G. Rudiger et Ll. Kitchatinov, Nonlocal density wave theory for gravitational instability of protoplanetary disks without sharp boundaries, ASTRON NACH, 321(3), 2000, pp. 181-192
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.