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This paper argues that the counterintuitive increase in gravitational-wave background significance when cutting EPTA DR2 from 25 to 10.3 years is a ~2σ random noise fluctuation driven by sparse frequency coverage, not an anomaly; it also pi

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2026-08-03 19:54 UTC pith:PUCNUCY4

load-bearing objection A careful simulation study that plausibly explains the EPTA DR2 significance flip as a ~2σ noise artifact and, more convincingly, identifies spectral leakage as the dominant bias in the short dataset; worth refereeing, though the headline rates are conditioned on a single injected SMBHB population. the 3 major comments →

arxiv 2511.21933 v1 pith:PUCNUCY4 submitted 2025-11-26 astro-ph.HE astro-ph.COastro-ph.IM

Data span and frequency coverage requirements for robust detection and inference in PTAs: A case study with EPTA DR2

Irene Ferranti , Mikel Falxa , Federico Fantoccoli , Alberto Sesana , Golam Mohiuddin Shaifullah This is my paper
classification astro-ph.HE astro-ph.COastro-ph.IM
keywords pulsar timing arraysgravitational-wave backgroundstochastic backgroundsupermassive black hole binariesfrequency coveragespectral leakageHellings-Downs correlationBayesian inference
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper explains a puzzling result in pulsar timing array data: the second data release of the European Pulsar Timing Array shows a stronger gravitational-wave background signal when the dataset is cut from 25 years (about 2σ significance) to only the last 10.3 years (about 3.5σ). The authors argue this is not an anomaly. Using 100 realistic simulations with the same injected supermassive-black-hole-binary background, they show the first 10 years add almost no evidence because those legacy observations have very narrow frequency coverage, making dispersion-measure noise degenerate with the achromatic background. As a result, the significance distributions of the full and short datasets overlap heavily: random noise alone produces the observed reversal in about 15% of realisations, and 5% of realisations match the real data's numbers, consistent with a ~2σ fluctuation. The paper also shows that the short dataset's biased amplitude and slope estimates come mainly from spectral leakage, which is neglected in standard analyses; modelling it removes the bias. If correct, the paradox needs no exotic explanation and future data combinations can be designed around frequency coverage.

Core claim

The paper's central claim is that the apparent paradox in the second data release of the European Pulsar Timing Array—where the 10.3-year subset shows stronger gravitational-wave background evidence (HD S/N ≈3.5) than the full 25-year set (HD S/N ≈1.3)—is a normal statistical outcome. In 100 realistic simulations with an injected SMBHB background, the first decade of observations contributes almost nothing to the significance because those measurements are mostly single-frequency, so dispersion-measure noise cannot be separated from the achromatic background. The HD S/N distributions of the full and short datasets therefore overlap substantially: the short dataset wins by chance in about 15%

What carries the argument

Three mechanisms carry the argument. (1) A set of 100 realistic DR2-like simulations, each injecting the same gravitational-wave background from a circular SMBHB population (amplitude 2.4×10⁻¹⁵, slope 13/3) with different noise realisations, cut at 25, 10 and 5 years. (2) The noise-marginalised optimal statistic HD S/N and the weighted-average Jensen–Shannon divergence degeneracy coefficient, which together quantify how well individual pulsar noise can be separated from the common background. (3) Spectral leakage: a finite observation window correlates Fourier frequency bins that the standard diagonal-covariance analysis neglects; the FFTInt method accounts for this and removes the parameter

Load-bearing premise

All simulations inject a single realisation of the SMBHB background with a fixed amplitude and slope, and adopt the noise parameters and frequency coverage of the real EPTA data; if the true background spectrum or noise budget differs, the quoted 15%/5% rates and leakage-induced bias could change.

