Detectability of Nonlinear Gravitational-Wave Memory

Nonlinear gravitational-wave memory is a robust prediction of general relativity, but a robust waveform contribution need not yet be measurable. At the evidence cutoff of 2026-08-20, neither an individual LIGO–Virgo–KAGRA event nor the analyzed population separates the general-relativistic memory amplitude from zero. The current GWTC-5 hierarchical posterior contains both zero and the GR value by a wide margin, and its forecast requires roughly 2,000 detections for even a one-standard-deviation population separation under the adopted model. The observational question remains open, with insufficient evidence for detection and high confidence in that limited verdict.

Helpful background. Nonlinear Christodoulou Memory derives the null-memory contribution, its relation to radiative flux, and its waveform-mode and Bondi-frame conventions. Here “detectability” means statistical separation in actual detector data, not theoretical existence.

The measurable memory proposition

Several questions called “memory detection” must be kept apart. Displacement or null memory differs from spin memory. A search triggered by an observed oscillatory merger differs from an orphan burst-with-memory search. An event-level amplitude differs from a population-shared enhancement parameter. Ground-based interferometers, pulsar timing arrays, and space detectors occupy distinct frequency and noise regimes and should not have their evidence pooled.

For compact-binary LVK searches, write the modeled memory as $A\,h_{\rm mem}^{\rm GR}$, where $A=1$ is the chosen GR waveform and $A=0$ removes it. The inference depends on the oscillatory parent waveform, binary orientation and therefore memory sign, low-frequency calibration and conditioning, event selection, priors, and population model. A posterior containing $A=1$ is “consistent with GR”; it is not a detection if it also contains $A=0$.

Assessment at 2026-08-20	Meaning
Question status	Open
Evidence status	Insufficient evidence
Confidence	High that present LVK data do not identify memory; not high confidence about future yield
Domain	Event and hierarchical population searches for nonlinear/null memory in compact-binary LVK data through GWTC-5 products
What could change the conclusion	A new observing release, calibrated search, or robust null result

Entry project: find what controls a population memory constraint

Memory offers an accessible statistical entry if you already understand waveform polarizations, importance weights, and posterior distributions. Start with released inference products rather than attempting a new low-frequency strain analysis. The former can be explored on a laptop; the latter requires detector-noise expertise, calibrated waveform generation, and a larger injection campaign.

Read Mitman, Isi, and Farr, arXiv:2605.27500v2, hierarchical model and results, extracting the shared memory-amplitude parameter and how orientation uncertainty enters. Open Mitman, Isi, and Farr, Zenodo 20734696 v2, file descriptions. Begin with the 19 MB hierarchical_results.zip, whose stored posteriors support a summary-level reproduction; the separate event archive is about 1 GB. Record the archive checksum and model labels. Regenerate a posterior interval using the paper’s interval convention and distinguish the fitted population from its forecast.

The finite deliverable is a notebook that reconstructs that summary and explains which data products would be required to remove an event or change a waveform model. If you undertake those changes, use the supplied event likelihood information and importance weights correctly: multiplying event posteriors without removing their priors changes the hierarchical problem. Replotting the archive is a training baseline, not an independent detection test.

A candidate extension, with novelty unchecked, is a leave-one-event-out sensitivity study within the same released likelihood approximation, followed by an orientation-sign or waveform-family comparison. Stop if importance weights collapse onto a few samples or the needed likelihood information is absent; report effective sample size and return to the underlying inference instead of quoting a sharpened bound. If only the summary archive is usable, pivot to diagnosing forecast assumptions. Distinguish uncertainty shared by all events from independent noise: adding detections does not automatically average away the former.

What present searches establish

The first-catalogue analysis found no event-level memory preference and showed through simulated populations why coherent accumulation could help Hübner et al. 2020, event Bayes factors, population forecast, and conclusion. That work established a practical Bayesian search strategy, not a detection.

