Probing soft signals of gravitational-wave memory with space-based interferometers

Abstract

Gravitational-wave displacement memory is a remarkable and ubiquitous phenomenon predicted by general relativity, which has not yet been detected. Unlike the oscillatory components of gravitational waveforms, displacement memory is associated with soft gravitons, making it the only observable signal of its parent event at sufficiently low frequencies. Similarly, soft waveforms may arise from velocity and integrated-displacement memory. The simple and universal spectral shapes of soft waveforms also provide effective templates for matched filtering and parameter estimation. In this paper, we systematically investigate the detection prospects for such soft memory signals with future space-based laser interferometers. As realistic examples, we examine the infrared spectral features of gravitational waves from moderately relativistic compact binary scattering and quasi-circular, non-precessing black hole mergers. In both cases, the low-frequency spectrum can be described by a soft waveform of displacement memory with a real correction factor. The results of simulated Bayesian parameter estimation demonstrate that independent measurement of a soft displacement-memory signal with a single LISA-like detector is achievable at signal-to-noise ratios $\gtrsim 10$. The measurement precision can be significantly improved by joint observations with a LISA-Taiji network. A single BBO detector would be capable of separately measuring the null memory from stellar-mass compact binary mergers. We also evaluate the detectability of an idealized stochastic background of soft displacement-memory signals. Our results indicate that gravitational-wave bursts with memory can be promising targets for space-based interferometers.

Figures (27)

• Figure 1: Relative deviations from the soft waveform in $\tilde{h}_{2,2}$ (black), $\tilde{h}_{2,-2}$ (blue) and $\tilde{h}_{2,0}$ (green).
• Figure 2: Relative deviations from the soft waveform in $\text{arg}\,\tilde{h}$ for various eccentricities, at $\{\Theta,\Phi\}=\{\pi/6,\pi/3\}$.
• Figure 3: CM-frame orbits (top panel) and gravitational waveforms in the time domain (middle panel) and frequency domain (bottom panel) of a compact binary scattering, with $\nu=0.2$, $b/M=100$, $v_0=0.13$ (corresponding to $e=2$), and $\{\Theta,\Phi\}=\{\pi/6,\pi/3\}$. In the middle panel, the 0PN waveform is computed using the 0PN orbit, whereas the 0.5PN and 1PN waveforms are computed using the 2PN orbit. The bottom panel shows the spectrum of the 1PN waveform, with $\Omega=\sqrt{M/a^3} = v_0^3/M \approx \pi (v_0/0.13)^3(100\,M_\odot/M)\times 1.4\,\text{Hz}$. Before computing the spectrum, we shift the time coordinate such that the periastron crossing happens at $t=0$. The horizontal line in the bottom panel represents the soft waveform corresponding to $\Delta h_\lambda$ in the time domain.
• Figure 4: Spectra of $f\,\text{Im}\,\tilde{h}'(f)$ and $f\,\text{Re}\,\tilde{h}'(f)$. The linear and quadratic fits to the low-frequency part of the spectra are also shown. The horizontal line represents the soft waveform corresponding to $\Delta h_\lambda$ in the time domain.
• Figure 5: Ordinary displacement memory from the scattering of a test body with mass $\nu M$ by a non-spinning BH with mass $M$, for $b/M=100$, and $\{\Theta,\Phi\}=\{\pi/5,\pi/7\}$. The blue and black solid lines show the test-body approximation. The red (green) dashed lines show the 0PN (1PN) approximations. The pink dashed lines show the results computed from Eq. \ref{['EMR_memory']}, using the 1PN approximation to the deflection angle. The critical incident velocity $v_\text{plunge}\approx 0.04$. The figure inset shows the results for small incident velocities, with the horizontal axis given by $v_0-v_\text{plunge}$. For comparison, the gray dot-dashed lines show the results for a central BH with dimensionless spin $\chi=1$ along the $Z$-axis, for which $v_\text{plunge}=0.02$.