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Tidal interactions in coalescing binary neutron stars modify the dynamics of the inspiral and hence imprint a signature on their gravitational wave (GW) signals in the form of an extra phase shift. We need accurate models for the tidal phase shift in order to constrain the supranuclear equation of state from observations. In previous studies, GW waveform models were typically constructed by treating the tide as a linear response to a perturbing tidal field. In this work, we incorporate non-linear corrections due to hydrodynamic three- and four-mode interactions and show how they can improve the accuracy and explanatory power of waveform models. We set up and numerically solve the coupled differential equations for the orbit and the modes and analytically derive solutions of the system’s equilibrium configuration. Our analytical solutions agree well with the numerical ones up to the merger and involve only algebraic relations, allowing for fast phase shift and waveform evaluations for different equations of state over a large parameter space. We find that, at Newtonian order, non-linear fluid effects can enhance the tidal phase shift by $\gtrsim 1\, {\rm radian}$ at a GW frequency of 1000 Hz, corresponding to a $10{{\%}}-20{{\%}}$ correction to the linear theory. The scale of the additional phase shift near the merger is consistent with the difference between numerical relativity and theoretical predictions that account only for the linear tide. Non-linear fluid effects are thus important when interpreting the results of numerical relativity and in the construction of waveform models for current and future GW detectors.

 

Abstract In recent years, there have been significant advances in multimessenger astronomy due to the discovery of the first, and so far only confirmed, gravitational wave event with a simultaneous electromagnetic (EM) counterpart, as well as improvements in numerical simulations, gravitational wave (GW) detectors, and transient astronomy. This has led to the exciting possibility of performing joint analyses of the GW and EM data, providing additional constraints on fundamental properties of the binary progenitor and merger remnant. Here, we present a new Bayesian framework that allows inference of these properties, while taking into account the systematic modeling uncertainties that arise when mapping from GW binary progenitor properties to photometric light curves. We extend the relative binning method presented in Zackay et al. to include extrinsic GW parameters for fast analysis of the GW signal. The focus of our EM framework is on light curves arising from r -process nucleosynthesis in the ejected material during and after merger, the so-called kilonova, and particularly on black hole−neutron star systems. As a case study, we examine the recent detection of GW190425, where the primary object is consistent with being either a black hole or a neutron star. We show quantitatively how improved mapping between binary progenitor and outflow properties, and/or an increase in EM data quantity and quality are required in order to break degeneracies in the fundamental source parameters.