Determining the long living quasi-normal modes of relativistic stars

doi:10.1088/1674-1056/20/4/040401

Abstract Methods of finding quasi-normal modes of non-rotating relativistic stars have been well established, however, none of the existing treatments which take spacetime and fluid oscillations fully into account can determine modes of long decay time, e.g., the p and g mode series, or the f modes for stars with low compactness ratio (M/R). In this paper we show how the quasi-normal modes of long lifetime can be determined through refinements of a treatment originally due to Detweiler and Lindblom. The determination of the p mode series has been argued in the literature to have implication on the life time of gravitational wave sources and stellar stability. In this paper we 1) provide detailed steps in our treatment to facilitate future effort in this direction; 2) correct mistakes in the literature on the formulation; and 3) analyse the accuracy of the quasi-normal mode frequencies obtained and the limitations of the treatment.

Keywords: relativistic stars non-radial perturbations gravitational wave quasi-normal modes

Received: 13 September 2010
Revised: 06 November 2010
Accepted manuscript online:

PACS:	04.20.-q	(Classical general relativity)
	04.25.D-	(Numerical relativity)
	04.30.-w	(Gravitational waves)

Fund: Project supported by the Science Foundation of the Education Department of Hunan Province of China (Grant No. 07c578) and in part by the US National Science Foundation NRAC, the McDonnell Center for the Space Sciences of the Washington University (Grant No. MCA93S025).

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Lü Jun-Li(吕君丽) and Suen Wai-Mo(孙纬武) Determining the long living quasi-normal modes of relativistic stars 2011 Chin. Phys. B 20 040401

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