A Caltech Library Service

The excitation of density waves at the Lindblad and corotation resonances by an external potential

Goldreich, Peter and Tremaine, Scott (1979) The excitation of density waves at the Lindblad and corotation resonances by an external potential. Astrophysical Journal, 233 (3). pp. 857-871. ISSN 0004-637X. doi:10.1086/157448.

PDF - Published Version
See Usage Policy.


Use this Persistent URL to link to this item:


We calculate the linear response of a differentially rotating two-dimensional gas disk to a rigidly rotating external potential. The main assumptions are that the sound speed is much smaller than the orbital velocity and that the external potential varies on the scale of the disk radius. We investigate disks both with and without self-gravity. The external potential exerts torques on the disk only at the Lindblad and corotation resonances. The torque is positive at the outer Lindblad resonance and negative at the inner Lindblad resonance; at corotation the torque has the sign of the radial gradient of vorticity per unit surface density. The torques are of the same order of magnitude at both types of resonance and are independent of the sound speed in the disk. The external potential also excites density waves in the vicinity of the Lindblad and corotation resonances. The long trailing wave is excited at a Lindblad resonance. It transports away from the resonance all of the angular momentum which is deposited there by the external torque. Short trailing waves are excited at the corotation resonance. The amplitudes of the excited waves are the same on both sides of the resonance and are small unless the disk is almost gravitationally unstable. No net angular momentum is transported away from the corotation region by the waves. Thus the angular momentum deposited there by the external torque accumulates in the gas. We briefly discuss the behavior of particle disks and prove that the external torques on particle disks are identical to those on gas disks.

Item Type:Article
Related URLs:
URLURL TypeDescription
Additional Information:© 1979 American Astronomical Society. Received 1978 September 22; accepted 1979 May 2. We thank Drs. J. Bardeen, Y. Y. Lau, C. C. Lin, D. Lynden-Bell, and A. Toomre for helpful discussions. This work was supported by NSF grant AST 76-23281 and NASA grant NGL-05-002-003.
Funding AgencyGrant Number
NSFAST 76-23281
Subject Keywords:galaxies: structure, hydrodynamics, stars: stellar dynamics
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Caltech Division of Geological and Planetary Sciences3118
Issue or Number:3
Record Number:CaltechAUTHORS:20130306-153254452
Persistent URL:
Official Citation:The excitation of density waves at the Lindblad and corotation resonances by an external potential Goldreich, P. & Tremaine, S. Astrophysical Journal, Part 1, vol. 233, no. 3, Nov. 1, 1979, p. 857-871.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37358
Deposited On:06 Mar 2013 23:45
Last Modified:09 Nov 2021 23:28

Repository Staff Only: item control page