Abstract

Context. The eccentric shape of the debris disk observed around the star Fomalhaut was first attributed to Fom b, a companion detected near the belt inner edge, but new constraints on its orbit revealed that it is belt-crossing, highly eccentric (e ~ 0.6-0.9), and can hardly account for the shape of the belt. The best scenario to explain this paradox is that there is another massive body in this system, Fom c, which drives the debris disk shape. The resulting planetary system is highly unstable, which hints at a dynamical scenario involving a recent scattering of Fom b on its current orbit, potentially with the putative Fom c. Aims: Our goal is to give insights on the probability for Fom b to have been set on its highly eccentric orbit by a close encounter with the putative Fom c. We aim to study in particular the part played by mean-motion resonances with Fom c, which could have brought Fom b sufficiently close to Fom c for it to be scattered on its current orbit, but also delay this scattering event. Methods: We assumed that Fom c is much more massive than Fom b, that is, Fom b behaves as a massless test particle compared to Fom c. This allowed us to use N-body numerical simulations and to study the influence of a fixed orbit Fom c on a population of massless test particles, that is, to study the generation of Fom b-like orbits by direct scattering events or via mean-motion resonance processes. We assumed that Fom b originated from an orbit inner to that of the putative Fom c. Results: We found that the generation of orbits similar to that of Fom b, either in terms of dimensions or orientation, is a robust process involving a scattering event and a further secular evolution of inner material with an eccentric massive body such as the putative Fom c. We found in particular that mean-motion resonances can delay scattering events, and thus the production of Fom b-like orbits, on timescales comparable to the age of the system, thus explaining the witnessing of an unstable configuration. Conclusions: We conclude that Fom b probably originated from an inner resonance with a Neptune-Saturn mass Fom c, and was set on its current orbit by a scattering event with Fom c. Since Fom b could not have formed from material in resonance, our scenario also hints at former migration processes in this planetary system.