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 $\mathrm{SPA}+\mathrm{PN}$ 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 $\mathrm{SPA}+\mathrm{PN}$ 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.

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• Astrophysical studies of gravity
• Gravitational waves
• Astronomical black holes
• Numerical relativity