2023ApJ...944...53G

The r-mode oscillations of rotating neutron stars are promising candidates for continuous gravitational-wave (GW) observations. The r-mode frequencies for slowly rotating Newtonian stars are well known and independent of the equation of state (EOS), but for neutron stars several mechanisms can alter the r-mode frequency for which the relativistic correction is dominant and relevant for most of the neutron stars. The most sensitive searches for continuous GWs are those for known pulsars for which GW frequencies are in targeted narrow frequency bands of a few hertz. In this study, we investigate the effect of several state-of-the-art multimessenger constraints on the r-mode frequency for relativistic, slowly rotating, barotropic stars. Imposing these recent constraints on the EOS, we find that the r-mode frequency range is slightly higher than that from the previous study and the narrowband frequency range can increase by up to 25% for the most promising candidate PSR J0537-6910 depending on the range of compactness. We also derive universal relations between r-mode frequency and dimensionless tidal deformability that can be used to estimate the dynamical tide of the r-mode resonant excitation during the inspiral signal. These results can be used to construct the parameter space for r-mode searches in GW data and also constrain the nuclear EOS following a successful r-mode detection.