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. If Fom b is the dominant perturber of the belt, then to produce the observed disk morphology it must have a mass M-pl < 3M(J), an orbital semimajor axis a(pl) > 101.5 AU, and an orbital eccentricity e(pl) = 0.11-0.13. These conclusions are independent of Fom b's photometry. To not disrupt the disk, a greater mass for Fom b demands a smaller orbit farther removed from the disk; thus, future astrometric measurement of Fom b's orbit, combined with our model of planet-disk interaction, can be used to determine the mass more precisely. The inner edge of the debris disk at a approximate to 133 AU lies at the periphery of Fom b's chaotic zone, and the mean disk eccentricity of e approximate to 0.11 is secularly forced by the planet, supporting predictions made prior to the discovery of Fom b. However, 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 similar to 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 similar to 0.1 Myr by destructive grain-grain collisions. The single planet model predicts that planet and disk orbits be apsidally aligned. Fomalhaut b's nominal space velocity does not bear this out, but the astrometric uncertainties may be large. If the apsidal misalignment proves real, our calculated upper mass limit of 3MJ still holds. If the orbits are aligned, our model predicts M-pl = 0.5M(J), a(pl) = 115 AU, and e(pl) = 0.12. Parent bodies are evacuated from mean-motion resonances with Fom b; these empty resonances are akin to the Kirkwood gaps opened by Jupiter. The belt contains at least 3M(circle plus) of solids that are grinding down to dust, their velocity dispersions stirred so strongly by Fom b that collisions are destructive. Such a large mass in solids is consistent with Fom b having formed in situ.