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 \sim 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 mass-less 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 mass-less 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 term 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 Fom c , which is at least Neptune-Saturn size , 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 .