Lumpy structures in self-gravitating disks

Following Toomre & Kalnajs ([CITE]), local models of slightly dissipative self-gravitating disks show how inhomogeneous structures can be maintained over several galaxy rotations. Their basic physical ingredients are self-gravity, dissipation and differential rotation. In order to explore the structures resulting from these processes on the kpc scale, local simulations of self-gravitating disks are performed in this paper in 2D as well as in 3D. The third dimension becomes a priori important as soon as matter clumping causes a tight coupling of the 3D equations of motion. The physically simple and general framework of the model permits to make conclusions beyond the here considered scales. A time dependent affine coordinate system is used, allowing to calculate the gravitational forces via a particle-mesh FFT-method, increasing the performance with respect to previous direct force calculations. Persistent patterns, formed by transient structures, whose intensity and morphological characteristic depend on the dissipation rate are obtained and described. Some of our simulations reveal first signs of mass-size and velocity dispersion-size power-law relations, but a clear scale invariant behavior will require more powerful computer techniques