# Long-Lived Eccentricities in Accretion Disks

## TL;DR

This paper demonstrates that eccentric modes in accretion disks with realistic boundaries are trapped and long-lived, potentially explaining observed asymmetries in protoplanetary disks, through a simple WKB theoretical framework.

## Contribution

It shows that in pressure-only accretion disks with realistic boundaries, eccentric modes are trapped and long-lived, providing a new understanding of disk asymmetries.

## Key findings

- Eccentric modes are trapped in disks with rapid surface density drops.
- The longest-lived mode is the zero-node aligned elliptical streamline mode.
- Such modes decay on the viscous timescale, living for the disk's lifetime.

## Abstract

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 long-lived. 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, will live for the lifetime of the disk. It may be responsible for asymmetries seen in recent images of protoplanetary disks.