Waveform models for the gravitational-wave memory effect: II. Time-domain and frequency-domain models for nonspinning binaries

TL;DR

The nonlinear gravitational-wave memory effect remains undetected in individual events but accessible statistically across BBH populations. This paper delivers a fast, analytically tractable memory waveform by constructing a time-domain model with a PN inspiral, multimode QNM ringdown, and a phenomenological intermediate bridge, plus an exact analytic Fourier transform to obtain a frequency-domain memory model. Calibration against NR surrogate data for nonspinning binaries with mass ratios up to $8$ shows typical mismatches around $10^{-3}$ and worst cases near $10^{-2}$, with SNR mismatches sometimes larger. The work enables efficient memory searches in LVK data and lays groundwork for extending to spins and precession, potentially improving prospects for detecting the GR memory effect in the near future.

Abstract

The nonlinear gravitational-wave (GW) memory effect$\unicode{x2014}$a permanent shift in the GW strain that arises from nonlinear GW interactions in the wave zone$\unicode{x2014}$is a prediction of general relativity which has not yet been observed. The amplitude of the GW memory effect from binary-black-hole (BBH) mergers is small compared to that of primary (oscillatory) GWs and is unlikely to be detected by current ground-based detectors. Evidence for its presence in the population of all the BBH mergers is more likely, once thousands of detections are made by these detectors. Having an accurate and computationally efficient waveform model of the memory signal will assist detecting the memory effect with current data-analysis pipelines. In this paper, we build on our prior work to develop analytical time-domain and frequency-domain models for the dominant nonlinear memory multipole signal ($l=2$, $m=0$) from nonspinning BBH mergers in quasicircular orbits. The model is calibrated for mass ratios between one and eight. There are three parts to the time-domain signal model: a post-Newtonian inspiral, a quasinormal-mode-based ringdown, and a phenomenological signal during the late inspiral and merger (which interpolates between the inspiral and ringdown). The time-domain model also has an analytical Fourier transform, which we compute in this paper. We assess the accuracy of our model using the mismatch between our waveform model and the memory signal computed from the oscillatory modes of a numerical-relativity surrogate model. We use the advanced LIGO sensitivity curve from the fourth observing run and find that the mismatch increases with the total mass of the system and is of order $10^{-2}\unicode{x2013}10^{-4}$.

Figures (9)

• Figure 1: Inspiral memory model and its relative error versus time: Top: The hybridized surrogate memory signal computed from the NRHybSur3dq8 surrogate waveform modes (solid, blue curve) and the inspiral time-domain memory model (dashed, orange curve) for an equal-mass non-spinning BBH merger (left) and for a mass ratio $q=8$ (right). Bottom: The relative error $\delta h_{20}$ in Eq. \ref{['eq:relative_error']} the inspiral memory model for each of the corresponding mass ratios shown above.
• Figure 2: Waveform for the $h_{21}$ mode: Top: The real part of the $h_{21}$ mode computed from the surrogate model shown as a solid, blue curve, and the same mode computed from our ringdown model in Eq. \ref{['eq:hlm_ringdown_model']} is shown as an orange, dashed curve. Bottom: The residuals between the $h_{21}$ waveform evaluated from the surrogate model and our ringdown model waveform.
• Figure 3: Waveform for the $h_{22}$ and $h_{32}$ modes: Top: The real part of the $h_{22}$ mode (left) from the surrogate model shown in solid, blue curve. The same mode computed from our ringdown model is the orange, dashed curve. On the right are the equivalent results for the $h_{32}$ mode. Bottom: The residuals between the $h_{22}$ waveform evaluated from the surrogate model and our ringdown model waveform (left) and the same quantity for the $h_{32}$ mode (right).
• Figure 4: Ringdown memory model and relative error versus time: Top: The hybridized surrogate memory signal computed from the NRHybSur3dq8 surrogate waveform modes (solid, blue curve) and the ringdown memory model (dashed, orange curve) for non-spinning BBH mergers. The left panel contains the results for the mass ratio $q=1$ and the right shows the mass ratio $q=8$. Bottom: The relative error of the ringdown memory model and the memory signal computed directly from the NR surrogate for the corresponding mass ratios in the panels above.
• Figure 5: Memory model and relative error versus time: Top: The GW memory signal computed directly from the hybridized surrogate (solid blue) and from the time-domain model (dashed orange). The left panel is for an equal mass binary ($q=1$), whereas the right panel is for the largest mass ratio of $q=8$ that we model. Bottom: The relative error between the surrogate and the time-domain model for the two mass ratios.