AI 中文总结
研究双中子星系统合并时的潮汐现象，通过仿射近似推导耦合系数，揭示通用关系，指出不考虑三波非线性潮汐会致引力波形有系统误差，还阐述了单星及双星的相移情况及四波相互作用对快慢旋转中子星的影响。
AI 中文摘要
我们研究双中子星（BNS）系统在合并过程中的潮汐现象，包括非线性流体动力学相互作用。通过仿射近似将受扰中子星视为椭球体，我们在哈密顿量中解析推导了f模和径向模到四波阶（即次近领先阶）的耦合系数，考虑了背景恒星的任意旋转。我们的模型从第一性原理论证中揭示了一系列通用关系。除了已知关系外，我们表明三波（次领先阶）相互作用系数完全由线性潮汐的性质决定，不探测中子星的新物理。然而，不包括三波非线性潮汐会在引力波形中导致显著的系统误差。我们通过一种混合方法支持这一观点，该方法同时捕捉牛顿流体动力学中预期的模式共振，并与低频展开中的相对论计算一致。与线性潮汐模型相比，单个中子星中的非线性潮汐在合并前可导致约1.7弧度的相移积累；对于质量相似的双星，相移约加倍。我们的计算扩展到四波相互作用，对于缓慢旋转的中子星，它只提供小的修正，与轨道上的潮汐反作用相比是次要的。对于快速旋转的中子星，f模的非线性离心驱动和四波非谐性为研究与内部浮力相关的绝热指数提供了一个窗口，这在缓慢旋转系统中的线性和三波潮汐中无法探测到。非谐性不会导致f模的共振锁定。
英文摘要
We study tides during the inspiral of a binary neutron star system, including nonlinear hydrodynamical interactions. Using an affine approximation that treats the perturbed neutron star (NS) as an ellipsoid, we analytically derive coupling coefficients among the quadrupolar f-modes and the radial mode to the four-wave order (next-to-next-to-leading order) in the Hamiltonian, allowing for arbitrary (aligned or anti-aligned) spin of the background star. Our model reveals a series of universal relations from first-principles arguments. We show that the three-wave (next-to-leading-order) interaction coefficients in a non-spinning star are fully determined by the properties of the linear tide. They do not probe new physics of the NS. Nonetheless, three-wave nonlinear tides are significant corrections to the gravitational waveform. We support this via a hybrid approach that simultaneously captures mode resonances expected in Newtonian hydrodynamics and is consistent with relativistic calculations in the low-frequency expansion. The nonlinear tide in a single NS can cause a phase shift of around 1.8 radians accumulated up to merger compared to the linear tide model; for a binary, the phase shift is approximately doubled. In a low-frequency expansion, the nonlinear tide is degenerate with the finite-frequency correction of the linear tide, introducing systematic bias when ignored. Our calculation extends to four-wave interactions, which, for a slowly spinning neutron star, provide only small corrections. For a rapidly rotating neutron star, the nonlinear centrifugal drive of the f-mode provides a window to study the internal buoyancy that cannot be probed by the linear and three-wave f-mode tides in slowly spinning systems. The four-wave anharmonicity cannot lead to resonance locking of the f-mode.
Comments43 pages, 11 figures, to be submitted
