Collisional Cascades in Planetesimal Disks. I. Stellar Flybys

We use a new multiannulus planetesimal accretion code to investigate the evolution of a planetesimal disk following a moderately close encounter with a passing star. The calculations include fragmentation, gas and Poynting-Robertson drag, and velocity evolution from dynamical friction and viscous stirring. We assume that the stellar encounter increases planetesimal velocities to the shattering velocity, initiating a collisional cascade in the disk. During the early stages of our calculations, erosive collisions damp particle velocities and produce substantial amounts of dust. For a wide range of initial conditions and input parameters, the time evolution of the dust luminosity follows a simple relation, Ld/L* = L0/[α + (t/td)β]. The maximum dust luminosity L0 and the damping time td depend on the disk mass, with L0 ∝ Md and td ∝ M. For disks with dust masses of 1%–100% of the "minimum-mass solar nebula" (1–100 M⊕ at 30–150 AU), our calculations yield td ∼ 1–10 Myr, α ≈ 1–2, β = 1, and dust luminosities similar to the range observed in known "debris disk" systems, L0 ∼ 10-3 to 10-5. Less massive disks produce smaller dust luminosities and damp on longer timescales. Because encounters with field stars are rare, these results imply that moderately close stellar flybys cannot explain collisional cascades in debris disk systems with stellar ages of ∼100 Myr or longer.