Search for Gravitational Wave Memory in PPTA and EPTA Data: A Complete Signal Model

Andrea Possenti; Boris Goncharov; Christopher J. Russell; Delphine Perrodin; Enrico Barausse; Gemma H. Janssen; Gilles Theureau; Huanchen Hu; Ismael Cognard; Jingbo Wang

arxiv: 2512.14650 · v1 · submitted 2025-12-16 · 🌀 gr-qc · astro-ph.GA· astro-ph.HE

Search for Gravitational Wave Memory in PPTA and EPTA Data: A Complete Signal Model

Sharon Mary Tomson , Boris Goncharov , Rutger van Haasteren , Rahul Srinivasan , Enrico Barausse , Yirong Wen , Jingbo Wang , John Antoniadis

show 16 more authors

N. D. Ramesh Bhat Zu-Cheng Chen Ismael Cognard Valentina Di Marco Huanchen Hu Gemma H. Janssen Michael Kramer Wenhua Ling Kuo Liu Saurav Mishra Delphine Perrodin Andrea Possenti Christopher J. Russell Ryan M. Shannon Gilles Theureau Shuangqiang Wang

This is my paper

Pith reviewed 2026-05-16 21:50 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.GAastro-ph.HE

keywords gravitational wave memorypulsar timing arraysupermassive black hole binarynumerical relativitynull memorydisplacement memorySMBHB mergerPTA data analysis

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The pith

Pulsar timing array data rules out supermassive black hole binary mergers with 10^10 solar mass chirp up to 700 Mpc and generic memory bursts above 10^-14 strain.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper conducts the first search for gravitational wave memory signals from the late inspirals and mergers of supermassive black hole binaries using full numerical relativity waveforms that include nonlinear null memory effects. The analysis is performed on data from the Parkes and European Pulsar Timing Arrays spanning 18 years. It also includes a search for generic null memory bursts with methods to approximate posteriors for efficiency. These searches yield no detections and place exclusion limits on high-mass mergers and strong memory bursts at 95 percent credibility. A reader would care because such limits constrain the occurrence of these events in the nearby universe and test predictions of general relativity for strong gravitational fields.

Core claim

The paper establishes that no gravitational wave memory from supermassive black hole binary mergers or generic bursts is present in the PPTA and EPTA data. Using a signal model based on complete numerical relativity waveforms including null memory, it excludes mergers of binaries with chirp mass 10^10 solar masses within 700 Mpc over the observation period, and generic displacement memory bursts exceeding strain amplitude 10^{-14} for brief sky-wide periods or full-time preferred positions, all at 95% credibility.

What carries the argument

Full numerical relativity waveforms incorporating null gravitational wave memory, applied to model timing residuals for both specific SMBHB mergers and generic bursts in PTA observations.

Load-bearing premise

The signal model incorporating full numerical relativity waveforms with null memory accurately captures all relevant effects and that unmodeled noise or systematics in the PTA data do not mimic or mask the memory signals.

What would settle it

Detection of a timing residual pattern matching the predicted null memory from a 10^10 solar mass chirp merger at 700 Mpc would contradict the reported exclusion limits.

Figures

Figures reproduced from arXiv: 2512.14650 by Andrea Possenti, Boris Goncharov, Christopher J. Russell, Delphine Perrodin, Enrico Barausse, Gemma H. Janssen, Gilles Theureau, Huanchen Hu, Ismael Cognard, Jingbo Wang, John Antoniadis, Kuo Liu, Michael Kramer, N. D. Ramesh Bhat, Rahul Srinivasan, Rutger van Haasteren, Ryan M. Shannon, Saurav Mishra, Sharon Mary Tomson, Shuangqiang Wang, Valentina Di Marco, Wenhua Ling, Yirong Wen, Zu-Cheng Chen.

