Fomalhaut’s Debris Disk and Planet: Constraining the Mass of Fomalhaut B from Disk Morphology

Following the optical imaging of exoplanet candidate Fomalhaut b (Fom b), we present a numerical model of how Fomalhaut’s debris disk is gravitationally shaped by a single interior planet. The model is simple, adaptable to other debris disks, and can be extended to accommodate multiple planets. We find that to not disrupt the belt, Fom b must have a massMpl < 3MJ. Previous mass constraints based on disk morphology rely on several oversimplifications. We explain why our constraint is more reliable. It is based on a global model of the disk that is not restricted to the planet’s chaotic zone boundary. Moreover, we screen disk parent bodies for dynamical stability over the system age of ∼100 Myr, and model them separately from their dust grain progeny; the latter’s orbits are strongly affected by radiation pressure and their lifetimes are limited to ∼0.1 Myr by destructive grain-grain collisions. The single planet model predicts that planet and disk orbits be apsidally aligned. Preliminary analysis of Fom b’s space velocity does not bear this out. The disagreement might be resolved by having additional perturbers in the Fomalhaut system, for which there is independent evidence from the star’s anomalous Hipparcos acceleration. Our upper mass limit of 3MJ for Fom b is not affected by these considerations. The belt contains at least 3M⊕ of solids that are grinding down to dust. Such a large mass in solids is consistent with Fom b having formed in situ. Subject headings: stars: planetary systems — stars: circumstellar matter — planetary systems: protoplanetary disks — celestial mechanics — stars: individual (Fomalhaut)