Determination of the internal structure of neutron stars from gravitational wave spectra

In this paper the internal structure of a neutron star is shown to be inferrable from its gravitational-wave spectrum. Iteratively applying the inverse scheme of the scaled coordinate logarithmic perturbation method for neutron stars proposed by Tsui and Leung [Astrophys. J. 631, 495 (2005)], we are able to determine the mass, the radius and the mass distribution of a star from its quasinormal mode frequencies of stellar pulsation. In addition, accurate equation of state of nuclear matter can be obtained from such inversion scheme. Explicit formulas for the case of axial w-mode oscillation are derived here and numerical results for neutron stars characterized by different equations of state are shown