What would settle it

Reanalyse the real 10.3-year dataset with a leakage-aware method and check whether the recovered (log₁₀ A, γ) moves from roughly (−13.9, 2.7) toward the steeper spectrum expected from a SMBHB population; if it does not, spectral leakage is not the dominant bias. Also repeat the 100-realisation study with a different injected GWB spectrum or noise budget and see whether the 15%/5% rates change by more than statistical uncertainty.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The observed DR2new versus DR2full discrepancy can be reproduced in controlled simulations as a ~2σ noise fluctuation, so no data or pipeline anomaly needs to be invoked.
  • When spectral leakage is included in the model, the short 10.3-year dataset yields unbiased gravitational-wave background parameters, meaning short datasets can be trusted if properly modelled.
  • Combining the full EPTA dataset with complementary long-baseline arrays and low-frequency radio observations roughly doubles the HD S/N (from about 2.0 to 3.8) and makes the significance grow monotonically with observation time.
  • Very short baseline datasets (about 5 years) with low S/N bias amplitude estimates toward high values and constrain the GWB slope poorly; slope precision depends more strongly on observation time than amplitude precision.
  • The orientation of the recovered (amplitude, slope) posterior is predictable from a Fisher matrix and depends on timespan, not S/N, explaining the different orientations seen in real datasets of different lengths.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The quoted 15% and 5% rates are computed for a single injected SMBHB background realisation and a single noise budget; with different true spectra or noise levels these probabilities would shift, so the 5% figure should not be read as a universal p-value.
  • The spectral-leakage bias identified here is likely to affect other short-baseline pulsar timing array datasets, so any ~4-5 year dataset claiming gravitational-wave background parameters should be checked with a leakage-aware analysis.
  • The timespan-dependent posterior orientation implies that when combining datasets of very different lengths, joint analyses should explicitly account for their different correlation structures rather than assuming a common covariance.
  • A testable extension: if this explanation is right, reanalysing the real 10.3-year dataset with the leakage-aware method should move the recovered amplitude and slope toward the steeper spectrum expected from a SMBHB population.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper addresses a counterintuitive feature of the EPTA second data release: the 10.3-year subset DR2new yields a higher GWB significance (HD S/N ~3.5) than the full 25-year DR2full (HD S/N ~1.3). Using 100 realistic simulations of EPTA DR2 that share a single injected SMBHB background (A=2.4e-15, gamma=13/3) and realistic per-pulsar noise, the authors show that the first ten years contribute little because of sparse frequency coverage, so the HD S/N distributions of DR2full and DR2new overlap substantially. They find that DR2new exceeds DR2full in 15% of noise realizations and that 5% of realizations match the real data within 90% C.I., which they interpret as a ~2 sigma noise fluctuation. They further show that DR2new parameter estimates are biased toward low gamma and high amplitude, that this bias is largely removed by modeling spectral leakage with the FFTInt method, and that adding IPTA-like frequency coverage from NANOGrav, PPTA, LOFAR, and NenuFAR restores monotonic S/N growth and unbiased parameters. Short-baseline (5 yr) datasets are shown to be strongly biased, consistent with the posterior orientation predicted by a Fisher-matrix calculation.

Significance. If correct, the paper provides a coherent explanation of the EPTA DR2new/DR2full significance flip without invoking data anomalies, and it underlines two practical lessons for PTA analyses: frequency coverage can matter as much as time span, and neglect of spectral leakage can dominate parameter biases. The simulation pipeline is grounded in the real DR2 setup (libstempo, SPNA noise maxima, actual TOA epochs and cadences), and the analysis uses standard tools with 100 realizations, P-P plots, and direct comparisons to the real data. The main quantitative conclusion—a 5% occurrence rate corresponding to roughly 2 sigma—is nevertheless conditional on the chosen fixed GWB realization and on a data-dependent selection criterion, which limits the strength of the claim.

