Towards Claiming a Detection of Gravitational Memory

TL;DR

The paper develops a principled, multiscale framework for defining and modeling gravitational displacement memory as a time-dependent rise atop a permanent DC offset in the asymptotic metric. Grounded in the Isaacson formalism and BMS symmetry, it separates memory from oscillatory radiation and provides an explicit spin-weighted spherical-harmonic expansion to compute nonlinear memory for compact-binary mergers. Focusing on LISA, it analyzes the detector response, demonstrates memory’s suppression in in-band data but potential observability in out-of-band mergers, and presents a Bayes-factor methodology to quantify detection prospects, with MBHB populations suggesting a strong chance of a single-event memory detection in the next decade. The work establishes a robust theoretical and statistical pathway toward an eventual observational claim of gravitational memory, linking it to the infrared structure of gravity and soft theorems while outlining practical strategies for future data analyses.

Abstract

Gravitational memory is a zero-frequency effect associated with a permanent change in the asymptotic spacetime metric induced by radiation. While its universal manifestation is a net change of proper distances, gravitational-wave detectors are intrinsically insensitive to the final offset and can only probe the associated transition. A central challenge for any claim of detection therefore lies in defining a physically meaningful and operationally robust model of this time-dependent signal, which is uniquely attributable to gravitational memory and distinguishable from purely oscillatory radiation. In this work, we propose a general solution to this challenge. Building on a self-contained review of the theory of gravitational memory, we discuss a theoretical framework for defining and modeling a gravitational memory rise, in particular applicable to compact binary coalescences. Specializing to space-based detectors, we analyze the response of LISA to gravitational radiation including a memory contribution, with particular emphasis on mergers of supermassive black hole binaries, which offer the most promising prospects for a first single-event detection. The framework developed here provides the theoretical foundation for statistically well-defined hypothesis testing between memory-free and memory-full radiation and quantitative assessments of detection prospects. As such, these results establish a principled pathway toward a future observational claim of gravitational memory.

Figures (16)

• Figure 1: Penrose diagram of a conformally compactified asymptotically flat spacetime in asymptotic light-cone coordinates $\{u,r,\theta,\phi\}$, with $u=t-r$ and where time $t$ flows vertically. A localized source emits null radiation (yellow) toward future null infinity $\mathscr{I}^+$, defined as the $r\to\infty$ limit at fixed retarded time $u$. The angular coordinates are not shown, but the asymptotic two-spheres at retarded times $u_0$ and $u$ are depicted schematically as blue circles. The BMS balance laws state that the supermomentum flux reaching $\mathscr{I}^+$ between $S^2_{u_0}$ and $S^2_u$ is exactly balanced by the change in supermomentum charge between these two times. [Figure adapted from DAmbrosio:2022clkZosso:2024xgy.]
• Figure 2: Illustration of type $(a)$ and type $(b)$ waveform models. The type $a$ waveform (orange) includes no memory and is based off the extrapolation method (EXT) while the CCE waveform (blue) is type $b$ and includes memory.
• Figure 3: Top panel: We show the full CCE waveform strain (blue, waveform type $b$), the $(2,0)$ mode of the extrapolated surrogate model (green, waveform type $a$), and the memory content (red) of the $(2,0)$ mode as calculated from the extrapolated waveform through Eq. \ref{['eq:memorymodes20']}. Bottom panel: A close-up around the merger (orange dashed line) of the $(2,0)$ mode used to compare the CCE (purple, waveform type $b$), EXT (green, waveform type $a$), and memory calculation (dashed red). Parameters:$Q=1.5$, $\chi = 0.6$.
• Figure 4: Top: Dominant oscillatory waveform and memory for an equal-mass, nonspinning binary (edge-on). The green band marks the interval $t \in [-30M,\,30M]$, during which approximately $66\%$ of the total radiated energy is emitted. Bottom: Instantaneous gravitational-wave frequency $f_{\rm GW}$ of the dominant $(2,2)$ mode, together with the characteristic memory-growth timescale $\dot{f}_{\rm H}/f_{\rm H}$, and the corresponding energy flux $dE^{\rm GW}/dt$.
• Figure 5: Characteristic strain in frequency space of the memory (solid) and of the dominant GW signal (dashed) the system in Fig. \ref{['fig:memwith freq']} with zero spin (blue) and with spin $\chi=0.8$ (grey). The signal of the oscillatory GWs follows the typical shape of an IMR event, with a powerlaw increase in frequency during inspiral of $|\tilde{h}|\sim f^{-7/6}$, followed by a merger feature that ends in a sharp, damped ringdown at the highest frequencies. The memory signal on the other hand approaches a constant value $\Delta h_{\rm mem}/(2\pi)$ (dot-dashed) at low frequencies and decays at frequencies higher than $\sim f_L^{\rm M}$, as explained in the main text.