SPIRAL MODE SATURATION IN SELF-GRAVITATING DISKS

This paper examines a second-order nonlinear mechanism that appears to bear responsibility for (1) eliciting transport of mass and angular m omentum in self-gravitating gaseous disks and (2) inducing mode satura tion that can preclude the onset of disk fragmentation. Our analysis i ndicates in quantitative detail how torques arising from gravitational ly unstable spiral modes can lead to disk accretion. We begin by perfo rming a linear global stability analysis on an idealized model equilib rium disk that is prone to a single, rapidly growing two-armed spiral. We compare the linearized predictions with the full hydrodynamical ev olution of the disk provided by numerical simulations. We then retain second-order terms in a perturbative reanalysis of the hydrodynamic go verning equations. We derive equations that describe how mass and angu lar momentum are redistributed in the disk. Then we solve these equati ons numerically and compare the results with the simulations. We concl ude with a discussion of how nonlinear mode interactions and self-inte ractions are responsible for mode saturation in the disk and the devel opment of steady mass accretion.