major comments (3)
  1. [Sec. 3.1.1 and Sec. 3.1.2] The central probabilities (15% of realizations with DR2new>DR2full, 5% compatible with the real HD S/N values) are computed for a single fixed injection of the SMBHB population. The GWB is a stochastic process; different population realizations with the same power spectrum (A=2.4e-15, gamma=13/3) will change the source positions, phases, and individual binary contributions, and therefore the HD S/N distributions. Since the real data are one GWB realization, the '~2σ noise fluctuation' claim in the abstract and conclusions should either be marginalized over GWB cosmic variance (by generating several population realizations) or explicitly qualified as conditional on the one tested population. The note in Sec. 3.1.2 that 'we only tested one SMBHB population realisation' makes the limitation clear, but it is not reflected in the strength of the abstract and summary statements.
  2. [Sec. 3.1.1, Table 2] The '5% compatible with the real data' is not a calibrated p-value. It is the fraction of simulations that satisfy a criterion defined after examining the real data: DR2new yields higher HD S/N than DR2full and the median simulated HD S/N values are within the 90% C.I. of the real values. Because the event was not pre-specified and the match definition was chosen post hoc, interpreting this fraction as 'the probability of observing the EPTA scenario' is problematic. Please report the exact selection rule, quote the Poisson sampling uncertainty (5/100 leads to a 95% interval of roughly 2–11%), and either use a pre-defined statistic or clearly label this as a descriptive conditional frequency rather than a p-value.
  3. [Sec. 3.1.3, Fig. 4c] The P-P plot and the quoted bias significances (3σ for DR2full, 5.6σ for DR2new standard, 1.5σ with FFTInt) use γ=13/3 as the 'true' value. The injected GWB is the sum of individual SMBHBs (Fig. 1), whose spectrum is not a pure power law; the power-law recovery model is therefore misspecified by construction, as the authors acknowledge in Sec. 3.1.2. Consequently, the measured 'bias' and its reduction by FFTInt are not purely attributable to spectral leakage. To support the claim that leakage is 'the main source of bias', the comparison should be made against the actual injected spectrum (e.g., the effective spectral index of the simulated GWB), or a control injection with a strictly power-law GWB should be added.
minor comments (5)
  1. [Abstract / Conclusions] The '≈2σ' language should be softened to reflect the conditional nature of the 5% rate, e.g., 'within our controlled simulations', rather than appearing as a general statement about the real-data probability.
  2. [Fig. 1 and Sec. 2.2.3] The power-law approximation line in Fig. 1 is not defined; state how it is fit. Also, the caveat that only one SMBHB population realization is used would be better placed at the first statement of the 15%/5% numbers.
  3. [Sec. 3.2] The simulated IPTA backends are added with fixed TOA errors (2 µs for high-frequency, 7 µs for low-frequency) and fixed epochs. Since the real backends have heterogeneous errors and cadences, please justify these choices against the actual NANOGrav/PPTA/LOFAR/NenuFAR data or state how sensitive the conclusions are to them.
  4. [Appendix B, Eq. (B.7)] Equation (B.7) depends on constants a and b that are fit to the simulated data. This should be stated explicitly in the main text where the Fisher prediction is invoked (Sec. 3.3), and the posterior uncertainty on these constants should be reported.
  5. [Typos] Minor typographical issues: 'Weigthed' in the captions of Figs. 3 and 9; 'stastistic' in Sec. 3.1.1; 'prividing' in Sec. 4; 'ampliutde' in Table 2; and the inconsistent use of 'EPOCH' vs 'epoch' in Sec. 3.2.

Circularity Check

1 steps flagged

Simulation-based ~2sigma noise-fluctuation explanation is self-contained; only the Appendix B angle formula is a fitted-input prediction.

specific steps
  1. fitted input called prediction [Appendix B, Eq. B.7 and Figure B.1]
    "Since for F^{-1}_{Aγ} and F^{-1}_{γγ} we do not know the exact value, but only an approximation, we can write the exact expression for θ by adding two unknown variables ... By fitting this function to the θ measured from the 100 realisation of DR2, we find that the relation is in very good agreement with the behaviour of the data, as can be seen from Figure B.1."

