Improved Frequency Spectra of Gravitational Waves with Memory in a Binary-Black-hole Simulation

Numerical relativists can now produce gravitational waveforms with memoryeffects routinely and accurately. The gravitational-wave memory effect containsvery low-frequency components, including a persistent offset. The presence ofthese components violates basic assumptions about time-shift behaviorunderpinning standard data-analysis techniques in gravitational-wave astronomy.This poses a challenge to the analysis of waveform spectra: How to preserve thelow-frequency characteristics when transforming a time-domain waveform to thefrequency domain. To tackle this challenge, we revisit the preprocessingprocedures applied to the waveforms that contain memory effects. We findinconsistency between the zero-frequency limit of displacement memory and thelow- frequency spectrum of the same memory preprocessed using the common schemein literature. To resolve the inconsistency, we propose a new robustpreprocessing scheme that produces the spectra of memory waveforms morefaithfully. Using this new scheme, we inspect several characteristics of thespectrum of a memory waveform. In particular, we find a discernible beatingpattern formed by the dominant oscillatory mode and the displacement memory.This pattern is absent in the spectrum of a waveform without memory. Thedifference between the memory and no-memory waveforms is too small to beobserved by current-generation detectors in a single binary-black-hole event.Detecting the memory in a single event is likely to occur in the era ofnext-generation detectors.