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

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.

5 pages, 3 figures, Accepted for publication as a Letter in Astronomy & Astrophysics

References in corpus (3)

• Herschel images of Fomalhaut. An extrasolar Kuiper Belt at the height of its dynamical activity
• Outer edges of debris discs: how sharp is sharp?
• Collisional and Thermal Emission Models of Debris Disks: Towards Planetesimal Population Properties

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