Long-lived Eccentricities in Accretion Disks

Accretion disks can be eccentric: they support m = 1 modes that are global and slowly precessing. But whether the modes remain trapped in the disk—and hence are long-lived—depends on conditions at the outer edge of the disk. Here we show that in disks with realistic boundaries, in which the surface density drops rapidly beyond a given radius, eccentric modes are trapped and hence can live for as long as the viscous time. We focus on pressure-only disks around a central mass, and show how this result can be understood with the help of a simple second-order WKB theory. We show that the longest-lived mode is the zero-node mode in which all of the disk's elliptical streamlines are aligned, and that this mode decays coherently on the viscous timescale of the disk. Hence, such a mode, once excited, could live as long as the lifetime of the disk. It may be responsible for asymmetries seen in recent images of protoplanetary disks.