Collisional processes in extrasolar planetesimal discs – dust clumps in Fomalhaut’s debris disc

This paper presents a model for the outcome of collisions between planetesimals in a debris disc, and assesses the impact of collisional processes on the structure and size distribution of the disc. The model is presented by its application to Fomalhaut’s collisionally replenished dust disc; a recent 450-μm image of this disc shows a clump embedded within it with a flux ∼5 per cent of the total. The following conclusions are drawn. (i) Spectral energy distribution modelling is consistent with Fomalhaut’s disc having a collisional cascade size distribution extending from bodies 0.2 m in diameter (the largest that contribute to the 850-μm flux) down to 7-μm-sized dust (smaller grains are blown out of the system by radiation pressure). (ii) Collisional lifetime arguments imply that the collisional cascade starts with planetesimals 1.5–4 km in diameter, and so has a mass of 20–30 M⊕. Any larger bodies must be predominantly primordial. (iii) Constraints on the time-scale for the ignition of the collisional cascade from planet formation models are consistent with these primordial planetesimals having the same distribution as the cascade extending up to 1000 km, resulting in a disc mass of 5–10 times the minimum solar nebula mass. (iv) The debris disc is expected to be intrinsically clumpy, as planetesimal collisions result in dust clumps that can last up to 700 orbital periods. The intrinsic clumpiness of Fomalhaut’s disc is below current detection limits, but it could be detectable by future observatories such as ALMA, and could provide the only way of determining this primordial planetesimal population. Also, we note that such intrinsic clumpiness in an exozodiacal cloudlike disc could present a confusion limit when trying to detect terrestrial planets. (v) The observed clump could have originated in a collision between two runaway planetesimals, both larger than 1400 km in diameter. It appears unlikely that we should witness such an event unless both the formation of these runaways and the ignition of the collisional cascade occurred relatively recently (within the last ∼10 Myr), however this is a topic which would benefit from further exploration using planet formation and collisional models. (vi) Another explanation for Fomalhaut’s clump is that ∼5 per cent of the planetesimals in the ring were trapped in 1:2 resonance with a planet orbiting at 80 au when it migrated out as a result of the clearing of a residual planetesimal disc. The motion on the sky of such a clump would be 0.2 arcsec yr−1, and it would be more prominent at shorter wavelengths.