Space-borne Interferometers to Detect Thousands of Memory Signals Emitted by Stellar-mass Binary Black Holes

TL;DR

This work demonstrates that space-borne decihertz interferometers like DECIGO can detect memory signals from thousands of stellar-mass BBHs over a 5-year mission, with typical SNRs $>3$ totaling around a few thousand events. By deriving the nonlinear memory waveform in the frequency domain via flux-balance laws and applying an LVK GWTC-3–based BBH population, the study shows memory signals can be strong in DECIGO’s band even for relatively low-frequency emission, enabling statistical tests of memory and asymptotic symmetries, breaking inclination–distance degeneracies, and providing dark-siren avenues for cosmology. The results highlight a practical path to memory-dominated science with space-based detectors and suggest extending the approach to other missions (e.g., LISA) for heavier binaries. Eccentricity within the explored range has negligible impact on memory detectability, and the method offers robust, model-grounded forecasts for memory-based fundamental-physics constraints. Overall, the paper makes a strong case that memory detection transitions from theoretical curiosity to a practical, population-level probe with next-generation space interferometers.

Abstract

The gravitational memory effect manifests gravitational nonlinearity, degenerate vacua, and asymptotic symmetries; its detection is considered challenging. We propose using the space-borne interferometer to detect memory signals from stellar-mass binary black holes (BBHs), typically targeted by ground-based detectors. We use DECIGO detector as an example. Over 5 years, DECIGO is estimated to detect $\sim$2,036 memory signals (SNRs $>$3) from stellar-mass BBHs. Simulations used frequency-domain memory waveforms for direct SNR estimation. Predictions utilized a GWTC-3 constrained BBH population model (Power Law + Peak mass, DEFAULT spin, Madau-Dickinson merger rate). The analysis used conservative lower merger rate limits and considered orbital eccentricity. The high detection rate stems from strong memory signals within DECIGO's bandwidth and the abundance of stellar-mass BBHs. This substantial, conservative detection count enables statistical use of the memory effect for fundamental physics and astrophysics. DECIGO exemplifies that space interferometers may better detect memory signals from smaller mass binaries than their typical targets. Detectors in lower frequency bands are expected to find strong memory signals from $\sim 10^4 M_\odot$ binaries.

Figures (5)

• Figure 1: Time-domain waveforms produced by PyCBC from a GW150914-like binary system. The blue curve represents the $+$-polarization of the oscillatory mode $h_+^\text{osc}$ generated with IMRPhenomXPHM Pratten:2020ceb, while the red curve illustrates the memory waveform $h_\text{D}$ calculated with Eq. \ref{['eq-hd']}. The inclination angle is set to $\iota = \pi/2$.
• Figure 2: Left: $h_\text{D+}$ and $h_{\text{D}\times}$ as functions of the inclination angle $\iota$ for a GW150914-like binary system. Right: the Fourier transformed waveforms $|\tilde{h}_+^\text{osc}|^2$ and $|\tilde{h}_\text{D}|^2$ for different values of $\iota$, together with the sensitivity curves of DECIGO and LISA. It should be noted that in the left panel, the solid lines corresponding to $\iota = 0.99\pi$ and $\iota = 0.00\pi$ almost coincide, so they appear as a single curve.
• Figure 3: The distributions of the source-frame chirp mass $\mathcal{M}$, the dimensionless spins $\chi_{1,2}$, the mass ratio $q$, the tilt angles $\theta_{1,2}^\text{tilt}$, and the redshift $z$, sampled from binary black hole population model obtained by LVK using GWTC-3. The vertical dashed lines indicate the $1\sigma$ confidence level.
• Figure 4: Distributions of $\mathcal{M}$, $q$, and $z$ for all simulated events ("Simulated/30", scaled by $1/30$ for readability) and for detectable memory events with $\mathrm{SNR}\geq 3$ and $\mathrm{SNR}\geq 8$.
• Figure 5: Equivalence between our frequency-domain memory model and the FFT of the time-domain memory.