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 km/sec, systems of solids with initial eccentricity $e\gtrsim 10^{-3}$ generate a collisional cascade where objects with radii $r\lesssim$ 100--300 km are ground to dust. This process converts 1-100 km asteroids into 1 $\mu$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 $\dot{M}$ enables the system to find an equilibrium where the mass in solids is roughly constant. This equilibrium depends on $\dot{M}$ and $r_0$, the radius of the largest solid added to the swarm. When $r_0\lesssim$ 10 km, this equilibrium is stable. For larger $r_0$, the mass oscillates between high and low states; the fraction of time spent in high states ranges from 100% for large $\dot{M}$ to much less than 1% for small $\dot{M}$. During high states, the stellar luminosity reprocessed by the solids is comparable to the excess infrared emission observed in many metallic line white dwarfs.

37 pages of text, 12 figures, ApJ, accepted

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