Constraints on non-linear tides due to $p$-$g$ mode coupling from the neutron-star merger GW170817

It has been suggested by Weinberg et al. (2013) that an instability due to 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 (2016) 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 to models that do not. We find that the observations of GW170817 strongly disfavor the existence of $p$-$g$ mode coupling with Bayes factors $\log_{10} \mathcal{B} < -4$. We conclude that the observation of GW170817 does not support the existence of nonlinear tides due to $p$-$g$ mode coupling in binary neutron stars.

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