With GWTC-3, Cheung, Lasky, and Thrane found $\ln\mathrm{BF}=0.01$ and constrained a free amplitude only to $A\lt23$ at 95% credibility Cheung, Lasky, and Thrane 2024, §§ 3–4. A Bayes factor so close to unity is an informative null: the data do not prefer the memory model, while the broad amplitude limit remains far from a precision test of $A=1$.

The most current analysis changes the population statistic and the catalogue. Mitman, Isi, and Farr infer a shared enhancement with posterior $0.26^{+4.09}_{-4.08}$ at 68% credibility using GWTC-5 inputs. It is compatible with both zero and unity; their forecast places a one-standard-deviation separation from zero at about 2,000 detections Mitman, Isi, and Farr 2026, hierarchical-result and forecast sections. Hierarchical modeling avoids some pathologies of simply multiplying event Bayes factors, but it still inherits a common waveform and population structure.

Results and open questions at 2026-08-20

Claim or evidence	What it supports	What it does not establish
GWTC-1 event search	No individual preference and a workable stacking framework	Population detection
GWTC-3 $\ln\mathrm{BF}=0.01$ and $A\lt23$	Direct published null and loose bound	Exclusion of GR memory
GWTC-5 $A=0.26^{+4.09}_{-4.08}$	Current hierarchical constraint consistent with GR	Separation from zero
Roughly 2,000-event forecast	Scale of accumulation under the stated model	Guaranteed yield or resilience to future systematics
PN/self-force memory comparisons	Theoretical waveform cross-checks	Detector evidence
Zenodo v2 plus stable-release-9 inputs	A concrete posterior/forecast reproduction boundary	Independent waveform or calibration validation

The null rows directly answer the observational proposition and therefore receive the greatest weight. The theory calculations determine what signal is sought; forecasts determine planning; neither substitutes for a nonzero posterior in data.

Strongest competing interpretations

The optimistic interpretation emphasizes coherent accumulation. Memory is weak in each event but has a correlated amplitude fixed by the oscillatory source. As the catalogue grows, a hierarchical analysis can combine subthreshold information without requiring any one spectacular event. Improved low-frequency sensitivity and better orientation measurement could reduce the required event count.

The cautious interpretation notes that coherent accumulation also coherently accumulates shared model error. Memory lives at low frequencies where calibration, high-pass filtering, nonstationarity, and waveform conditioning are difficult. Orientation uncertainty can scramble the sign. The population used in a forecast may differ from the observed population. Boersma and collaborators show that detection forecasts change materially with the memory approximation and detector curve Boersma et al. 2020, approximation comparison and five-year design-sensitivity forecast. The current data favor neither a pessimistic impossibility claim nor an imminent-detection claim.

Counterexamples, null results, and failed routes

The GWTC-3 and GWTC-5 posteriors are the strongest null evidence. They do not rule out $A=1$; they rule out describing the current catalogue as a measurement. The superseded GWTC-4-era preprint state reported $0.32^{+6.30}_{-5.12}$, but the accepted analysis uses GWTC-5 and a narrower, still nondiscriminating posterior. Mixing those versions would double count one evolving analysis.

Multiplying per-event Bayes factors can appear decisive because each factor depends on the prior volume and because event-level orientation information is uneven. The accepted hierarchical study explains why that route should not be the sole population statistic. Similarly, aggressive high-pass filtering can remove part of the slowly rising signal: a pipeline that is stable for oscillatory mergers is not automatically calibrated for memory. These are failed inference routes or scope limitations, not counterexamples to the GR flux law.

Theory accuracy and detector identifiability

The memory waveform itself is being cross-checked. Cunningham and collaborators compare memory modes using post-Newtonian and self-force information, while showing that Bondi–Metzner–Sachs frame handling matters Cunningham et al. 2025, corrected v2 memory-mode and PN/SF comparison sections. This supports the physical template in restricted sectors but also identifies a shared-systematic route if catalog analyses use one convention without transformation.

