Constraints on Nonlinear Tides due to p–g Mode Coupling from the Neutron Star Merger GW170817

Abstract

It has been suggested by Weinberg et al. that an instability due to the nonlinear coupling of a neutron star’s tide to its p - and g -modes could affect the gravitational-wave phase evolution of a neutron star binary. Weinberg suggests that this instability can turn on as the gravitational waves pass through the sensitive band of ground-based detectors, although the size of the effect is not known. The discovery of the binary neutron star merger GW170817 provides an opportunity to look for evidence of nonlinear tides from p – g mode coupling. We compute Bayesian evidences that compare waveform models that include the p – g mode coupling with models that do not. We find that the consistency between GW170817 signal and the p – g mode model reported by Abbott et al. is due to a degeneracy between the phenomenological waveform used to model the effect of nonlinear tides and the standard post-Newtonian waveform. We investigate the consistency of the GW170817 signal with regions of the parameter space where the effect of nonlinear tides is not degenerate with the standard model. Regions of the nonlinear tide parameter space that have a fitting factor of less than 99% (98.5%) are disfavored by a Bayes factor of 15 (25). We conclude that regions of the parameter space where nonlinear tides produce a measurable effect are strongly disfavored and improved theoretical modeling will be needed if future observations are to constrain nonlinear tides from p – g mode coupling in neutron stars.