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Generalized r-modes of the Maclaurin spheroids

Lindblom, Lee and Ipser, James (1999) Generalized r-modes of the Maclaurin spheroids. Physical Review D, 59 (4). Art. No. 044009. ISSN 2470-0010. doi:10.1103/PhysRevD.59.044009.

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Analytical solutions are presented for a class of generalized r-modes of rigidly rotating uniform density stars—the Maclaurin spheroids—with arbitrary values of the angular velocity. Our analysis is based on the work of Bryan; however, we derive the solutions using slightly different coordinates that give purely real representations of the r-modes. The class of generalized r-modes is much larger than the previously studied “classical” r-modes. In particular, for each l and m we find l−m (or l−1 for the m = 0 case) distinct r-modes. Many of these previously unstudied r-modes (about 30% of those examined) are subject to a secular instability DRIVEN by gravitational radiation. The eigenfunctions of the “classical” r-modes, the l = m+1 case here, are found to have particularly simple analytical representations. These r-modes provide an interesting mathematical example of solutions to a hyperbolic eigenvalue problem.

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Additional Information:© 1999 American Physical Society. (Received 20 July 1998; published 15 January 1999) We particularly thank J. Friedman, K. Lockitch and N. Stergioulas for reading and criticizing the first draft of this manuscript. We also thank P. Brady, C. Cutler, B. J. Owen, and K. S. Thorne for helpful discussions concerning this work; and we thank S. Morsink for providing us with her notes on the non-existence of pure axial modes in the Maclaurin spheroids. This research was supported by NSF grants PHY-9408910 and PHY-9796079, and by NASA grants NAG5-3936 and NAG5-4093.
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Issue or Number:4
Classification Code:PACS number~s!: 04.40.Dg, 04.30.Db, 97.10.Sj, 97.60.Jd
Record Number:CaltechAUTHORS:20170408-163122992
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:76200
Deposited By: 1Science Import
Deposited On:07 Mar 2018 18:56
Last Modified:15 Nov 2021 16:58

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