Collisional Processes in Extrasolar Planetsimal Disks - Dust Clumps in Fomalhaut's Debris Disk

Abstract

This paper presents a model for the outcome of collisions between planetesimals in a debris disk and assesses the impact of collisional processes on the structure and size distribution of the disk. The model is presented by its application to Fomalhaut's collisionally replenished dust disk; a recent 450 micron image of this disk shows a clump embedded within it with a flux ~5 per cent of the total. The following conclusions are drawn: (i) SED modelling is consistent with Fomalhaut's disk having a collisional cascade size distribution extending from bodies 0.2 m in diameter down to 7 micron-sized dust. (ii) Collisional lifetime arguments imply that the cascade starts with planetesimals 1.5-4 km in diameter. Any larger bodies must be predominantly primordial. (iii) Constraints on the timescale for the ignition of the cascade are consistent with these primordial planetesimals having a distribution that extends up to 1000km, resulting in a disk mass of 5-10 times the minimum mass solar nebula. (iv) The debris disk is expected to be intrinsically clumpy, since planetesimal collisions result in dust clumps. The intrinsic clumpiness of Fomalhaut's disk is below current detection limits, but could be detectable by future observatories such as the ALMA, and could provide the only way of determining the primordial planetesimal population. (v) The observed clump could have originated in a collision between two runaway planetesimals, both larger than 1400 km diameter. It is unlikely that we should witness such an event unless both the formation of these runaways and the ignition of the collisional cascade occurred within the last ~10 Myr. (vi) Another explanation for Fomalhaut's clump is that ~5 per cent of the planetesimals in the ring are trapped in 1:2 resonance with a planet orbiting at 80 AU.