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Here we investigate the axial w quasi-normal modes of neutron stars forseveral equations of state. In particular, we study the influence of thepresence of hyperons in the core of the neutron stars. We have obtained thatw-modes can be used to distinguish between neutron stars with hyperons andwithout hyperons for compact enough stars. We present phenomenologicalrelations for the frequency and damping times with the compactness of theneutron star for wI and wII modes showing the differences of the stars withhyperons in the core. Also, we obtain a new phenomenological relation betweenthe real part and the imaginary part of the frequency of the w quasi-normalmodes, which can be used to estimate the central pressure of the neutron stars.We are able to construct explicitly the low compactness limit configuration forwhich the fundamental wII mode vanishes. Finally, we have studied the influenceof changes in the core-crust transition pressure obtaining that it is verysmall. To obtain these results we have developed a new method based on theExterior Complex Scaling technique with variable angle, appropriate for thetreatment of the exterior part of the quasi-normal modes, which allow us toimpose constringent enough conditions to generate pure outgoing quasi-normalmodes. For the interior part we use a piece-wise polytrope approximation forseveral equations of state. A complete study of the junction conditions havebeen done.

Phenomenological Relations for Axial Quasi-normal Modes of Neutron Stars with Realistic Equations of State