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

TL;DR

This study compares relativistic calculations of neutron star shear and interface modes with the Cowling approximation, finding it has negligible effect on shear modes but significantly shifts interface mode frequencies, and introduces a robust damping time estimation scheme.

Contribution

It demonstrates the limited impact of the Cowling approximation on shear modes and develops a new, efficient method to estimate damping times of neutron star oscillation modes.

Findings

Cowling approximation has minimal effect on shear mode frequencies and eigenfunctions.

Interface mode frequencies are significantly affected by the Cowling approximation.

The new damping time estimation scheme is computationally efficient and robust.

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.