Non-Power Law Behavior in Fragmentation Cascades

Abstract

Collisions resulting in fragmentation are important in shaping the mass spectrum of minor bodies in the asteroid belt, the Kuiper belt, and debris disks. Models of fragmentation cascades typically find that in steady-state, the solution for the particle mass distribution is a power law in the mass. However, previous studies have typically assumed that the mass of the largest fragment produced in a collision with just enough energy to shatter the target and disperse half its mass to infinity is directly proportional to the target mass. We show that if this assumption is not satisfied, then the power law solution for the steady-state particle mass distribution is modified by a multiplicative factor, which is a slowly varying function of the mass. We derive analytic solutions for this correction factor and confirm our results numerically. We find that this correction factor proves important when extrapolating over many orders of magnitude in mass, such as when inferring the number of large objects in a system based on infrared observations. In the course of our work, we have also discovered an unrelated type of non-power law behavior: waves can persist in the mass distribution of objects even in the absence of upper or lower cutoffs to the mass distribution or breaks in the strength law.

37 pages, 5 figures, accepted to Icarus

References in corpus (6)

• Steady-State Size Distributions for Collisional Populations: Analytical Solution with Size-Dependent Strength
• Collisional processes and size distribution in spatially extended debris discs
• Collisional Evolution of Irregular Satellite Swarms: Detectable Dust around Solar System and Extrasolar Planets
• Variations on Debris Disks II. Icy Planet Formation as a Function of the Bulk Properties and Initial Sizes of Planetesimals
• Collisional and Thermal Emission Models of Debris Disks: Towards Planetesimal Population Properties
• The Collisional Divot in the Kuiper belt Size Distribution

Cited by in corpus (10)

• Debris disk size distributions: steady state collisional evolution with P-R drag and other loss processes
• Modeling Collisional Cascades In Debris Disks: Steep Dust-Size Distributions
• Self-consistent size and velocity distributions of collisional cascades
• Coagulation Calculations of Icy Planet Formation at 15--150 AU: A Correlation Between the Maximum Radius and the Slope of the Size Distribution for Transneptunian Objects
• Fomalhaut b as a Cloud of Dust: Testing Aspects of Planet Formation Theory
• Multi-Epoch Observations of HD69830: High Resolution Spectroscopy and Limits to Variability
• Planet formation in stellar binaries: Global simulations of planetesimal growth
• Multiwavelength Vertical Structure in the AU Mic Debris Disk: Characterizing the Collisional Cascade
• Coagulation Calculations of Icy Planet Formation Around 0.1--0.5~\msun\ Stars: Super-Earths From Large Planetestimals
• O(N^2) fragmentation algorithm