Eccentric Modes in Disks with Pressure and Self-gravity

Accretion disks around stars, or other central massive bodies, can support long-lived, slowly precessing $m=1$ disturbances in which the fluid motion is nearly Keplerian with non-zero eccentricity. We study such `slow modes' in disks that are subject to both pressure and self-gravity forces. We derive a second-order WKB dispersion relation that describes the dynamics quite accurately, and show that the apparently complicated nature of the various modes can be understood in a simple way with the help of a graphical method. We also solve the linearized fluid equations numerically, and show that the results agree with the theory. We find that when self-gravity is weak ($Q\gtrsim 1/h$, where $Q$ is Toomre's parameter, and $h$ is the disk aspect ratio) the modes are pressure dominated. But when self-gravity is strong ($1

Keywords:

• Eccentric
• Mechanics
• Physics

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