    The constants a and b in Eq. B.7 are free parameters fit to the same 100 simulated orientation angles that are then used to claim agreement. The 'prediction' is therefore matched to the data by construction, so the agreement shown in Figure B.1 is not an independent verification of the Fisher-matrix formula. This is a side result used in Sec. 3.3 to support the posterior-orientation discussion; it does not drive the paper's central noise-fluctuation claim.

full rationale

The central claim—that the DR2new vs DR2full significance flip can be a ~2sigma noise fluctuation—is a genuine simulation-based statement. The 15% and 5% frequencies are counted from 100 noise realisations of a fixed injected SMBHB-population GWB (A=2.4e-15, gamma=13/3) and noise parameters taken from the EPTA DR2 SPNA; no parameter is adjusted to reproduce the observed significance flip. The 5% selection uses the real HD S/N values to define a compatibility box, which is a posterior predictive check rather than an equivalence-by-construction. The frequency-coverage explanation is supported by the DR2 vs DR2FC controlled comparison inside the paper, not only by the self-cited Ferranti et al. (2025) degeneracy metric, so that self-citation is not load-bearing. The spectral-leakage bias is diagnosed with an external FFTInt method (Crisostomi et al. 2025) and compared against the injected spectrum, so no circularity arises there. The only genuine circular step is in Appendix B, where free constants a and b are fit to the same 100 simulated angles that are then declared to be in good agreement with the fitted formula. That is a minor, side-result circularity and does not undermine the paper's main inference.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

The paper's quantitative conclusions rest on a realistic but hand-calibrated simulation: a single injected GWB spectrum, per-pulsar noise parameters inherited from SPNA, a simplified IPTA coverage model, and a Fisher check with two fitted constants. No new physical entities are introduced.

free parameters (5)
  • Injected GWB amplitude and slope = A_GWB = 2.4e-15, γ = 13/3 (α = -2/3)
    Fixed to a value consistent with EPTA DR2 constraints; the central 15%/5% rates and bias estimates depend on this injected signal, and only one SMBHB population realization is tested.
  • Per-pulsar noise injection parameters (RN, DM, EFAC/EQUAD) = Per-pulsar maximum-likelihood values from EPTA DR2 SPNA
    Injected as the maximum-likelihood noise budget from single-pulsar noise analysis of the real data; this sets the noise fluctuations that drive the HD S/N distribution overlap.
  • FFTInt low-frequency cutoff = 1/3 T_obs
    Choice used in the leakage-corrected analysis; the authors report the induced parameter change is compatible with zero, so it is not critical to the main claim.
  • Fisher-formula constants a and b = Fitted to 100 simulated principal-axis angles
    Equation B.7 introduces unknown a and b and fits them to the simulated θ values, so the agreement with the Fisher prediction is partly a fit, not an independent derivation.
  • Simulated IPTA backend properties = TOA errors 2µs and 7µs; start epochs 53000, 56500, 58300; 100 LOFAR and NenuFAR TOAs
    Hand-chosen representative values for NANOGrav/PPTA/LOFAR/NenuFAR; the reported IPTA significance boost depends on these simplified choices.
axioms (6)
  • domain assumption Gaussian stationary noise and timing-model-marginalized likelihood (van Haasteren & Vallisneri 2014)
    Used throughout the analysis (Eq. 7); if noise is non-Gaussian or non-stationary, the simulated rates could change.
  • domain assumption Injected SMBHB population consists of circular binaries with a power-law spectrum
    The injected spectrum in Fig. 1 is a power law; eccentricity or environmental coupling would alter the spectral shape and the HD recovery characterization.
  • standard math Standard analysis assumes a diagonal frequency-domain covariance matrix
    This is the very assumption the spectral-leakage section shows is violated for 10-year datasets; the paper's leakage claim depends on the FFTInt method correctly fixing this violation.
  • domain assumption Noise parameters from SPNA are representative of the true noise in all realizations
    Noise realizations are drawn around the SPNA maximum-likelihood values; the authors acknowledge that epoch-correlated white noise and transient noise were not injected.
  • domain assumption FFTInt/Discovery implementation correctly models spectral leakage
    The claim that leakage is the dominant bias (5.6σ to 1.5σ) relies on the correctness of the external FFTInt method from Crisostomi et al. (2025).
  • ad hoc to paper The selection criterion for 'compatible with the real data' defines the reported 5% probability
    Realizations are selected if DR2new gives higher HD S/N than DR2full and the values fall within 90% C.I. of the real data; this post-hoc criterion defines the '~2σ' statement.

