Impact of a third body on binary neutron star tidal interactions

For waveform modelling of compact binary coalescence, it is conventionally assumed that the binary is in isolation. In this work, we break that assumption and introduce a third body at a distance. The primary goal is to understand how the distant third body would affect the binary dynamics. However, in the present work, we treat the three-body problem perturbatively and study tidal interaction in the binary due to the third body's presence. We introduce appropriate modifications to the equations governing the orbital motions and the evolution equations of the binary component's quadrupole moment. Further, we obtain the radiated energy and accumulated dephasing for the binary. We show that for b-EMRI, the effect is weak in the tidal sector, while for systems such as b-IMRIs, it would be most relevant to study these effects.