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 momentum in self-gravitating gaseous disks and (2) inducing mode saturation that can preclude the onset of disk fragmentation. Our analysis indicates in quantitative detail how torques arising from gravitationally unstable spiral modes can lead to disk accretion. We begin by performing a linear global stability analysis on an idealized model equilibrium disk that is prone to a single, rapidly growing two-armed spiral. We compare the linearized predictions with the full hydrodynamical evolution of the disk provided by numerical simulations. We then retain second-order terms in a perturbative reanalysis of the hydrodynamic governing equations. We derive equations that describe how mass and angular momentum are redistributed in the disk. Then we solve these equations numerically and compare the results with the simulations. We conclude with a discussion of how nonlinear mode interactions and self-interactions are responsible for mode saturation in the disk and the development of steady mass accretion.