Novel method to construct frequency-domain gravitational waveforms for accelerating sources
构建加速源频域引力波形的新方法
Accurately modeling the inspiral-merger-ringdown (IMR) signal of coalescing compact objects is essential for the test of general relativity. However, it is known that astrophysical environments can distort gravitational-wave (GW) signal and, if ignored, may bias parameter estimation or even our understanding of gravity. Previous studies suggest that the leading-order effects of many astrophysical environments can be modeled in a unified way by introducing an effective acceleration. However, such models are based on stationary phase approximation (SPA) and post-Newtonian (PN) formalism, which are inconsistent with the fast orbital evolution and strong gravity in the final merger-ringdown phase. To overcome this limit, we introduce frequency-domain spectral differentiation (FSD), which maps the time shift of the signal caused by acceleration into a differentiation in the frequency domain. The mapping does not rely on SPA or PN formalism, therefore can be used to construct the accelerated waveform across the entire IMR phases. We compare the FSD waveforms with the conventional <inline-formula><mml:math><mml:mrow><mml:mi>SPA</mml:mi><mml:mo>+</mml:mo><mml:mi>PN</mml:mi></mml:mrow></mml:math></inline-formula> ones, and find that the former more faithfully match the simulated signals of accelerating sources, especially in the merger-ringdown phase and when higher-order FSD corrections are included. A Fisher information matrix analysis suggests that FSD waveforms can achieve higher precision than <inline-formula><mml:math><mml:mrow><mml:mi>SPA</mml:mi><mml:mo>+</mml:mo><mml:mi>PN</mml:mi></mml:mrow></mml:math></inline-formula> waveforms in measuring effective acceleration. Therefore, the FSD method offers a more self-consistent treatment of the accelerationlike class of astrophysical environmental effects in the final merger-ringdown phase of binary GW sources.
展开 ▾FSD 不依赖 SPA/PN,可在并合–铃铛阶段更忠实地建模加速度效应;高阶 FSD 展开可显著提升吸气阶段精度,比传统 SPA+PN 方法更接近时间域拉伸基准。
以往研究已尝试将多种天体物理环境影响统一为有效加速度,并借助稳态相位近似(SPA)与后牛顿(PN)展开的解析相位修正建模(Chamberlain+ 2019、Vijaykumar+ 2023、Lazarow+ 2024)。本文提出频域谱微分(FSD),把加速度引起的时域伸缩映射为频域导数,不依赖 SPA 或 PN,因此可直接作用于 IMRPhenomXPHM、SEOBNRv5PHM 等完整 IMR 模板(Pratten+ 2021)。与时间域拉伸基准相比,FSD 在并合–铃铛阶段更准确,高阶展开可进一步改善吸气和低频精度。展望上,该方法为未来数值相对论模板、偏心率与旋进波形以及空间探测器的周期加速场景提供了可扩展的统一框架,有助于在强场检验中分离环境效应与真实非广义相对论信号。
刊出 2026-09-04 · 收录 2026-09-12