### 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 ≳ 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 language | English (US) |
---|---|

Article number | 184 |

Journal | Astrophysical Journal |

Volume | 872 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2019 |

### Fingerprint

### Keywords

- accretion, accretion disks
- hydrodynamics
- protoplanetary disks
- waves

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Space and Planetary Science

### Cite this

*Astrophysical Journal*,

*872*(2), [184]. https://doi.org/10.3847/1538-4357/ab010c

}

*Astrophysical Journal*, vol. 872, no. 2, 184. https://doi.org/10.3847/1538-4357/ab010c

**Eccentric Modes in Disks with Pressure and Self-gravity.** / Lee, Wing Kit; Dempsey, Adam M.; Lithwick, Yoram.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Eccentric Modes in Disks with Pressure and Self-gravity

AU - Lee, Wing Kit

AU - Dempsey, Adam M.

AU - Lithwick, Yoram

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - accretion, accretion disks

KW - hydrodynamics

KW - protoplanetary disks

KW - waves

UR - http://www.scopus.com/inward/record.url?scp=85063507103&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063507103&partnerID=8YFLogxK

U2 - 10.3847/1538-4357/ab010c

DO - 10.3847/1538-4357/ab010c

M3 - Article

AN - SCOPUS:85063507103

VL - 872

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

M1 - 184

ER -