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The stability of accretion tori. II. Non-linear evolution to discrete planets

Goodman, Jeremy and Narayan, Ramesh and Goldreich, Peter (1987) The stability of accretion tori. II. Non-linear evolution to discrete planets. Monthly Notices of the Royal Astronomical Society, 225 (3). pp. 695-711. ISSN 0035-8711.

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Hawley has shown through two-dimensional computer simulations that a slender torus in which a linear Papaloizou-Pringle (PP) instability with azimuthal wavenumber m, is excited evolves non-linearly to a configuration with m nearly disconnected 'planets'. We present an analytical fluid equilibrium that we believe represents his numerical planets. The fluid has an ellipsoidal figure and is held together by the Corio lis force associated with the retrograde fluid motion. There is a bifurcation between the torus and planet configurations at precisely the vorticity below which the PP instability switches on. Although the solution is three-dimensional, there is perfect hydrostatic equilibrium and the motion is entirely two-dimensional. We analyse the linear modes of the analytical planet and find that there are numerous instabilities, though they are not as violent as the PP instability in the torus. We also discuss the energy and vorticity of neutral modes, and we argue that when the torus breaks up into planets, neutral modes with negative energy and non-zero vorticity are excited in order to conserve total energy and specific vorticity. We speculate that the fluid in Hawley's simulations may be approaching two-dimensional turbulence.

Item Type:Article
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Narayan, Ramesh0000-0002-1919-2730
Additional Information:© 1987 Royal Astronomical Society. Accepted 1986 October 30. Received 1986 October 2. We thank John Hawley for sharing with us his exciting numerical results well before publication, and James Binney, Roger Blandford, Sterl Phinney, and Scott Tremaine for valuable discussions. JG was supported by a W. M. Keck Foundation grant and by NSF grant PHY8217352, RN by NSF grant AST-8611121 and PG was supported by NSF grant AST83-13725.
Group:UNSPECIFIED, Division of Geological and Planetary Sciences
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W. M. Keck FoundationUNSPECIFIED
Issue or Number:3
Record Number:CaltechAUTHORS:20130313-100854712
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Official Citation:The stability of accretion tori. II - Non-linear evolution to discrete planets Goodman, J.; Narayan, R.; Goldreich, P. Monthly Notices of the Royal Astronomical Society, vol. 225, April 1, 1987, p. 695-711.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37489
Deposited By: Ruth Sustaita
Deposited On:13 Mar 2013 17:28
Last Modified:02 Nov 2019 20:07

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