TY - JOUR

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

AU - Lee, Wing Kit

AU - Dempsey, Adam M.

AU - Lithwick, Yoram

N1 - Funding Information:
We thank the referee, Jean Teyssandier, for his constructive comments. We thank Pak-Shing Li for a discussion on the self-gravity kernels, and Phil Nicholson and Yanqin Wu for helpful discussions. Y.L. acknowledges NSF grant AST-1352369 and NASA grant NNX14AD21G.

PY - 2019

Y1 - 2019

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

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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 -