A dearth of small particles in debris disks: An energy-constrained smallest fragment size

TL;DR

This paper derives an energy-based lower limit for the smallest dust fragments in debris disks, explaining why observed grains are often larger than the radiation blow-out size and improving modeling accuracy.

Contribution

It introduces a new analytical method to determine the smallest fragment size in debris disks based on energy conservation, enhancing existing collision models.

Findings

Smallest fragments depend on collision velocity, material properties, and largest fragment size.

Results align with observations of grains larger than the blow-out size in specific debris disks.

Provides a practical recipe for implementation in debris disk modeling codes.

Abstract

A prescription for the fragment size distribution resulting from dust grain collisions is essential when modelling a range of astrophysical systems, such as debris disks and planetary rings. While the slope of the fragment size distribution and the size of the largest fragment are well known, the behaviour of the distribution at the small size end is theoretically and experimentally poorly understood. This leads debris disk codes to generally assume a limit equal to, or below, the radiation blow-out size. We use energy conservation to analytically derive a lower boundary of the fragment size distribution for a range of collider mass ratios. Focussing on collisions between equal-sized bodies, we apply the method to debris disks. For a given collider mass, the size of the smallest fragments is found to depend on collision velocity, material parameters, and the size of the largest fragment. We provide a physically motivated recipe for the calculation of the smallest fragment, which can be easily implemented in codes for modelling collisional systems. For plausible parameters, our results are consistent with the observed predominance of grains much larger than the blow-out size in Fomalhaut's main belt and in the Herschel cold debris disks.