Nonlocal density wave theory for gravitational instability of protoplanetary disks without sharp boundaries

The stability of a self-gravitating infinitesimally thin gaseous disk rotat ing around a central mass is studied. Our global linear analysis concerns m arginal stability, i.e, it yields the critical temperature for the onset of instability for any given ratio of the disk mass to the central mass. Both axisymmetric and low-m nonaxisymmetric excitations are analysed. When the fractional disk mass increases, the symmetry character of the instability c hanges from rings (m = 0) to one-armed trailing spirals (m = 1). The distri bution of the surface density along the spiral arms is not uniform, but des cribes a sequence of maxima that might be identified with forming planets. The number of the mass concentrations decreases with increasing fractional disk mass. We also obtain solutions in the form of global nonaxisymmetric v ortices, which are, however, never excited.