Clearing Residual Planetesimals by Sweeping Secular Resonances in Transitional Disks: A Lone-planet Scenario for the Wide Gaps in Debris Disks around Vega and Fomalhaut

Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent "lone-planet" scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. With a series of numerical simulations, we show that the gravitational potential of the natal disk induces the planet to precess. At the locations where its precession frequency matches the precession frequency the planet imposes on the residual planetesimals, their eccentricity is excited by its resonant perturbation. Due to the hydrodynamic drag by the residual disk gas, the planetesimals undergo orbital decay as their excited eccentricities are effectively damped. During the depletion of the disk gas, the planet's secular resonance propagates inward and clears a wide gap over an extended region of the disk. Although some residual intermediate-size planetesimals may remain in the gap, their surface density is too low to either produce super-Earths or lead to sufficiently frequent disruptive collisions to generate any observable dusty signatures. The main advantage of this lone-planet sweeping-secular-resonance model over the previous multiple gas giant tidal truncation scenario is the relaxed requirement on the number of gas giants. The observationally inferred upper mass limit can also be satisfied provided the hypothetical planet has a significant eccentricity. A significant fraction of solar or more massive stars bear gas giant planets with significant eccentricities. If these planets acquired their present-day kinematic properties prior to the depletion of their natal disks, their sweeping secular resonance would effectively impede the retention of neighboring planets and planetesimals over a wide range of orbital semimajor axes.