On the nature of clumps in debris disks

The azimuthal substructure observed in some debris disks, as exemplified by epsilon Eridani, is usually attributed to resonances with embedded planets. In a standard scenario, the Poynting-Robertson force, possibly enhanced by the stellar wind drag, is responsible for the delivery of dust from outer regions of the disk to locations of external mean-motion planetary resonances; the captured particles then create characteristic clumps. Alternatively, it has been suggested that the observed features in systems like epsilon Eri may stem from populations of planetesimals that have been captured in resonances with the planet, such as Plutinos and Trojans in the solar system. A large fraction of dust produced by these bodies would stay locked in the same resonance, creating the dusty clumps. To investigate both scenarios and their applicability limits for a wide range of stars, planets, disk densities, and planetesimal families we construct simple analytic models for both scenarios. In particular, we show that the first scenario works for disks with the pole-on optical depths below about similar to 10(-4)-10(-5). Above this optical depth level, the first scenario will generate a narrow resonant ring with a hardly visible azimuthal structure, rather than clumps. It is slightly more efficient for more luminous/massive stars, more massive planets, and planets with smaller orbital radii, but all these dependencies are weak. The efficiency of the second scenario is proportional to the mass of the resonant planetesimal family, as example, a family with a total mass of similar to 0.01 to 0.1 Earth masses could be sufficient to account for the clumps of epsilon Eridani. The brightness of the clumps produced by the second scenario increases with the decreasing luminosity of the star, increasing planetary mass, and decreasing orbital radius of the planet. All these dependencies are much stronger than in the first scenario. Models of the second scenario are quantitatively more uncertain than those of the first one, because they are very sensitive to poorly known properties of the collisional grinding process.