations the latter situation has been observed for the super-Earth. It follows from the results presented here that the presence of a Jupiter-like planet might have a strong influence on the architecture of planetary systems. Moreover, the planet ejections due to the gas giant action may lead to the formation of a population of low-mass freely floating planets.