Nonlinear Relativistic Tidal Response of Neutron Stars

We investigate the nonlinear tidal response of relativistic neutron stars by computing the fully relativistic, static, quadratic Love numbers. Using both the worldline effective field theory for extended gravitating bodies and second-order perturbations of relativistic stellar models, we derive the nonlinear tidal deformation induced by an external gravito-electric tidal field to quadratic order. Through a suitable matching procedure, we provide for the first time the leading nonlinear tidal corrections to the conservative dynamics and gravitational-wave signal of binary systems. Quadratic Love numbers are enhanced more than the linear ones in the small-compactness limit. Because of this, despite entering the gravitational-wave phase at 8th post-Newtonian (PN) order, the leading quadratic Love number can be as important as the next-to-next-to-leading order linear tidal correction, which enters at 7th PN order, and is larger than the subleading point-particle contribution entering at 4th PN order. In particular, quadratic Love numbers can be as large as ~10% of the linear Love numbers in the late inspiral phase. Our approach provides a framework to also compute the (subleading) nonlinear effects induced by magnetic tidal fields and higher multipole moments, and sets the foundations for incorporating nonlinear tidal effects in high-precision gravitational-wave modeling.