Improved frequency spectra of gravitational waves with memory in a binary-black-hole simulation

TL;DR

This paper introduces a new preprocessing method for gravitational waveforms with memory effects, improving spectral analysis accuracy and revealing a beating pattern absent in non-memory waveforms, with implications for future detector observations.

Contribution

A novel preprocessing scheme that accurately captures low-frequency memory effects in gravitational wave spectra, addressing limitations of previous methods.

Findings

New preprocessing scheme produces more faithful spectra of memory waveforms.

Discovered a beating pattern in the spectrum caused by memory effects.

Memory effects are undetectable with current detectors but may be observable with future technology.

Abstract

Numerical relativists can now produce gravitational waveforms with memory effects routinely and accurately. The gravitational-wave memory effect contains very low-frequency components, including a persistent offset. The presence of these components violates basic assumptions about time-shift behavior underpinning standard data-analysis techniques in gravitational-wave astronomy. This poses a challenge to the analysis of waveform spectra: How to preserve the low-frequency characteristics when transforming a time-domain waveform to the frequency domain. To tackle this challenge, we revisit the preprocessing procedures applied to the waveforms that contain memory effects. We find inconsistency between the zero-frequency limit of displacement memory and the low- frequency spectrum of the same memory preprocessed using the common scheme in literature. To resolve the inconsistency, we propose a new robust preprocessing scheme that produces the spectra of memory waveforms more faithfully. Using this new scheme, we inspect several characteristics of the spectrum of a memory waveform. In particular, we find a discernible beating pattern formed by the dominant oscillatory mode and the displacement memory. This pattern is absent in the spectrum of a waveform without memory. The difference between the memory and no-memory waveforms is too small to be observed 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 of next-generation detectors.