Gravitational stirring in planetary debris disks

We describe gravitational stirring models of planetary debris disks using a new multiannulus planetesimal evolution code. The current code includes gr avitational stirring and dynamical friction; future studies will include co agulation, fragmentation, Poynting-Robertson drag, and other physical proce sses. We use the results of our calculations to investigate the physical co nditions required for small bodies in a planetesimal disk to reach the shat tering velocity and begin a collisional cascade. Our results demonstrate th at disks composed primarily of bodies with a single size will not undergo a collisional cascade that produces small dust grains at 30-150 AU on timesc ales of 1 Gyr or smaller. Disks with a size distribution of bodies reach co nditions necessary for a collisional cascade in 10 Myr to 1 Gyr if the disk is at least as massive as a minimum mass solar nebula and if the disk cont ains objects with radii of 500 km or larger. The estimated similar to 500 M yr survival time for these disks is close to the median age of similar to 4 00 Myr derived for nearby stars with dusty disks.