pith-pipeline@v1.3.0-alltime-deepseek · 22148 in / 12078 out tokens · 106030 ms · 2026-08-03T19:54:00.904735+00:00 · methodology

0 comments
read the original abstract

Pulsar Timing Arrays (PTAs) are approaching the sensitivity required for a $5\sigma$ detection of the nanohertz stochastic gravitational-wave background (GWB). This makes it crucial to deeply understand the behaviour of our analysis pipelines. A counterintuitive feature of the European Pulsar Timing Array (EPTA) second data release is that restricting the dataset to the last 10.3 years (DR2new) increases the inferred GWB significance from $\leq2\sigma$ for the full 25-year dataset (DR2full) to $\geq3.5\sigma$. We investigate whether this behaviour indicates an anomaly or is a possible outcome of the pipeline. Using realistic, DR2-like simulations with varying timespans, we find that the first 10 years contribute little to the GWB evidence due to their limited frequency coverage. This produces substantial overlap between the HD S/N distributions of DR2full and DR2new. Random noise fluctuations therefore yield a higher GWB evidence in DR2new than in DR2full in $15\%$ of cases. Furthermore, $5\%$ of simulations match the HD S/N of the real data, indicating that the observed behaviour is consistent with being a $\sim2\sigma$ outcome due to noise fluctuations. Regardless of significance, DR2new simulations introduce biases in the GWB parameter estimation due to spectral leakage effects that are ignored in standard analyses and which flatten the inferred spectrum. Including leakage removes these biases, demonstrating the reliability of DR2new when the signal is properly modelled. Furthermore, we demonstrate that combining EPTA DR2full with long-baseline data from NANOGrav and PPTA, as well as low-frequency data from LOFAR and NenuFAR, significantly enhances GWB evidence and parameter accuracy. Finally, we examine the impact of the observation timespan and find that short-baseline datasets introduce strong amplitude biases and are ineffective at constraining the GWB.

Figures

Figures reproduced from arXiv: 2511.21933 by Alberto Sesana, Federico Fantoccoli, Golam Mohiuddin Shaifullah, Irene Ferranti, Mikel Falxa.

Figure 1
Figure 1. Figure 1: Characteristic strain spectrum of the injected GWB. Pur [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top: Distribution of the SNR computed from the 100 real [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: 2-d distributions of the noise marginalised HD S [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of the precision and accuracy of the GWB parameter estimation performed with [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Median of the marginalised posterior distributions of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: For pulsar PSR J1022+1001 Top panel: data from the real EPTA DR2full, NANOGrav 16yr, PPTA 20yr, LOFAR and NenuFAR. Bottom panel: Simplified simulation of the three PTAs combination. percentages suggest that the observed scenario is consistent with an ≈ 2σ random fluctuations around the average behaviour. 3.1.3. Spectral Leakage As mentioned in the previous section, we can identify three sources of the sign… view at source ↗
Figure 7
Figure 7. Figure 7: GWB significance and parameter estimation from the 100 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Median of the marginalised posterior distributions of [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Degeneracy coefficient (weighted averag JSD) and me￾dian of the marginal posterior distribution of log10AGWB from the 100 simulations of DR2 5yr and DR2* 5yr. found that the prediction from the Fisher matrix agrees with the distribution of the orientation values within 68%C.I. (see Ap￾pendix B) for all the observation times investigated. In addition, the values of the orientation computed from the posterio… view at source ↗

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

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Reference graph

Works this paper leans on

36 extracted references · 2 linked inside Pith · cited by 1 Pith paper

  1. [1]

    2023, ApJ, 951, L11

    Afzal, A., Agazie, G., Anumarlapudi, A., et al. 2023, ApJ, 951, L11

    2023

  2. [2]

    M., et al

    Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2023, arXiv e-prints, arXiv:2306.16221

    Pith/arXiv arXiv 2023

  3. [3]

    M., et al

    Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2023, The Astrophysical Journal Letters, 951, L10

    2023

  4. [4]

    2024, Phys

    Babak, S., Falxa, M., Franciolini, G., & Pieroni, M. 2024, Phys. Rev. D, 110, 063022

