Nonlinear Single-Armed Spiral Density Waves in Nearly Keplerian Disks

Single-armed, stationary density waves can exist even in disks with only weak selfgravity, provided that the rotation curve is dominated by a central mass. Such waves could play a significant role in the transport of angular momentum. By variational methods, we derive nonlinear versions of the dispersion relation, angular momentum flux, and propagation velocity in the tight-winding limit. The pitch angle increases with amplitude until the tight-winding approximation breaks down. By other methods, we find a series of nonlinear logarithmic spirals which is exact in the limit of small disk mass and which extends to large pitch angle. These waves may be supported by low-mass protoplanetary disks, and perhaps by compact molecular disks in galactic nuclei.