  The frequencies of r-mode oscillations of rotating neutron stars can be
useful for guiding and interpreting gravitational wave and electromagnetic
observations. The frequencies of slowly rotating, barotropic, and non-magnetic
Newtonian stars are well known, but subject to various corrections. After
making simple estimates of the relative strengths of these corrections we
conclude that relativistic corrections are likely to be the most important. For
this reason we extend the formalism of K. H. Lockitch, J. L. Friedman, and N.
Andersson [Phys. Rev. D 68, 124010 (2003)], who consider relativistic
polytropes, to the case of realistic equations of state. This formulation
results in perturbation equations which are solved using a spectral method. We
find that for realistic equations of state the r-mode frequency ranges from
1.39 to 1.57 times the spin frequency of the star when the relativistic
compactness parameter (M/R) is varied over the astrophysically motivated
interval 0.11 to 0.31. The results presented here are relevant to the design of
gravitational wave and electromagnetic r-mode searches, and following a
successful r-mode detection could help constrain the high density equation of
state.
