Modeling Collisional Cascades In Debris Disks: The Numerical Method

TL;DR

This paper introduces a novel numerical algorithm for modeling collisional cascades in debris disks, accounting for erosive and catastrophic collisions with improved stability and convergence, revealing faster particle decay when erosive collisions are included.

Contribution

The paper presents a new numerical method that accurately models erosive and catastrophic collisions in debris disks, improving upon previous approaches.

Findings

Erosive collisions accelerate particle decay in debris disks.

The algorithm demonstrates stability and convergence in simulations.

Inclusion of erosive collisions yields faster decay rates.

Abstract

We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.