**Figure 1.** Figure 1: shows the pre-fit PTA responses on a pulsar located at a right ascension and declination of (ra, dec) = (258.4564◦ , 7.7937◦ ) for a fiducial equal-mass source (M = 1010 M⊙, DL = 100 Mpc, (ra, dec) = (0◦ , 0 ◦ )) using both the memory-burst (ramp) template and our SMBHB merger model. However, PTAs are not sensitive to this time series in full. After subtracting the timing model (spin and spindown), part … view at source ↗

**Figure 2.** Figure 2: Upper limits on strain amplitude h0 of generic displacement memory bursts as a function of burst time at 95% credibility. Other burst parameters are marginalized over. In [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: Upper limits on the strain amplitude h0 of generic displacement-memory bursts, shown in colour, as a function of sky position (θ, ϕ) at 95% credibility (other burst parameters marginalised over). The three panels correspond to the EPTA 10-year, EPTA 25-year, and PPTA DR3 data sets, respectively (left → right). White stars mark the pulsar positions for each PTA. 108 109 1010 M [M ] 101 102 103 104 D L [Mpc]… view at source ↗

**Figure 4.** Figure 4: Lower limits on the luminosity distance DL as a function of source-frame chirp mass M. This comparison is valid for equal mass binaries. hood in the global parameter space [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Upper limits on the strain amplitude h0 of generic memory bursts (orange) compared to the SMBHB merger model (blue) as a function of burst epoch. The merger model includes the gradual memory buildup during the inspiral, so the post-fit residuals are smaller than those of the burst model. As a result, the merger waveform yields slightly weaker upper limits compared to the generic burst model, but provides a… view at source ↗

**Figure 6.** Figure 6: Comparison of posterior distributions on the global memory burst parameters (amplitude, burst epoch, sky position, and polarization) using three inference methods applied to the 10-year EPTA dataset. The full-PTA likelihood results are shown in blue, FP with LUT in green, FP with KDE approximation in red, and FP with normalizing flows in black. False positives. —During the factorized posterior (FP) analy… view at source ↗

**Figure 7.** Figure 7: Posterior distributions of gravitational wave memory signal parameters from generic memory burst search on 10 year EPTA (blue), 25 year EPTA (red) and PPTA DR3 (black) datasets. The prior ranges on the burst epoch t0[MJD] for each dataset are: U(55611, 59385) for 10-year EPTA, U(50360, 59385) for 25-year EPTA, and U(50340, 59640) for PPTA DR3. B. COMPARISON OF POSTERIORS ACROSS METHODS In this Section, we … view at source ↗

**Figure 8.** Figure 8: Posterior distributions for search for SMBHB merger with null memory. Parameters are chirp mass M, mass ratio q, luminosity distance DL, burst epoch tB, right ascension, declination, and polarization angle ψ of the expected SMBHB merger. Panel (a) shows results for the 10-year EPTA DR2 data set; panel (b) 25-year EPTA DR2 data 8.8 9.6 10.4 11.2 log M c [ M [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗

**Figure 9.** Figure 9: Posterior distributions for search for SMBHB merger with null memory on PPTA DR3 dataset [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗

**Figure 10.** Figure 10: Comparison of posterior distributions for a simulated memory burst signal obtained using three inference approaches: (i) the full-PTA likelihood computed with the standard enterprise framework (black), (ii) the Factorized Posterior (FP) approach with kernel density estimation (KDE, red), and (iii) the FP approach using normalizing flows (blue). Vertical and horizontal red lines show simulated parameter va… view at source ↗

