This paper studies whether future space‑based gravitational‑wave detectors can find a faint, non‑oscillating signal known as displacement memory. Displacement memory is a prediction of general relativity. It is not the normal wobbling wave detectors usually see. Instead it is a very low‑frequency, step‑like change in the waveform that is tied to so‑called soft gravitons. It has not yet been observed.

The authors examine how well planned instruments such as LISA (Laser Interferometer Space Antenna), Taiji, Tian‑Qin and the planned Big Bang Observer (BBO) could detect these soft signals. They study concrete examples: moderately relativistic scattering of two compact objects (a hyperbolic encounter) and quasi‑circular, non‑precessing black hole mergers. They use simple, universal spectral templates for the soft signals and run simulated Bayesian parameter estimation — a statistical way to infer signal properties from noisy data — to test detectability.

At a basic level the soft memory signal has a simple spectral shape at low frequency. Different realistic time‑domain shapes (for example arctan, tanh or a short linear ramp) all give the same zero‑frequency limit in the frequency domain. That shared shape makes compact templates useful for matched filtering, which means searching by comparing the data against these expected templates. The authors stress one important technical point: the actual zero‑frequency jump that defines memory is not directly observable, because real detectors only measure finite frequencies. Measuring the low‑frequency spectrum that matches the soft template provides strong evidence for memory, but not a direct detection of the idealized zero‑frequency jump.

The simulated results give concrete sensitivity estimates. A single LISA‑like detector could independently measure a soft displacement‑memory signal when the signal‑to‑noise ratio is roughly 10 or higher. In the study that corresponds to displacement amplitudes on the order of 10^−20 for LISA‑class sensitivity, and a velocity‑memory amplitude scale of about 10^−22 Hz. Using a network of detectors, for example LISA and Taiji together, improves the measurement precision and helps break degeneracies that limit single‑detector measurements. A proposed BBO detector, which is sensitive at higher end of the low‑frequency band (f ≲ 1 Hz), would do even better and could separately measure the so‑called null memory from stellar‑mass compact binary mergers; the paper reports BBO reach for displacement memory around 10^−24 and velocity memory near 10^−23 Hz. The authors also simulated an idealized stochastic background made of many soft bursts and assessed its detectability.