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The gravitational wave signal from a binary neutron star merger carries theimprint of the deformability properties of the coalescing bodies, and then ofthe equation of state of neutron stars. In current models of the waveformsemitted in these events, the contribution of tidal deformation is encoded in aset of parameters, the tidal Love numbers. More refined models includetidal-rotation couplings, described by an additional set of parameters, therotational tidal Love numbers, which appear in the waveform at $6.5$post-Newtonian order. For neutron stars with spins as large as $\sim0.1$, weshow that neglecting tidal-rotation couplings may lead to a significant errorin the parameter estimation by third-generation gravitational wave detectors.By performing a Fisher matrix analysis we assess the measurability ofrotational tidal Love numbers, showing that their contribution in the waveformcould be measured by third-generation detectors. Our results suggest thatcurrent models of tidal deformation in late inspiral should be improved inorder to avoid waveform systematics and extract reliable information fromgravitational wave signals observed by next generation detectors.

Impact and detectability of spin-tidal couplings in neutron star inspirals