  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 ~ 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.
