Asteroseismology of rapidly rotating neutron stars: An alternative approach

We examine gravitational wave asteroseismology relations for $f$-modes of rapidly rotating neutron stars. A different approach than previous studies is employed. First, the moment of inertia is used instead of the stellar radius and, second, the normalization of the oscillation frequencies and damping times is different. It is shown that in the nonrotating case this can lead to a much stronger equation of state independence, and our goal is to generalize the static relations to the rapidly rotating case and values of the spherical mode number $l\ensuremath{\ge}2$. We employ realistic equations of state that cover a very large range of stiffness in order to better check the universality of the relations. We later explore the inverse problem; i.e., we obtain the neutron star parameters from the observed gravitational frequencies and damping times. It turns out that, with this new set of relations, we can solve the inverse problem with very good accuracy using three frequencies. This was not possible in the previous studies, where one also needed damping times. The asteroseismology relations are also quite accurate for the massive rapidly rotating models that are subject to secular instabilities.

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