| Abstract : | R-mode oscillations of rotating neutron stars are promising candidates for continuous gravitational wave (GW) observations. The r-mode frequencies for 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 of which the relativistic correction which depends on the EOS 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 few Hz. Recently, the binary neutron star merger GW170817 and its electromagnetic counterpart, NICER observations have been extensively used to constrain the EOS. In this study, we investigate the effect of these state-of-the-art multi-messenger constraints on the r-mode frequency for relativistic, slowly rotating, barotropic stars. We find that the parameter space for r-mode frequency is higher than the range currently used in continuous wave searches and it can increase up to 8-25% 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 which can be used to estimate the dynamical tide effect of the r-mode resonant excitation during the inspiral . These results can be used to construct the parameter space for r-mode searches in gravitational wave data and also constrain the nuclear equation of state following a successful r-mode detection. |
