Gravitational wave asteroseismology reexamined

The frequencies and damping times of the non radial oscillations of non rotating neutron stars are computed for a set of recently proposed equations of state (EOS) which describe matter at supranuclear densities. These EOS are obtained within two different approaches, the nonrelativistic nuclear many-body theory and the relativistic mean field theory, that model hadronic interactions in different ways leading to different composition and dynamics. Being the non radial oscillations associated to the emission of gravitational waves, we fit the eigenfrequencies of the fundamental mode and of the first pressure and gravitational-wave mode (polar and axial) with appropriate functions of the mass and radius of the star, comparing the fits, when available, with those obtained by Andersson and Kokkotas in 1998. We show that the identification in the spectrum of a detected gravitational signal of a sharp pulse corresponding to the excitation of the fundamental mode or of the first p-mode, combined with the knowledge of the mass of the star—the only observable on which we may have reliable information—would allow to gain interesting information on the composition of the inner core. We further discuss the detectability of these signals by gravitational detectors.

Figure 1

NS mass versus radius for the models of EOS described in the text. The two horizontal lines denote the boundaries of the region of observationally allowed NS masses, while the straight crossing line corresponds to the mass-radius relation extracted from the redshift measurement of Cottam et al. (2002)

Figure 2

The frequency of the fundamental mode is plotted in the upper panel as a function of the square root of the average density for the different EOS considered in this paper. We also plot the fit given by Andersson and Kokkotas (AK-fit) and our fit (New fit). The new fit is systematically lower (about 100 Hz) than the old one. The damping time of the fundamental mode is plotted in the lower panel as a function of the compactness $M/R$. The AK-fit and our fit, plotted, respectively, as a dashed and continuous line, do not show significant differences.

Figure 3

The frequency (upper panel) and the damping time (lower panel) of the first p-mode are plotted as a function of the compactness of the star. The AK-fit and the new fit for the frequency are plotted, in the upper panel, as a dashed and continuous line, respectively. As already noted in [2] the data referring to the damping time are so spread that a fit has no significance.

Figure 4

The frequency of the fundamental mode is plotted as a function of the mass of the star.

Figure 5

The frequency of the first p-mode is plotted as a function of the mass of the star.