Observations of dusty debris disks can be used to test theories of planetesimal coagulation .
Planetesimals of sizes up to a couple thousand kms are embedded in these disks and their mutual collisions generate the small dust grains that are observed .
The dust luminosities , when combined with information on the dust spatial extent and the system age , can be used to infer initial masses in the planetesimal belts .
Carrying out such a procedure for a sample of debris disks around Sun-like stars , we reach the following two conclusions .
First , if we assume that colliding planetesimals satisfy a primordial size spectrum of the form dn / ds \propto s ^ { - q } , observed disks strongly favor a value of q between 3.5 and 4 , while both current theoretical expectations and statistics of Kuiper belt objects favor a somewhat larger value .
Second , number densities of planetesimals are two to three orders of magnitude higher in detected disks than in the Kuiper belt , for comparably-sized objects .
This is a surprise for the coagulation models .
It would require a similar increase in the solid surface density of the primordial disk over that of the Minimum Mass Solar Nebula , which is unreasonable .
Both of our conclusions are driven by the need to explain the presence of bright debris disks at a few Gyrs of age .