Impact of the relativistic Cowling approximation on shear and interface modes of neutron stars

Abstract: We investigate shear and interface modes excited in neutron stars with an elastic crust in the full general relativistic framework and compare them to the results obtained within the relativistic Cowling approximation. We observe that the Cowling approximation has virtually no impact on the frequencies or the eigenfunctions of the shear modes; in contrast, the interface modes that arise due to the discontinuities of the shear modulus experience a considerable shift in frequency when applying the Cowling approximation . Furthermore, we extend a scheme based on the properties of the phase of amplitude ratios, which allows us to estimate the damping times of slowly damped modes; our extension can provide an estimation of the damping time even if the features of the amplitude ratio are incomplete or if some of them violate the underlying linearity assumption. The proposed scheme is also computationally less expensive and numerically more robust and we provide accurate estimates as well as lower bounds for damping times of shear and interface modes. We estimate the damping times also via the quadrupole formula and find that it provides good order-of-magnitude estimates.