Nonlinear Tides of Binary Neutron Stars

Abstract

Nonlinear tides couple stellar oscillations and reshape the gravitational wave (GW) signal from inspiralling binaries. We present hydrodynamic simulations of nonlinear tides in inspiralling neutron-star binaries and, within a mode-coupling model, derive a semi-analytic quadrupolar fundamental mode-frequency shift through second order in the tidal strength. The two approaches agree in the perturbative regime, but diverge at stronger tidal fields, where perturbation theory breaks down. In the late inspiral, nonlinear tides reduce the fundamental-mode frequency by ${\sim}10\%$ for equal-mass binaries and add a GW phase shift of $\mathcal{O}(1)$ radian beyond the linear tidal response. These effects make nonlinear tides a promising target for next-generation GW detectors.