Dust in Resonant Extrasolar Kuiper Belts — Grain Size and Wavelength Dependence of Disk Structure

This paper considers the distribution of dust which originates in the break-up of planetesimals that are trapped in resonance with a planet. The effect of radiation pressure on small dust grains causes their orbits and so their spatial distribution to be significantly different to that of the parent planetesimals which previous work has shown to be clumpy. It is shown that there are three distinct grain populations: (I) large grains (> a few mm) have the same clumpy resonant distribution as the planetesimals; (II) moderate sized grains (a few μm to a few mm) are no longer in resonance and have an axisymmetric distribution; (III) small grains (< a few μm) are blown out of the system by radiation pressure immediately on creation and so have a density distribution which falls off as τ ∝ 1/r, however the structure of these grains can be further divided into two subclasses: (IIIa) grains produced in the destruction of population I grains that exhibit trailing spiral structure which emanates from the resonant clumps; and (IIIb) grains produced from population II grains that have an axisymmetric distribution. Since observations in different wavebands are sensitive to different sized dust grains, multi-wavelength imaging of debris disks provides a valuable observational test of models which explain structure seen in sub-mm observations as due to resonant trapping of planetesimals. For example, a disk with a collisional cascade dust size distribution with no blow-out grains would appear clumpy in the sub-mm (which samples population I grains), and smooth at midto far-IR wavelengths (which sample population II grains). 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 in the light of the recent Spitzer observations showing that collisions with the large quantities of population III grains seen in the midto far-IR may be responsible for the low levels of population II grains in this system. The origin of these population III grains must be in the destruction of the grains seen in the sub-mm images, and so at high resolution and sensitivity the far-IR and mid-IR structure of the Vega disk is predicted to include spiral structure emanating from the sub-mm clumps. Such structure could be detected with MIRI on the JWST and, if so, would confirm the presence of a planet at 65 AU in the Vega disk as well as determine the direction of its orbit. Subject headings: celestial mechanics — circumstellar matter — planetary systems: formation — stars: individual (Vega)