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Abstract

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 associated with the Coriolis effect, whose
frequencies are proportional to the NS's spin frequency, and for which the spin
orientation determines the subclass of modes that are predominantly excited. We
advance the GW models for these effects that are needed for data analysis by
first developing a description for the adiabatic signatures from
gravitomagnetic modes in slowly rotating NSs. We show that they can be
encapsulated in an effective Love number which differs before and after a mode
resonance. Combining this with a known generic model for abrupt changes in the
GWs at the mode resonance and a point-mass baseline leads to an efficient
description 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.