Effect of dynamical gravitomagnetic tides on measurability of tidal parameters for binary neutron stars using gravitational waves

Gravitational waves (GWs) from binary neutron stars (NSs) have opened unique opportunities to constrain the nuclear equation of state by measuring tidal effects associated with the excitation of characteristic modes of the NSs. This includes gravitomagnetic modes induced by the Coriolis effect whose frequencies are proportional to the NS's spin frequency. The NS's spin orientation determines which subclass of gravitomagnetic modes are predominantly excited. We incorporate these effects in GW models needed for data analysis by encapsulating the adiabatic signatures from gravitomagnetic modes in slowly rotating NSs in an effective Love number which differs before and after a mode resonance and combining this with a known generic model for abrupt changes in the GWs at the mode resonance. This leads to an efficient approximate model that adds to a point-mass baseline and which we use to perform case studies of the impacts of gravitomagnetic effects for measurements with Cosmic Explorer, an envisioned next generation GW detector. We quantify the extent to which neglecting (including) the effect of gravitomagnetic modes induces biases (significantly reduces statistical errors) in the measured tidal deformability parameters, which depend on the equation of state. Our results substantiate the importance of dynamical gravitomagnetic tidal effects for measurements with third-generation detectors.