1998/07/31 by Lee Lindblom, James R. Ipser · 2 citations
Physics and Astronomy · #Nonlinear Waves and Solitons #Pulsars and Gravitational Waves Research #Stellar, planetary, and galactic studies #astro-ph #gr-qc
paper · pdf · doi:10.1103/physrevd.59.044009
published as Phys.Rev. D59 (1999) 044009 · 12 pages, 3 figures; minor changes and additions as will appear in the version to be published in Physical Review D, January 1999
arxiv created 1998/12/04 · openalex publication_date 1999/01/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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\ensuremath-m (or l\ensuremath-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.