Effective one body description of tidal effects in inspiralling compact binaries

The late part of the gravitational wave signal of binary neutron-star (or black-hole--neutron-star) inspirals can in principle yield crucial information on the nuclear equation of state via its dependence on relativistic tidal parameters. In the hope of analytically describing the gravitational wave phasing during the late inspiral (essentially up to merger) we propose an extension of the effective one body (EOB) formalism which includes tidal effects. We compare the prediction of this tidal-EOB formalism to recently computed nonconformally flat quasiequilibrium circular sequences of binary neutron-star systems. Our analysis suggests the importance of higher-order (post-Newtonian) corrections to tidal effects, even beyond the first post-Newtonian order, and their tendency to significantly increase the ``effective tidal polarizability'' of neutron stars. We propose to use the EOB description up to the moment where the tidally deformed compact objects formally enter ``into contact.'' We compare the EOB predictions to some recently advocated, nonresummed, post-Newtonian based (``Taylor-T4'') description of the phasing of inspiralling systems. This comparison shows the strong sensitivity of the late-inspiral phasing to the choice of the analytical model. A sufficiently accurate numerical--relativity--``calibrated'' EOB model might, however, give us a reliable analytical description of the late inspiral of compact binaries (and might also help in predicting the conditions necessary for the generation of short gamma-ray bursts).