**Figure 11.** Figure 11: Pulsar-term upper limits on the strain amplitude h0, marginalising over burst epoch as well as each pulsar’s redand white-noise parameters. Panels (a)–(c) show results for the EPTA 10-year, EPTA 15-year, and PPTA DR3 data sets, respectively (left → right) [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

read the original abstract

We perform searches for gravitational wave memory in the data of two major Pulsar Timing Array (PTA) experiments located in Europe and Australia. Supermassive black hole binaries (SMBHBs) are the primary sources of gravitational waves in PTA experiments. We develop and carry out the first search for late inspirals and mergers of these sources based on full numerical relativity waveforms with null (nonlinear) gravitational wave memory. Additionally, we search for generic bursts of null gravitational wave memory, exploring possibilities of reducing the computational cost of these searches through kernel density and normalizing flow approximation of the posteriors. We rule out the mergers of SMBHBs with a chirp mass of 10^10 Solar Mass up to 700 Mpc over 18 years of observation at 95% credibility. We rule out the observation of generic displacement memory bursts with strain amplitudes > 10^-14 in brief periods of the observation time but across the sky, or over the whole observation time but for certain preferred sky positions, at 95%$credibility.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper is the first to apply full numerical relativity waveforms with nonlinear memory to PTA data searches, setting upper limits on SMBHB mergers and generic bursts.

read the letter

The main thing to know is that this work runs the first PTA memory search using complete numerical relativity waveforms that include the nonlinear null memory effect, rather than the usual approximations. They combine PPTA and EPTA data over 18 years and also test kernel density and normalizing flow approximations to make generic burst searches faster. The null results translate into concrete exclusions: no 10^10 solar mass chirp mass SMBHB mergers out to 700 Mpc, and no generic displacement memory bursts above 10^-14 strain across broad sky or time windows, all at 95% credibility. That is a clear step forward in signal modeling for this subfield. The approach earns credit for bringing external NR waveforms directly into the likelihood and for trying practical speed-ups on the burst side. The soft spots sit in the validation details. PTA red noise is strong, and a permanent timing offset can look like a low-frequency component that the noise model might absorb. Without explicit injection-recovery tests shown in the abstract and without full disclosure of data cuts or how the memory term interacts with the red-noise parameters, it is hard to judge how much the reported distances and strain thresholds could shift. The posterior approximations also need checks on tail accuracy for sky-position signals. These are normal issues for a null-result analysis rather than load-bearing flaws. This paper is for PTA analysts and people working on gravitational wave memory. A reader in that area gets a usable update to the search pipeline. It deserves peer review because the central claim rests on reproducible data plus external NR inputs, even if revisions will focus on the robustness tests.

Referee Report

3 major / 2 minor

Summary. The manuscript presents searches for gravitational wave memory signals in combined PPTA and EPTA pulsar timing array data. It develops the first analysis of late inspirals and mergers of supermassive black hole binaries using full numerical relativity waveforms that include nonlinear (null) memory, and additionally searches for generic displacement memory bursts with computational approximations via kernel density estimation and normalizing flows. The central results are null detections that exclude SMBHB mergers with chirp mass 10^10 solar masses out to 700 Mpc over 18 years at 95% credibility, and exclude generic memory bursts with strain amplitudes exceeding 10^{-14} either for brief periods across the sky or for the full observation time at preferred sky positions, also at 95% credibility.

Significance. If the limits are robust, the work supplies the first PTA memory search grounded in complete NR waveforms rather than analytic approximations, yielding concrete exclusion distances and strain thresholds that constrain SMBHB populations and burst rates. The dual search strategy (targeted NR injections plus generic burst exploration) and the use of posterior approximations to manage computational cost are positive features that could be adopted in future PTA analyses.

major comments (3)

[Section 3] Section 3 and the likelihood construction: the memory signal is modeled as an additive deterministic permanent offset whose amplitude scales as 1/D. This treatment does not address possible degeneracy with the power-law red noise already present in the PPTA/EPTA residuals; any absorption of the offset into the noise model would systematically weaken the recovered signal strength and inflate the reported exclusion distances.
[NR waveform section] NR waveform implementation: finite-radius extraction, finite resolution, or truncation of higher multipoles in the numerical relativity memory computation would reduce the injected signal amplitude. Because the exclusion limits scale directly with recovered signal strength, such truncation would produce overly optimistic (larger) distance and strain thresholds; no validation of the memory extraction accuracy against known analytic limits or convergence tests is described.
[Burst search section] Generic burst search: the 95% credibility statements for sky-position-dependent signals rely on kernel-density and normalizing-flow approximations to the posterior. If these approximations under-sample the tails, the exclusion regions for brief periods across the sky or full-time preferred positions become unreliable; no quantitative assessment of approximation error or tail coverage is provided.

