Dust in resonant extrasolar Kuiper Belts: Grain size and wavelength dependence of disk structure

This paper considers the distribution of dust that originates in the breakup of planetesimals that are trapped in resonance with a planet. It is shown that there are three distinct grain populations with different spatial distributions: (I) large grains have the same clumpy resonant distribution as the planetesimals; (II) moderate- sized grains are no longer in resonance and have an axisymmetric distribution; and (III) small grains are blown out of the system by radiation pressure and so have a density distribution that falls off as tau proportional to 1/r. Population III can be further divided into two subclasses: (IIIa) grains produced from population I that exhibit trailing spiral structure that emanates from the resonant clumps and (IIIb) grains produced from population II that have an axisymmetric distribution. Since observations in different wavebands are sensitive to different dust sizes, multiwavelength imaging of debris disks can be used to test models that explain the submillimeter structure of debris disks as due to resonant trapping of planetesimals. For example, a collisional cascade without blowout grains would appear clumpy in the submillimeter ( which samples population I) and smooth at mid- to far- IR wavelengths ( which sample population II). The wavelength of transition from clumpy to smooth structure is indicative of the mass of the perturbing planet. The size distribution of Vega's disk is modeled showing that the large quantities of population III grains detected recently by Spitzer must originate in the destruction of the grains seen in the submillimeter images. Thus, at high resolution and sensitivity the far- and mid- IR structure of Vega's disk is predicted to include spiral structure emanating from the submillimeter clumps.