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  Perturbations and Stability of Rotating Stars. 1: Completeness of Normal Modes

Dyson, J., & Schutz, B. F. (1979). Perturbations and Stability of Rotating Stars. 1: Completeness of Normal Modes. Proceedings of the Royal Society of London, Series A, 368(1734), 389-410. doi:10.1098/rspa.1979.0137.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-0F45-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-0F49-4
Genre: Journal Article

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PRSLAschutz.pdf (Publisher version), 728KB
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Dyson, J.1, Author
Schutz, Bernard F.1, 2, Author              
Affiliations:
1External Organizations, Department of Applied Mathematics and Astronomy, University College, Cardiff, Wales, U.K., escidoc:persistent22              
2Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24013              

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 Abstract: It is noted that linear adiabatic perturbations of a differentially rotating, axisymmetric, perfect fluid stellar model have normal modes described by a quadratic problem. The paper studies the problem and the associated time evolution equation. It is shown that in the Hilbert space H-prime, whose norm is square-integration weighted by A, the operators (A to the -1st power)(B) and (A to the -1st power)(C) are anti-selfadjoint and selfadjoint, respectively, when restricted to vectors belonging to a particular but arbitrary axial harmonic. Bounds are found on the spectrum of normal modes and it is shown that any initial data in the domain of C leads to a solution whose growth rate is limited by the spectrum and which can be expressed in a certain weak sense as a linear superposition of the normal modes.

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 Dates: 1979
 Publication Status: Published in print
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 Rev. Method: Peer
 Identifiers: eDoc: 335674
DOI: 10.1098/rspa.1979.0137
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Title: Proceedings of the Royal Society of London, Series A
Source Genre: Journal
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Pages: - Volume / Issue: 368 (1734) Sequence Number: - Start / End Page: 389 - 410 Identifier: ISSN: 0080-4630