NONLINEAR GENERATION OF ONE-ARMED SPIRALS IN SELF-GRAVITATING DISKS

Single-armed spiral instabilities may play an important role in self-g ravitating disks. However, past studies have indicated that disks whic h are less massive than an embedded central star are in general linear ly stable to m = 1 perturbations. In this paper, we outline how the no nlinear interaction of two growing modes with azimuthal mode numbers m = n and m = n + 1 can excite the development of a one-armed disturban ce which grows exponentially at a rate equal to the sum of the growth rates of the two linearly unstable modes. Within the context of a seco nd order, semianalytic analysis, we discuss the special case of a uniq ue nonwinding, exponentially growing solution, and then we consider fu rther solutions based on physically relevant initial conditions. We fi nd that the nonwinding solution describes the general dynamics of the mode at later times. We then compare the results of our nonlinear anal ysis with hydrodynamic simulations, illustrating that the process we h ave considered is indeed an important effect.