标题： 基于地基引力波探测器对紧凑双星信号的时间相关探测器响应的快速频域表达式 显示英文标题

标题： A fast frequency-domain expression for the time-dependent detector response of ground-based gravitational-wave detectors to compact binary signals

摘要： 对于提议的第三代引力波探测器，例如爱因斯坦望远镜和宇宙探索者，它们的敏感频段被提议扩展到 5 赫兹或更低，低质量致密双星（例如双中子星）的信号在探测器的敏感频段内停留足够长的时间（对于最低提议的低频截止值 1 赫兹，最长可达几天），因此不能忽略地球自转对探测器响应以及信号不断变化的多普勒频移的影响。在后一种情况下，还需要考虑地球轨道运动的影响，而目前这种影响仅在使用连续波技术分析致密双星信号时才被包括进来。 这些影响也适用于当前的探测器和假设的次太阳质量双星的信号。 在这里，我们提出了简单的傅里叶级数方法来计算频率域中的这些影响，并给出了地球轨道运动以低阶傅里叶级数形式的明确表达式，这将对所有致密双星信号足够准确，除了来自非常低质量次太阳质量双星的信号。 关于天线图案函数的地球自转效应的表达式没有使用驻相近似（SPA），因此我们能够表明 SPA 在这些情况下确实相当准确，并提出一个与之等效的傅里叶级数表达式，其速度要快一个数量级。 我们还提供了这些影响在探测器灵敏度以及随着频率积累关于各种双星参数的信息方面的示例。 显示英文摘要

摘要： For proposed third-generation gravitational-wave detectors such as the Einstein Telescope and Cosmic Explorer, whose sensitive bands are proposed to extend down to 5 Hz or below, the signals of low-mass compact binaries such as binary neutron stars remain in the detector's sensitive band long enough (up to a few days for the smallest proposed low-frequency cutoff of 1 Hz) that one cannot neglect the effects of the Earth's rotation on the detector's response and the changing Doppler shift of the signal. In the latter case, one also needs to consider the effects of the Earth's orbital motion, which is currently only included in analyses of compact binary signals using continuous wave techniques. These effects are also relevant for current detectors and signals from putative subsolar-mass binaries. Here we present simple Fourier series methods for computing these effects in the frequency domain, giving explicit expressions for the Earth's orbital motion in terms of low-order Fourier series, which will be sufficiently accurate for all compact binary signals except for those from very low-mass subsolar-mass binaries. The expression for the effects of the Earth's rotation on the antenna pattern functions does not use the stationary phase approximation (SPA), so we are able to show that the SPA is indeed quite accurate in these situations and present a Fourier series expression equivalent to it which is an order of magnitude faster. We also provide illustrations of these effects on detector sensitivity and the accumulation of information about various binary parameters with frequency.