A Novel Method to Construct Frequency-Domain Gravitational Waveform for Accelerating Sources

Abstract

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 various astrophysical environmental effects 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 SPA+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 SPA+PN waveforms in measuring effective acceleration. Therefore, the FSD method offers a more self-consistent treatment of various astrophysical environmental effects in the final merger-ringdown phase of binary GW sources.

Figures (6)

• Figure 1: Phase shifts as a function of frequency derived from different methods, including the time domain stretching (TDS, blue solid line), frequency-domain spectral differentiation (FSD, orange dashed line), and the SPA$+$PN method (green dot dashed line). Here we have assumed an effective acceleration of $a=e-5\per\s$, a cosmological redshift of $0.2$ for the BBH, and the standard $\upLambda$CDM cosmology. The other parameters used in the calculation are labeled at the top of each panel.
• Figure 2: Mismatch versus the mass of the primary BH. The orange solid curves show the mismatches between the TDS waveforms and SPA+PN ones, while the blue dashed curves refer to the mismatches relative to the FSD waveforms. Different symbols indicate different spin parameters, as detailed in the legend. All configurations assume a mass ratio of $m_1:m_2 = 2:1$, spin parameters of $\chi_1 = \chi_2 = \chi$, and an effective acceleration of $a = e-4\per\s$, and the aLIGO sensitivity curve. The left, middle, and right panels display the mismatches for the inspiral, merger--ringdown, and full IMR signal, respectively.
• Figure 3: The same as Figure \ref{['fig:td vs dev vs pn ligo']} but using the ET sensitivity. The duration of the waveforms are now longer due to the better sensitivity of ET.
• Figure 4: The same as Figure \ref{['fig:td vs dev vs pn 1e-4']} but reducing the effective acceleration to $a=e-5\per\s$.
• Figure 5: Similar to Figure \ref{['fig:td vs dev vs pn 1e-5']} but including different orders of corrections in the FSD waveform. Notice that in the merger--ringdown stage, the mismatches resulting from different orders of corrections overlap, because the duration of this stage is short.