A planetary system as the origin of structure in Fomalhaut's dust belt

Abstract

The Sun and >15 percent of nearby stars are surrounded by dusty debris disks that must be collisionally replenished by asteroids and comets, as the dust would otherwise be depleted on <10 Myr timescales (ref. 1). Theoretical studies show that disk structure can be modified by the gravitational influence of planets (ref. 2-4), but the observational evidence is incomplete, at least in part because maps of the thermal infrared emission from disks have low linear resolution (35 AU in the best case; ref. 5). Optical images provide higher resolution, but the closest examples (AU Mic and Beta Pic) are edge-on (ref. 6,7), preventing the direct measurement of azimuthal and radial disk structure that is required for fitting theoretical models of planetary perturbations. Here we report the detection of optical light reflected from the dust grains orbiting Fomalhaut (HD 216956). The system is inclined 24 degrees away from edge-on, enabling the measurement of disk structure around its entire circumference, at a linear resolution of 0.5 AU. The dust is distributed in a belt 25 AU wide, with a very sharp inner edge at a radial distance of 133 AU, and we measure an offset of 15 AU between the belt's geometric centre and Fomalhaut. Taken together, the sharp inner edge and offset demonstrate the presence of planet-mass objects orbiting Fomalhaut.

arXiv comment8 pages, 3 figures, 1 table

References in corpus (8)

• The COBE Diffuse Infrared Background Experiment Search for the Cosmic Infrared Background: II. Model of the Interplanetary Dust Cloud
• How Observations of Circumstellar Disk Asymmetries Can Reveal Hidden Planets: Pericenter Glow and its Application to the HR 4796 Disk
• Collisional Processes in Extrasolar Planetsimal Disks - Dust Clumps in Fomalhaut's Debris Disk
• Discovery of a large dust disk around the nearby star AU Microscopium
• HST/ACS Coronagraphic Imaging of the Circumstellar Disk around HD1415659A
• The Geometry of Resonant Signatures in Debris Disks with Planets
• A Study of the Dynamics of Dust from the Kuiper Belt: Spatial Distribution and Spectral Energy Distribution
• Apse Alignment of Narrow Eccentric Planetary Rings

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