Polar quasi-normal modes of neutron stars with equations of state satisfying the 2 M⊙ constraint

In this paper, we analyze the quasinormal mode spectrum of realistic neutron stars by studying the polar modes. In particular, we calculate the fundamental mode (f mode), the fundamental pressure mode (p mode), and the fundamental curvature mode (wI mode) for 15 different equations of state satisfying the 2 M-circle dot constraint, most of them containing exotic matter. Since f and p modes couple to matter perturbations, the influence of the presence of hyperons and quarks in the core of the neutron stars is more significant than for the axial component. We present phenomenological relations, which are compatible with previous results, for the frequency and damping time with the compactness of the neutron star. We also consider new phenomenological relations between the frequency and damping time of the wI mode and the f mode. These new relations are independent of the equation of state and could be used to estimate the central pressure, mass, or radius and eventually constrain the equation-of-state of neutron stars. To obtain these results, we have developed a new method based on the exterior complex scaling technique with a variable angle.