Detector identifiability needs an end-to-end injection: generate oscillatory plus signed memory signals, pass them through calibration draws and real off-source noise, condition them identically to the data, and recover a population parameter with correct coverage. Repeating only a published posterior from stored event objects tests computation after those choices; it does not validate the upstream strain treatment.

What would change the assessment

A credible detection would predeclare event selection, waveform families, low-frequency cutoffs, calibration treatment, priors, and the hierarchical statistic. The posterior would exclude $A=0$, recover $A=1$ within uncertainty, and remain nonzero under specified conditioning and waveform variations. Zero-memory injections would demonstrate false-positive control, while signed GR injections would demonstrate coverage.

A robust null result with much tighter uncertainty could instead constrain enhanced-memory theories even without measuring $A=1$. Either outcome must use current official strain and parameter-estimation products and survive an independent pipeline. A favorable forecast or one event with a high Bayes factor would not by itself resolve the population proposition.

Research checklist

• Pin the official strain, calibration, event list, and GWTC-5 stable-release-9 parameter-estimation products.
• Use Zenodo 20734696 v2 rather than superseded record 20347301 v1; verify file checksums.
• State oscillatory and memory waveform generators, BMS frame, orientation/sign convention, and low-frequency response.
• Record PSD segments, filtering, gating, calibration envelopes, priors, sampler diagnostics, and selection function.
• Compare hierarchical amplitude inference with Bayes-factor stacking on controlled injections.
• Include real off-source noise, zero-memory controls, calibration draws, and more than one oscillatory waveform family.
• Report coverage and sensitivity to low-frequency cutoffs before unblinding the catalogue.
• No independent likelihood rerun was performed for this assessment; the public archive defines a computational reproduction, while the strain-level challenge remains a prescription.

Source and data map

Hübner et al. provide the foundational event search; Cheung et al. provide the GWTC-3 null; Mitman, Isi, and Farr provide the accepted GWTC-5 hierarchical result. Boersma et al. quantify forecast dependence, and Cunningham et al. provide a current theory cross-check.

The exact current reproduction anchor is Zenodo record 20734696 v2: memory_posteriors.zip has MD5 a617c7bba2e1045e3cdd2ca70d6265be, and hierarchical_results.zip has MD5 5f030d91d63ea41bba7f8f664a4ebfdf. It links the farr/Memory code and catalogue products. Official event authority remains GWOSC GWTC-5.0, DOI 10.7935/bk00-6a89, whose event links use stable release 9, including Zenodo 20348004–20348006. Reproducing the archive does not make its shared waveform model independent.

References

• Boersma, O. M., Nichols, D. A., Schmidt, P., and Thompson, J. “Forecasts for detecting the gravitational-wave memory effect with Advanced LIGO and Virgo.” Physical Review D 101, 083026 (2020). DOI.
• Cheung, S. Y., Lasky, P. D., and Thrane, E. “Does spacetime have memories? Searching for gravitational-wave memory in the third Advanced LIGO–Virgo observing run.” Classical and Quantum Gravity 41, 115010 (2024). DOI.
• Cunningham, K., et al. “Gravitational memory: new results from post-Newtonian and self-force theory.” Classical and Quantum Gravity 42, 135009 (2025), with addendum 42, 199401 (2025). Article DOI; addendum DOI; corrected open preprint v2.
• Hübner, M., Talbot, C., Lasky, P. D., and Thrane, E. “Measuring gravitational-wave memory in the first LIGO/Virgo gravitational-wave transient catalog.” Physical Review D 101, 023011 (2020). DOI.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. “GWTC-5.0 open data.” GWOSC (2026). Official release.
• Mitman, K., Isi, M., and Farr, W. M. “Constraining gravitational wave memory with hierarchical inference.” Accepted in Physical Review D 30 July 2026; final volume and article number unverified at the cutoff. DOI; open preprint v2.
• Mitman, K., Isi, M., and Farr, W. M. “Data produced in ‘Constraining Gravitational Wave Memory with Hierarchical Inference’.” Data release v2, Zenodo (2026). DOI.