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Planetary embryos and planetesimals residing in thin debris disks

We consider constraints on the planetesimal population residing in the disks of AU Microscopii, Beta Pictoris and Fomalhaut taking into account their observed thicknesses and normal disk opacities. We estimate that bodies of radius 5, 180 and 70 km are responsible for initiating the collisional cascade accounting for the dust production for AU-Mic, Beta-Pic and Fomalhaut's disks, respectively, at break radii from the star where their surface brightness profiles change slope. Larger bodies, of radius 1000km and with surface density of order 0.01 g/cm^2, are required to explain the thickness of these disks assuming that they are heated by gravitational stirring. A comparison between the densities of the two sizes suggests the size distribution in the largest bodies is flatter than that observed in the Kuiper belt. AU Mic's disk requires the shallowest size distribution for bodies with radius greater than 10km suggesting that the disk contains planetary embryos experiencing a stage of runaway growth.