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Growth of Perturbations in Gravitational Collapse and Accretion

Lai, Dong and Goldreich, Peter (2000) Growth of Perturbations in Gravitational Collapse and Accretion. Astrophysical Journal, 535 (1). pp. 402-411. ISSN 0004-637X. doi:10.1086/308821.

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When a self-gravitating spherical gas cloud collapses or accretes onto a central mass, the inner region of the cloud develops a density profile ρ ∝ r^(-3/2) and the velocity approaches free fall. We show that in this region nonspherical perturbations grow with decreasing radius. In the linear regime, the tangential velocity perturbation increases as r^(-1), while the Lagrangian density perturbation, Δρ/ρ, grows as r^(-1/2). Faster growth occurs if the central collapsed object maintains a finite multiple moment, in which case Δρ/ρ increases as r^(-l), where l specifies the angular degree of the perturbation. These scaling relations are different from those obtained for the collapse of a homogeneous cloud. Our numerical calculations indicate that nonspherical perturbations are damped in the subsonic region and that they grow and approach the asymptotic scalings in the supersonic region. The implications of our results to asymmetric supernova collapse and to black hole accretion are briefly discussed.

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Additional Information:© 2000 American Astronomical Society. Received 1999 June 25; accepted 2000 January 14. A major portion of this research was done between 1995 and 1997, when D. L. was a postdoc in theoretical astrophysics at Caltech; support from a Richard C. Tolman fellowship is gratefully acknowledged. This work is supported in part by NASA grants NAG 5-8356 and NAG 8484, by a research fellowship from the Alfred P. Sloan foundation, and by NSF grant 94-14232.
Group:UNSPECIFIED, Division of Geological and Planetary Sciences
Funding AgencyGrant Number
Richard C. Tolman fellowshipUNSPECIFIED
NASANAG 5-8356
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:accretion, accretion disks - hydrodynamics - methods: numerical - supernovae: general
Issue or Number:1
Record Number:CaltechAUTHORS:20130227-091606977
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Official Citation:Growth of Perturbations in Gravitational Collapse and Accretion Dong Lai and Peter Goldreich 2000 ApJ 535 402
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37167
Deposited By: Ruth Sustaita
Deposited On:28 Feb 2013 15:37
Last Modified:09 Nov 2021 23:27

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