2001/01/31 by Shijun Yoshida
Physics and Astronomy · #Astrophysical Phenomena and Observations #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Gravitation #Gravitational collapse #Neutron star #Polytrope #Polytropic process #Pulsars and Gravitational Waves Research #Star (game theory) #Stars #astro-ph #gr-qc
paper · pdf · doi:10.1086/322275
published as Astrophys.J. 558 (2001) 263 · 14 pages, 4 figures, with minor revisions. Accepted for publication in ApJ
arxiv created 2001/05/10 · openalex publication_date 2001/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We investigate the properties of r -modes characterized by the regular eigenvalue problem in slowly rotating, relativistic polytropes. Our numerical results suggest that discrete r -mode solutions for the regular eigenvalue problem exist only for restricted polytropic models. In particular, the r -mode associated with l = m = 2, which is considered to be the most important for gravitational radiation-driven instability, does not have a discrete mode as a solution of the regular eigenvalue problem for polytropes with polytropic index N > 1.18, even in the post-Newtonian order. Furthermore, for an N = 1 polytrope, which is employed as a typical neutron star model, discrete r -mode solutions for the regular eigenvalue problem do not exist for stars whose relativistic factor M / R is larger than about 0.1, where M and R are stellar mass and stellar radius, respectively.