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The frequencies of r-mode oscillations of rotating neutron stars can beuseful for guiding and interpreting gravitational wave and electromagneticobservations. The frequencies of slowly rotating, barotropic, and non-magneticNewtonian stars are well known, but subject to various corrections. Aftermaking simple estimates of the relative strengths of these corrections weconclude that relativistic corrections are likely to be the most important. Forthis reason we extend the formalism of K. H. Lockitch, J. L. Friedman, and N.Andersson [Phys. Rev. D 68, 124010 (2003)], who consider relativisticpolytropes, to the case of realistic equations of state. This formulationresults in perturbation equations which are solved using a spectral method. Wefind that for realistic equations of state the r-mode frequency ranges from1.39 to 1.57 times the spin frequency of the star when the relativisticcompactness parameter (M/R) is varied over the astrophysically motivatedinterval 0.11 to 0.31. The results presented here are relevant to the design ofgravitational wave and electromagnetic r-mode searches, and following asuccessful r-mode detection could help constrain the high density equation ofstate.

R-mode frequencies of slowly rotating relativistic neutron stars with realistic equations of state