Phenomenological relations for axial quasinormal modes of neutron stars with realistic equations of state

Here we investigate the axial w quasinormal modes of neutron stars for 18 realistic equations of state, most of them satisfying the 2M(circle dot) condition. In particular, we study the influence of the presence of hyperons and quarks in the core of the neutron stars. We have obtained that w modes can be used to distinguish between neutron stars with exotic matter and without exotic matter for compact enough stars. We present phenomenological relations for the frequency and damping times with the compactness of the neutron star for wI and wII modes showing the differences of the stars with exotic matter in the core. Also, we obtain a new phenomenological relation between the real part and the imaginary part of the frequency of the w quasinormal modes, which can be used to estimate the central pressure of the neutron stars. Finally, we study the low compactness limit configuration of fundamental wII modes, and the influence of changes in the core-crust transition pressure. To obtain these results we have developed a new method based on the exterior complex scaling technique with variable angle.