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The excitation and evolution of density waves

Goldreich, Peter and Tremaine, Scott (1978) The excitation and evolution of density waves. Astrophysical Journal, 222 (1). pp. 850-858. ISSN 0004-637X. doi:10.1086/156203.

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We study the linear oscillations of a thin self-gravitating gas sheet. The unperturbed velocity field of the sheet is a parallel shear flow. A Coriolis acceleration is included to simulate the effects of rotation. The sheet exhibits Lindblad resonances, and it can sustain both short and long wavelength density waves. We derive equations which govern the excitation and evolution of density waves in all regions of space, including the Lindblad resonances and the forbidden region around corotation. These equations are solved in the tight winding limit. An initial disturbance in the form of a wave packet of short leading waves evolves as follows. The packet propagates toward corotation, is reflected at the boundary of the forbidden region, and becomes a packet of long leading waves. It then travels back to the Lindblad resonance, where it is reflected and becomes a packet of long trailing waves. Subsequently, this packet moves toward corotation and is reflected again at the boundary of the forbidden region. The packet is now made up of short trailing waves and propagates away from corotation indefinitely. For sufficiently stable disks, the forbidden region around corotation is wide and density waves are almost completely reflected at its boundaries. For marginally stable disks, some of the incident wave tunnels through the forbidden region and the reflected wave is amplified. The excitation of density waves by an arbitrary external potential is considered. In our model sheet, the sole effect of a barlike potential is to excite the long trailing wave at the Lindblad resonances. The amplitude of the excited wave is calculated.

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Additional Information:© 1978 American Astronomical Society. Received 1977 August 16; accepted 1978 January 4. We are indebted to Professor A. Toomre for encouraging us to carry out this investigation and for his wise counsel. This research was supported by NSF grants AST 76-24281 and AST 76-80801. S. Tremaine was supported by a Richard Chace Tolman Fellowship and a National Research Council of Canada Postdoctoral Fellowship.
Group:UNSPECIFIED, Division of Geological and Planetary Sciences
Funding AgencyGrant Number
NSFAST 76-24281
NSFAST 76-80801
Richard Chace Tolman FellowshipUNSPECIFIED
National Research Council of Canada Postdoctoral FellowshipUNSPECIFIED
Subject Keywords:galaxies: internal motions, galaxies: structure, hydrodynamics, stars: stellar dynamics
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Caltech Division of Geological and Planetary Sciences2958
Issue or Number:1
Record Number:CaltechAUTHORS:20130306-141115931
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Official Citation:The excitation and evolution of density wave Goldreich, P.; Tremaine, S. Astrophysical Journal, Part 1, vol. 222, June 15, 1978, p. 850-858.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37352
Deposited By: Ruth Sustaita
Deposited On:06 Mar 2013 22:46
Last Modified:09 Nov 2021 23:28

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