  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.

Astrophysics