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

## TL;DR

This study models the long-term collisional evolution of solid debris near white dwarf Roche limits, showing how asteroid-sized objects break down into dust and influence observed infrared excesses.

## Contribution

It introduces a detailed simulation of collisional cascades at white dwarf Roche limits, revealing equilibrium states and their dependence on input parameters.

## Key findings

- Small asteroids produce dust within 10^2 - 10^6 years.
- System stability depends on initial solid size and mass input rate.
- High states of dust production match observed infrared excesses.

## 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.