  Numerical hydrodynamics simulations have established that disks which are
evolved under the condition of local isothermality will fragment into small
dense clumps due to gravitational instabilities when the Toomre stability
parameter $Q$ is sufficiently low. Because fragmentation through disk
instability has been suggested as a gas giant planet formation mechanism, it is
important to understand the physics underlying this process as thoroughly as
possible. In this paper, we offer analytic arguments for why, at low $Q$,
fragments are most likely to form first at the corotation radii of growing
spiral modes, and we support these arguments with results from 3D hydrodynamics
simulations.
