Second-order rotational effects on the r-modes of neutron stars

TL;DR

This paper develops second-order techniques to evaluate r-modes in rotating neutron stars, providing more accurate frequencies, eigenfunctions, and damping timescales, with implications for gravitational wave emission.

Contribution

It introduces novel second-order calculations and numerical methods for r-modes, including eigenfunction determination and viscosity effects, advancing the modeling of rotating neutron stars.

Findings

Second-order eigenfunctions are computed using a new inhomogeneous hyperbolic boundary-value approach.

Bulk-viscosity timescales are longer for neutron stars than previously estimated.

Second-order effects do not significantly alter the gravitational radiation instability picture.

Abstract

Techniques are developed here for evaluating the r-modes of rotating neutron stars through second order in the angular velocity of the star. Second-order corrections to the frequencies and eigenfunctions for these modes are evaluated for neutron star models. The second-order eigenfunctions for these modes are determined here by solving an unusual inhomogeneous hyperbolic boundary-value problem. The numerical techniques developed to solve this unusual problem are somewhat non-standard and may well be of interest beyond the particular application here. The bulk-viscosity coupling to the r-modes, which appears first at second order, is evaluated. The bulk-viscosity timescales are found here to be longer than previous estimates for normal neutron stars, but shorter than previous estimates for strange stars. These new timescales do not substantially affect the current picture of the gravitational radiation driven instability of the r-modes either for neutron stars or for strange stars.