Exploring the recycling model of Phobos formation: rubble-pile satellites

Phobos is the target of the return sample mission Martian Moons eXploration that will provide a better understanding of the satellite's composition, giving clues about its formation. Some models propose that Phobos and Deimos were formed after a giant impact forming an extended debris disk.  Assuming that Phobos and it parents bodies have a low material cohesion Hesselbrock and Milton (2017) have showed that a "recycling process" may happen during the assembling of Phobos, by which Phobos' parents are destroyed into a Roche-interior ring and reaccreted several times. We explore in details the recycling model, and pay particular attention to the characteristics of the disk using 1D models of disk/satellite interactions. In agreement with previous studies we confirm that , if Phobos' parents bodies are indeed rubble piles, then the recycling process do occurs. However, Phobos should be accompanied today by a Roche-interior ring which characteristics are not reconcilable with today observations of Mars' environment. Indeed a residual ring should exist in addition to Phobos, that is not observed. Thus we conclude that, if Phobos formed in a giant impact, its parent bodies should have been cohesive and there was never a recycling process. In this hypothesis, Phobos is the last object of and old moonlets population that migrated toward and  crashed onto Mars. Alternatively, if Phobos' parent bodies were cohesive-less, then we do find one solution: the giant impact should have happened recently (<2 Gyrs ago) and that a Mars ring should exist today with optical depth 1e-5 with particle size about a few meters size.