Modeling Collisional Cascades In Debris Disks: The Numerical Method

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.

24 pages, 20 figues, Published in ApJ

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• Suspicious Siblings: The Distribution of Mass and Spin Across Component Black Holes in Isolated Binary Evolution
• SMACK: A New Algorithm for Modeling Collisions and Dynamics of Planetesimals in Debris Disks
• Spatially resolved imaging of the inner Fomalhaut disk using JWST/MIRI
• New HST data and modeling reveal a massive planetesimal collision around Fomalhaut
• Extreme Debris Disk Variability -- Exploring the Diverse Outcomes of Large Asteroid Impacts During the Era of Terrestrial Planet Formation
• Variations on Debris Disks III. Collisional Cascades and Giant Impacts in the Terrestrial Zones of Solar-type Stars
• A dearth of small particles in debris disks: An energy-constrained smallest fragment size
• Grain Size segregation in debris discs
• Resolved Millimeter Emission from the HD 15115 Debris Disk
• On the steady state collisional evolution of debris disks around M dwarfs
• Variations on Debris Disks IV. An Improved Analytical Model for Collisional Cascades
• Herschel Observations and Updated Spectral Energy Distributions of Five Sunlike Stars with Debris Disks
• Four new PLanetesimals Around TYpical and Pre-main seqUence Stars (PLATYPUS) Debris Discs at 8.8mm
• Conglomeration of kilometre-sized planetesimals
• JWST/MIRI Imaging of the Warm Dust Component of the Epsilon Eridani Debris Disk