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Wave Excitation in Three-Dimensional Disks by External Potential
We study the excitation of density and bending waves and the associated
angular momentum transfer in gaseous disks with finite thickness by a rotating
external potential. The disk is assumed to be isothermal in the vertical
direction and has no self-gravity. The disk perturbations are decomposed into
different modes, each characterized by the azimuthal index m and the vertical
index n, which specifies the nodal number of the density perturbation along the
disk normal direction. The n=0 modes correspond to the two-dimensional density
waves previously studied by Goldreich & Tremaine and others. In a
three-dimensional disk, waves can be excited at both Lindblad resonances (for
modes with n=0,1,2...) and vertical resonances (for the modes only).
The torque on the disk is positive for waves excited at outer Linblad/vertical
resonances and negative at inner Lindblad/vertical resonances. While the n=0
modes are evanescent around corotation, the modes can propagate into
the corotation region where they are damped and deposit their angular momenta.
We have derived analytical expressions for the amplitudes of different wave
modes excited at Lindblad and/or vertical resonances and the resulting torques
on the disk. It is found that for , angular momentum transfer through
vertical resonances is much more efficient than Lindblad resonances. This
implies that in some situations (e.g., a circumstellar disk perturbed by a
planet in an inclined orbit), vertical resonances may be an important channel
of angular momentum transfer between the disk and the external potential. We
have also derived new formulae for the angular momentum deposition at
corotation and studied wave excitations at disk boundaries.Comment: 20 pages, 2 figures. Minor changes/additions, references added.
MNRAS, in pres
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