A NEW ALGORITHM FOR SELF-CONSISTENT THREE-DIMENSIONAL MODELING OF COLLISIONS IN DUSTY DEBRIS DISKS

We present a new "collisional grooming" algorithm that enables us to model images of debris disks where the collision time is less than the Poynting-Robertson (PR) time for the dominant grain size. Our algorithm uses the output of a collisionless disk simulation to iteratively solve the mass flux equation for the density distribution of a collisional disk containing planets in three dimensions. The algorithm can be run on a single processor in similar to 1 hr. Our preliminary models of disks with resonant ring structures caused by terrestrial mass planets show that the collision rate for background particles in a ring structure is enhanced by a factor of a few compared to the rest of the disk, and that dust grains in or near resonance have even higher collision rates. We show how collisions can alter the morphology of a resonant ring structure by reducing the sharpness of a resonant ring's inner edge and by smearing out azimuthal structure. We implement a simple prescription for particle fragmentation and show how PR drag and fragmentation sort particles by size, producing smaller dust grains at smaller circumstellar distances. This mechanism could cause a disk to look different at different wavelengths, and may explain the warm component of dust interior to Fomalhaut's outer dust ring seen in the resolved 24 mu m Spitzer image of this system.