SIMBAD references

This paper is an extension of the work done by Pierens & Nelson in which they investigated the behaviour of a two-planet system embedded in a protoplanetary disc. They put a Jupiter mass gas giant on the internal orbit and a lower mass planet on the external one. We consider here a similar problem taking into account a gas giant with mass in the range 0.5 to 1 M_J and a Super-Earth (i.e. a planet with mass ≤10 M_⊕) as the outermost planet. By changing disc parameters and planet masses, we have succeeded in getting the convergent migration of the planets which allows for the possibility of their resonant locking. However, in the case in which the gas giant has the mass of Jupiter, before any mean-motion first-order commensurability could be achieved, the Super-Earth is caught in a trap when it is very close to the edge of the gap opened by the giant planet. This confirms the result obtained by Pierens & Nelson in their simulations. Additionally, we have found that, in a very thin disc, an apsidal resonance is observed in the system if the Super-Earth is captured in the trap. Moreover, the eccentricity of the small planet remains low, while the eccentricity of the gas giant increases slightly due to the imbalance between Lindblad and corotational resonances. We have also extended the work of Pierens & Nelson by studying analogous systems in which the gas giant is allowed to take sub-Jupiter masses. In this case, after conducting an extensive survey over all possible parameters, we have succeeded in getting the 1:2 mean-motion resonant configuration only in a disc with low aspect ratio and low surface density. However, the resonance is maintained just for a few thousand orbits. Thus, we conclude that for typical protoplanetary discs the mean-motion commensurabilities are rare if the Super-Earth is located on the external orbit relative to the gas giant.