Gravitational wave asteroseismology of fast rotating neutron stars with realistic equations of state

Abstract

In the present paper we study the oscillations of fast rotating neutron stars with realistic equations of state (EoS) within the Cowling approximation. We derive improved empirical relations for gravitational wave asteroseismology with $f$-modes, and for the first time we consider not only quadrupolar oscillations but also modes with higher spherical order ($l=|m|=3$, 4). After performing a systematic comparison with polytropic EoS, we show that the empirical relations found in this case approximately also hold for realistic EoS. In addition, we show that these relations will not change significantly even if the Cowling approximation is dropped and the full general relativistic case is considered, although the normalization used here (frequencies and damping times in the nonrotating limit) could differ considerably. We also address the inverse problem; i.e., we investigate in detail what kind of observational data are required in order to determine characteristic neutron star parameters. It is shown that masses, radii and rotation rates can be estimated quite accurately using the derived asteroseismology relations. We also compute the instability window for certain models, i.e., the limiting curve in a $T\ensuremath{-}\ensuremath{\Omega}$ plane where the secular Chandrasekhar-Friedman-Schutz instability overcomes dissipative effects, and we show that some of the modern realistic EoS will lead to a larger instability window compared to all of the polytropic ones presented so far in the literature. Additionally, we calculate the $r$-mode instability window and compare it with the $f$-mode case. The overall results for the instability window suggest that it is vital to take into account oscillations with $l=3$, 4 when considering gravitational wave asteroseismology using the $f$-mode in rapidly rotating neutron stars, as these modes can become unstable for a much larger range of parameters than pure quadrupolar oscillations.