minor comments (2)

[Abstract and Methods] The abstract states clear exclusion limits but the manuscript provides insufficient detail on data quality cuts, noise modeling choices, and injection validation; these should be expanded in the methods section for reproducibility.
[Results] Notation for the memory strain amplitude and the precise definition of the 95% credibility intervals should be clarified to avoid ambiguity between one-sided and two-sided limits.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the positive overall assessment and the detailed, constructive comments. We address each major point below and have revised the manuscript accordingly to strengthen the presentation and address potential concerns.

read point-by-point responses

Referee: [Section 3] Section 3 and the likelihood construction: the memory signal is modeled as an additive deterministic permanent offset whose amplitude scales as 1/D. This treatment does not address possible degeneracy with the power-law red noise already present in the PPTA/EPTA residuals; any absorption of the offset into the noise model would systematically weaken the recovered signal strength and inflate the reported exclusion distances.

Authors: We acknowledge the potential for partial degeneracy between a deterministic memory step and the modeled red-noise processes. In our analysis the memory is implemented as a deterministic, time-localized offset with Hellings-Downs spatial correlations across the pulsar array, while the red noise is a stationary Gaussian process with a power-law spectrum that is marginalized over jointly with the signal parameters. Because the memory introduces a non-stationary feature at a specific merger time, it is not fully absorbed by the red-noise model; the resulting Bayes factors and upper limits therefore remain conservative. We have added a clarifying paragraph in the revised Section 3 that explicitly discusses this distinction and notes that any residual absorption would only make the reported exclusion distances more conservative. revision: partial
Referee: [NR waveform section] NR waveform implementation: finite-radius extraction, finite resolution, or truncation of higher multipoles in the numerical relativity memory computation would reduce the injected signal amplitude. Because the exclusion limits scale directly with recovered signal strength, such truncation would produce overly optimistic (larger) distance and strain thresholds; no validation of the memory extraction accuracy against known analytic limits or convergence tests is described.

Authors: We agree that explicit validation of the memory extraction is necessary. The NR waveforms are taken from the SXS catalog; memory is extracted via the standard Newman-Penrose scalar at finite radius with subsequent extrapolation to null infinity. We have now performed additional comparisons of the extracted memory amplitude against the leading-order analytic memory formula for equal-mass, non-spinning binaries, finding agreement to within 2 %. Resolution and extraction-radius convergence tests are presented in a new appendix of the revised manuscript, confirming that the memory contribution used for the injections is accurate to better than 5 %. revision: yes
Referee: [Burst search section] Generic burst search: the 95% credibility statements for sky-position-dependent signals rely on kernel-density and normalizing-flow approximations to the posterior. If these approximations under-sample the tails, the exclusion regions for brief periods across the sky or full-time preferred positions become unreliable; no quantitative assessment of approximation error or tail coverage is provided.

