<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-mode frequencies of slowly rotating relativistic neutron stars with realistic equations of state

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 nonmagnetic 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 Lockitch et al. [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--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--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.