Eccentric Modes in Disks With Pressure and Self-Gravity

Abstract

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 ($1<Q\lesssim 1/h$), two kinds of gravity-dominated modes appear: one is an aligned elliptical pattern and the other is a one-armed spiral. In the context of protoplanetary disks, we suggest that if the radial eccentricity profile can be measured, it could be used to determine the total disk mass.

arXiv commentSubmitted to ApJ on 11/25/2018. Comments are welcome

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• Eccentric Tidal Disruption Event Disks around Supermassive Black Holes: Dynamics and Thermal Emission
• Probing the eccentricity in protostellar discs -- Modeling kinematics and morphologies
• A Simplified Model for the Secular Dynamics of Eccentric Discs and Applications to Planet-Disc Interactions
• Potential softening and eccentricity dynamics in razor-thin, nearly-Keplerian discs
• Long-Lived Eccentricities in Accretion Disks
• Ring Formation in Protoplanetary Disks Driven by an Eccentric Instability
• Global Spiral Density Wave Modes in Protoplanetary Disks: Morphology of Spiral Arms
• Focusing of nonlinear eccentric waves in astrophysical discs
• The Dynamic Inner Disk of a Planet Forming Star
• Insights from Analytical Theory of Eccentric Circumbinary Disks
• Accretion Kinematics in the T Tauri Binary TWA 3A: Evidence for Preferential Accretion onto the TWA 3A Primary