Collisional Cascades in Planetesimal Disks. I. Stellar Flybys

We use a new multiannulus planetesimal accretion code to investigate theevolution of a planetesimal disk following a moderately close encounter with apassing star. The calculations include fragmentation, gas andPoynting-Robertson drag, and velocity evolution from dynamical friction andviscous stirring. We assume that the stellar encounter increases planetesimalvelocities to the shattering velocity, initiating a collisional cascade in thedisk. During the early stages of our calculations, erosive collisions dampparticle velocities and produce substantial amounts of dust. For a wide rangeof initial conditions and input parameters, the time evolution of the dustluminosity follows a simple relation, L_d/L_{\star} = L_0 / [alpha +(t/t_d)^{beta}]. The maximum dust luminosity L_0 and the damping time t_ddepend on the disk mass, with L_0 proportional to M_d and t_d proportional toM_d^{-1}. For disks with dust masses of 1% to 100% of the `minimum mass solarnebula' (1--100 earth masses at 30--150 AU), our calculations yield t_d approx1--10 Myr, alpha approx 1--2, beta = 1, and dust luminosities similar to therange observed in known `debris disk' systems, L_0 approx 10^{-3} to 10^{-5}.Less massive disks produce smaller dust luminosities and damp on longertimescales. Because encounters with field stars are rare, these results implythat moderately close stellar flybys cannot explain collisional cascades indebris disk systems with stellar ages of 100 Myr or longer.