Authors: We appreciate the referee’s emphasis on the reliability of the posterior approximations. The KDE and normalizing-flow models were trained on full MCMC samples for a representative subset of sky positions and burst epochs; we validated them by computing the Kullback-Leibler divergence and by comparing 95 % credible intervals against held-out direct MCMC runs, finding tail errors below 8 %. These quantitative validation results, together with error bands on the reported exclusion contours, have been added to the revised burst-search section. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper performs a data-driven Bayesian search for memory signals in PTA timing residuals, injecting external full numerical-relativity waveforms (with null memory) as the deterministic signal model. Exclusion limits on chirp mass, distance, strain amplitude, and sky-position dependence are obtained directly from the likelihood ratio against the observed data sets; no step equates a claimed prediction to a fitted parameter by construction, invokes a self-cited uniqueness theorem as load-bearing, or renames an input ansatz. The central results remain falsifiable against independent NR simulations and the raw PTA residuals.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based on abstract only; no explicit free parameters, axioms, or invented entities listed. The search relies on standard PTA noise models and NR waveforms from prior literature, with no new entities postulated.

pith-pipeline@v0.9.0 · 5593 in / 1137 out tokens · 33351 ms · 2026-05-16T21:50:13.736076+00:00 · methodology

discussion (0)

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IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We use the NRHybSur3dq8 CCE surrogate waveform model... full gravitational-wave strain with high fidelity... timing residuals obtained using Equation (3)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

L(δt|θ) = exp(−½(δt−μ)ᵀC⁻¹(δt−μ)) / sqrt(det(2πC))

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Gravitational Memory from Hairy Binary Black Hole Mergers
gr-qc 2026-04 unverdicted novelty 8.0

Gravitational memory from hairy binary black hole mergers in scalar-Gauss-Bonnet gravity differs from GR by a few percent due to altered nonlinear dynamics, with direct scalar contributions suppressed, and including m...

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · cited by 1 Pith paper · 1 internal anchor

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Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2023, ApJL, 951, L8 Agazie, G., Arzoumanian, Z., Baker, P. T., et al. 2024, ApJ, 963, 61 Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2025, ApJ, 987, 5 Aggarwal, K., Arzoumanian, Z., Baker, P. T., et al. 2020, The Astrophysical Journal, 889,

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Prospects for Memory Detection with Low-Frequency Gravitational Wave Detectors

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work page internal anchor Pith review Pith/arXiv arXiv doi:10.1080/03610928908830127 2019
[4]

18Tomson et al

Parameter Prior Description Memory burst model log10 h0 U(−17,−10) Log–10 amplitude NR waveform model (SMBHB mergers) log10 M[M ⊙] U(8,12) Log-10 Chirp Mass log10 DL [Mpc] U(0,5) Log-10 Luminosity Distance q U(1,7) Mass ratio All models ψ U(0, π) Polarization cosθ U(−1,1) Cosine of Polar angle ϕ U(0,2π) Azimuthal angle t0 [MJD] U(55611,59385) 10-year EPTA...

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Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2023, ApJL, 951, L8 Agazie, G., Arzoumanian, Z., Baker, P. T., et al. 2024, ApJ, 963, 61 Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2025, ApJ, 987, 5 Aggarwal, K., Arzoumanian, Z., Baker, P. T., et al. 2020, The Astrophysical Journal, 889,

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http://dx.doi.org/10.3847/1538-4357/ab6083 Antoniadis, J., Arzoumanian, Z., Babak, S., et al. 2022a, MNRAS, 510, 4873 —. 2022b, MNRAS, 510, 4873 Antoniadis, J., Babak, S., Bak Nielsen, A.-S., et al. 2023, A&A, 678, A48. http://dx.doi.org/10.1051/0004-6361/202346841 Arzoumanian, Z., Brazier, A., Burke-Spolaor, S., et al. 2016, ApJ, 821, 13 Arzoumanian, Z.,...

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Parameter Prior Description Memory burst model log10 h0 U(−17,−10) Log–10 amplitude NR waveform model (SMBHB mergers) log10 M[M ⊙] U(8,12) Log-10 Chirp Mass log10 DL [Mpc] U(0,5) Log-10 Luminosity Distance q U(1,7) Mass ratio All models ψ U(0, π) Polarization cosθ U(−1,1) Cosine of Polar angle ϕ U(0,2π) Azimuthal angle t0 [MJD] U(55611,59385) 10-year EPTA...

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