On the non-radial oscillations of slowly rotating stars induced by the Lense-Thirring effect

Abstract
In a star that is rotating so slowly that the distortion of its figure may be ignored, the axial modes of non-radial oscillation exhibiting resonance can be excited by the polar modes of perturbation by the coupling derived from the dragging of the inertial frame by the rotation of the star (i. e. by the Lense-Thirring effect). The coupling of these two modes of opposite parity is subject to the standard selection rule, ∆ l = ±1. Also, the excitation of ( l + 1)-axial mode by the l -polar mode is favoured relative to the excitation of the ( l - 1)-axial mode, in conformity with the ‘propensity’ rule. As an illustrative example, the excitation of the sextupole axial modes of oscillation by the quadrupole polar perturbations is considered in some detail; and it is shown that both the real and the imaginary parts of the characteristic frequency of the quasi­-normal modes decrease dramatically with the amplitude of the coupling. The relatively very long damping times of these rotationally induced oscillations may be a decisive factor in their eventual detection in neutron stars following the glitches.

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