Detectability of Gravitational-Wave Memory with LISA: A Bayesian Approach

TL;DR

This work assesses the detectability and characterization of the gravitational-wave memory (displacement memory) with LISA using a Bayesian framework applied to simulated MBHB waveforms. It develops a memory model and constructs detectors comparing memory-containing and memory-free templates, quantifying detectability through Bayes factors and SNRs, and establishing a practical threshold of $\text{SNR}_{\rm mem} \approx 3$ for memory detection. It further analyzes how memory influences MBHB parameter estimation, showing limited impact at high SNR but potential degeneracy breaking in lower-SNR scenarios, and demonstrates how to estimate the memory amplitude with a parametric $\gamma$ factor, finding a power-law relation $\delta\gamma \approx 2.5 \times \text{SNR}_{\rm mem}^{-1.1}$. By applying population catalogs from Barausse et al., the paper projects memory-detection prospects, finding favorable outcomes in heavy-seed models and meaningful chances in light-seed models, thereby informing LISA's tests of GR and potential beyond-GR scenarios.

Abstract

Gravitational wave (GW) astronomy opens a new venue to explore the universe. Future observatories such as LISA, the Laser Interferometer Space Antenna, are expected to observe previously undetectable fundamental physics effects in signals predicted by General Relativity (GR).One particularly interesting such signal is associated to the displacement memory effect, which corresponds to a permanent deformation of spacetime due to the passage of gravitational radiation. In this work, we explore the ability of LISA to observe and characterize this effect. In order to do this, we use state-of-the-art simulations of the LISA instrument, and we perform a Bayesian analysis to assess the detectability and establish general conditions to claim detection of the displacement memory effect from individual massive black hole binary (MBHB) merger events in LISA. We perform parameter estimation both to explore the impact of the displacement memory effect and to reconstruct its amplitude. We discuss the precision at which such a reconstruction can be obtained thus opening the way to tests of GR and alternative theories. To provide astrophysical context, we apply our analysis to black hole binary populations models and estimate the rates at which the displacement memory effect could be observed within the LISA planned lifetime.

Figures (23)

• Figure 1: Example of the + polarization of a time-domain waveform with memory effect using the waveform NRHybSur3dq8_CCE. The blue curve shows the total signal ($(2,2)$-oscillatory + memory) and its associated $(2,0)$ memory component in red. The parameters are $Q=1.5$, $\chi_{\mathrm{1z}}=0.7$, $\chi_{\mathrm{2z}}=0.7$, $M=10^6 M_\odot$, $d_\mathrm{L}=10^4$ Mpc, $\iota=\frac{\pi}{2}$, $\varphi_{\mathrm{ref}}=0$, $\psi = 0$.
• Figure 2: Summarized steps to obtain mock data and templates. Red names indicate the package use for a given process.
• Figure 3: $\textrm{SNR}_{\textrm{tot}}$ (top subfigure) and $\textrm{SNR}_{\textrm{mem}}$ (bottom subfigure) depending on the total source mass $M$ and the mass ratio $Q$. Because of the different frequency content between the oscillatory and the memory signal, the peak of the sensitivity is different in the two cases. Here we used the NRHybSur3dq8_CCE waveform and the following parameters: $\chi_{\mathrm{1z}} = \chi_{\mathrm{2z}}=0.4$, $\iota = \pi/3$, $d_{\mathrm{L}} = 10^4 \textrm{Mpc}$, $\varphi_{\mathrm{ref}} = 1$, $\psi = 0$, $\alpha = 0.74$, $\delta = 0.29$.
• Figure 4: Memory waterfall plot from the Fig. \ref{['fig:WaterfallPlotsSurrogate']} with stars corresponding to the computed $\log_{10}\mathcal{B}$. The colour of the stars corresponds to the Jeffreys scale (Table \ref{['tab:JeffreysScale']}) as indicated by the colour-bar under the figure. The light gray dashed line represents the ISO-SNR contour $\textrm{SNR}_{\textrm{mem}} = 3$. This plot used the NRHybSur3dq8_CCE waveform and the same parameters as Fig. \ref{['fig:WaterfallPlotsSurrogate']}
• Figure 5: $\log_{10}$Bayes factor computation for different parameters. The colors stand for different parameters, except mass, which are indicated with different markers. This plot made use of NRHybSur3dq8_CCE waveform.