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 , L _ { d } / L _ { \star } = L _ { 0 } / [ \alpha + ( t / t _ { d } ) ^ { \beta } ] .
The maximum dust luminosity L _ { 0 } and the damping time t _ { d } depend on the disk mass , with L _ { 0 } \propto M _ { d } and t _ { d } \propto M _ { d } ^ { -1 } .
For disks with dust masses of 1 % to 100 % of the ‘ minimum mass solar nebula ’ ( 1–100 M _ { \oplus } at 30–150 AU ) , our calculations yield t _ { d } \sim 1–10 Myr , \alpha \approx 1–2 , \beta = 1 , and dust luminosities similar to the range observed in known ‘ debris disk ’ systems , L _ { 0 } \sim 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 can not explain collisional cascades in debris disk systems with stellar ages of \sim 100 Myr or longer .