标题： 超越线性潮汐：中子星非线性潮汐响应对双星旋近引力波形的影响 显示英文标题

标题： Beyond the linear tide: impact of the non-linear tidal response of neutron stars on gravitational waveforms from binary inspirals

摘要： 潮汐相互作用在合并的双中子星中会改变 inspiral 的动力学，因此会在引力波（GW）信号中留下额外相位偏移的特征。 为了从观测中约束超核物质状态方程，我们需要准确的潮汐相位偏移模型。 在以前的研究中，通常通过将潮汐视为对扰动潮汐场的线性响应来构建 GW 波形模型。 在这项工作中，我们引入了由于流体动力学三模和四模相互作用产生的非线性修正，并展示了它们如何提高波形模型的准确性和解释力。 我们建立了轨道和模式的耦合微分方程并数值求解，同时解析推导了系统平衡配置的解。 我们的解析解在合并前与数值解吻合良好，仅涉及代数关系，使得在大参数空间内对不同状态方程进行快速相位偏移和波形评估成为可能。 我们发现，在牛顿阶，非线性流体效应可以在 1000 Hz 的 GW 频率下使潮汐相位偏移增强$\gtrsim 1\,{\rm radian}$，对应于线性理论的一个$10-20\%$修正。 接近合并时额外相位偏移的尺度与仅考虑线性潮汐的理论预测和数值相对论之间的差异一致。 因此，当解释数值相对论的结果以及为当前和未来的 GW 探测器构建波形模型时，非线性流体效应非常重要。 显示英文摘要

摘要： 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.