Computing Gravitational Wave Frequencies of Neutron Stars

Abstract

Vibration modes of single neutron stars are important sources of continuous gravi- tational waves for detectors like the Laser Interferometer Gravitational-Wave Observa- tory (LIGO). In order for LIGO to identify the weak signal buried in the noise, they rely on a theoretical template of the signal amplitude and frequency. In this thesis, we utilize a technique rst described by Chandrasekhar to calculate the frequency of the quasi- normal mode oscillations of a single neutron star. We calculate the normalized (complex) frequency for the l=2 (quadrupole) oscillation of the entire family of general relativistic polytropes with polytropic index 1.5 and a central density to central pressure ratio of 9. We nd the real part of this normalized frequency to be =0.3383, compared to Chan- drasekhar's result in his paper from 1991 of =0.3248. We nd the imaginary part of this normalized frequency to be =1.448010[Special character(s) omitted]4, compared to Chandrasekhar's result in his paper from 1991 of =1.02610[Special character(s) omitted]4. The slight dierence is likely due to higher computa- tional accuracy of modern day computers