Constrain the primordial planetesimal size distribution in the Fomalhaut debris belt

Determine the power-law index a of the primordial size distribution of planetesimals larger than 0.3 km in the Fomalhaut debris belt, which was assumed to be a = 3.5 in the paper’s collision-rate and mass-budget calculations but has not been established observationally.

Background

In estimating collision rates and parent-body sizes that could produce dust clouds like Fom cs1 and Fom cs2, the analysis adopts a primordial planetesimal size distribution with power-law index a = 3.5 (Dohnanyi).

This assumption critically affects inferred parent-body sizes and total mass; for example, a = 3.5 implies parent bodies with ~30 km radii, whereas a = 3 or a = 4 would imply substantially different body sizes and mass requirements, some of which the authors argue are implausible.

However, the value of a for the Fomalhaut belt’s primordial bodies has not been constrained by observations, leaving a key input to the collisional modeling uncertain.