AI 中文总结
研究超大质量黑洞附近致密双星并合质心因周期性视线速度产生的引力波调制，给出波形相位和幅度校正，通过费希尔矩阵分析预测探测器对相关环境的约束，相比近似方法，所得约束显著改善。
AI 中文摘要
在超大质量黑洞附近、与任意第三体（如恒星质量）相互作用或处于密集恒星环境中发生的致密双星并合（CBC）的质心，会经历随时间变化的视线（LOS）速度。这进而导致随时间变化的多普勒频移和引力波（GW）形状的相应调制。已知由恒定LOS加速度及其高阶时间导数引起的相位和幅度校正，这些效应会在-4n后牛顿（PN）阶对GW波形产生校正。在CBC质心的圆形或偏心外轨道情况下，这些效应可视为在观测持续时间远小于外轨道周期的极限下对LOS速度的近似。本文给出了CBC质心圆形和偏心外轨道周期性非相对论LOS速度引起的GW波形的相位和幅度校正，这些校正导致4PN阶的相位和幅度调制，并在上述适当极限下简化为已知的恒定运动学参数校正。还进行了费希尔矩阵分析，以预测各种未来地面和空间探测器对产生随时间变化LOS速度的环境的约束。进一步表明，与从适用于恒定运动学参数的近似方法获得的约束相比，使用本文推导的GW波形获得的约束有显著改善。
英文摘要
The centre of mass (CoM) of compact binary coalescences (CBCs) occurring in the vicinity of a supermassive black hole, through interaction with an arbitrary third body (e.g., of stellar mass), or in a dense stellar environment, will undergo a time-varying line-of-sight (LOS) velocity. This in turn leads to a time-varying Doppler shift and corresponding modulations in the shape of the gravitational waves (GWs). The phase and amplitude corrections arising from constant LOS acceleration and its higher-order time derivatives are already known. Specifically, these effects lead to corrections to the GW waveform at $-4n$ post-Newtonian (PN) order, where $n$ is the $n^{th}$ time derivative of the LOS velocity. In the context of a circular or eccentric outer orbit of the CoM of the CBC, these effects can be thought of as approximations to the LOS velocity in the limit: observation duration $\ll$ period of the outer orbit. However, this condition is not necessarily always satisfied. In this {\it paper}, we present phase and amplitude corrections to the GW waveforms arising from a periodic non-relativistic LOS velocity for circular and eccentric outer orbits of the CBC's CoM. Specifically, these lead to phase and amplitude modulations at 4 PN order, and reduce to the known corrections for constant kinematic parameters under appropriate limits mentioned above. We also perform a Fisher matrix analysis to forecast constraints on the environment that is sourcing the time-varying LOS velocity, for various future ground and space-based detectors. We further show that constraints acquired using GW waveforms derived in this work improve significantly in comparison to those acquired from approximate methods valid for constant kinematic parameters.
