Numerical Simulations of Collisional Cascades at the Roche Limits of White Dwarf Stars

Abstract

We consider the long-term collisional and dynamical evolution of solid material orbiting in a narrow annulus near the Roche limit of a white dwarf. With orbital velocities of 300  , systems of solids with initial eccentricity generate a collisional cascade where objects with radii are ground to dust. This process converts 1–100 km asteroids into 1  μ m particles in 10 2 −10 6 yr. Throughout this evolution, the swarm maintains an initially large vertical scale height H . Adding solids at a rate enables the system to find an equilibrium where the mass in solids is roughly constant. This equilibrium depends on and , the radius of the largest solid added to the swarm. When  ≲ 10 km, this equilibrium is stable. For larger , the mass oscillates between high and low states; the fraction of time spent in high states ranges from 100% for large to much less than 1% for small . During high states, the stellar luminosity reprocessed by the solids is comparable to the excess infrared emission observed in many metallic line white dwarfs.