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Techniques are developed here for evaluating the r-modes of rotating neutronstars through second order in the angular velocity of the star. Second-ordercorrections to the frequencies and eigenfunctions for these modes are evaluatedfor neutron star models. The second-order eigenfunctions for these modes aredetermined here by solving an unusual inhomogeneous hyperbolic boundary-valueproblem. The numerical techniques developed to solve this unusual problem aresomewhat non-standard and may well be of interest beyond the particularapplication here. The bulk-viscosity coupling to the r-modes, which appearsfirst at second order, is evaluated. The bulk-viscosity timescales are foundhere to be longer than previous estimates for normal neutron stars, but shorterthan previous estimates for strange stars. These new timescales do notsubstantially affect the current picture of the gravitational radiation driveninstability of the r-modes either for neutron stars or for strange stars.Comment: 13 pages, 5 figures, revte

Second-order rotational effects on ther-modes of neutron stars