Eccentric Modes in Disks with Pressure and Self-gravity

Wing Kit Lee, Adam M. Dempsey, Yoram Lithwick

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 ≳ 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 ≲ 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.

Original languageEnglish (US)
Article number184
JournalAstrophysical Journal
Issue number2
StatePublished - 2019


  • accretion, accretion disks
  • hydrodynamics
  • protoplanetary disks
  • waves

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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