    2024

  5. [5]

    G., Janssen, G

    Bassa, C. G., Janssen, G. H., Stappers, B. W., et al. 2016, MNRAS, 460, 2207

    2016

  6. [6]

    & Figueroa, D

    Caprini, C. & Figueroa, D. G. 2018, Classical and Quantum Gravity, 35, 163001

    2018

  7. [7]

    M., & Vallisneri, M

    Crisostomi, M., van Haasteren, R., Meyers, P. M., & Vallisneri, M. 2025, arXiv e-prints, arXiv:2506.13866

    Pith/arXiv arXiv 2025

  8. [8]

    Y ., Verbiest, J

    Donner, J. Y ., Verbiest, J. P. W., Tiburzi, C., et al. 2020, A&A, 644, A153

    2020

  9. [9]

    T., Hobbs, G

    Edwards, R. T., Hobbs, G. B., & Manchester, R. N. 2006, MNRAS, 372, 1549

    2006

  10. [10]

    Ellis, J. A. 2013, Classical and Quantum Gravity, 30, 224004 EPTA and InPTA Collaboration, Antoniadis, J., Arumugam, P., et al. 2024, A&A, 685, A94 EPTA and InPTA Collaboration, Antoniadis, J., Arumugam, P., et al. 2023a, A&A, 678, A50 EPTA and InPTA Collaboration, Antoniadis, J., Arumugam, P., et al. 2023b, A&A, 678, A49 EPTA and InPTA Collaboration, Ant...

    2013

  11. [11]

    2025, A&A, 694, A38

    Ferranti, I., Falxa, M., Sesana, A., et al. 2025, A&A, 694, A38

    2025

  12. [12]

    Foster, R. S. & Backer, D. C. 1990, ApJ, 361, 300

    1990

  13. [13]

    & Sardana, S

    Goncharov, B. & Sardana, S. 2025, Monthly Notices of the Royal Astronomical Society, 537, 3470–3479

    2025

  14. [14]

    2025, Reading signatures of super- massive binary black holes in pulsar timing array observations

    Goncharov, B., Sardana, S., Sesana, A., et al. 2025, Reading signatures of super- massive binary black holes in pulsar timing array observations

    2025

  15. [15]

    Hellings, R. W. & Downs, G. S. 1983, ApJ, 265, L39

    1983

  16. [16]

    2025, arXiv e-prints, arXiv:2510.04639 Article number, page 15 of 16 A&A proofs:manuscript no

    Iraci, F., Chalumeau, A., Tiburzi, C., et al. 2025, arXiv e-prints, arXiv:2510.04639 Article number, page 15 of 16 A&A proofs:manuscript no. main

    arXiv 2025

  17. [17]

    Jaffe, A. H. & Backer, D. C. 2003, ApJ, 583, 616

    2003

  18. [18]

    Larsen, B., Mingarelli, C. M. F., Baker, P. T., et al. 2025, MNRAS, 542, 3028

    2025

  19. [19]

    M., Coles, W

    Lentati, L., Shannon, R. M., Coles, W. A., et al. 2016, MNRAS, 458, 2161

    2016

  20. [20]

    Lorimer, D. R. & Kramer, M. 2004, Handbook of Pulsar Astronomy, V ol. 4

    2004

  21. [21]

    T., Shannon, R

    Miles, M. T., Shannon, R. M., Reardon, D. J., et al. 2025, MNRAS, 536, 1489 Quelquejay Leclere, H., Li, K., V olonteri, M., et al. 2025, arXiv e-prints, arXiv:2510.14613

    arXiv 2025

  22. [22]

    & Romani, R

    Rajagopal, M. & Romani, R. W. 1995, ApJ, 446, 543

    1995

  23. [23]

    J., Zic, A., Shannon, R

    Reardon, D. J., Zic, A., Shannon, R. M., et al. 2023, ApJ, 951, L6

    2023

  24. [24]

    A., Sesana, A., & Gair, J

    Rosado, P. A., Sesana, A., & Gair, J. 2015, Monthly Notices of the Royal Astro- nomical Society, 451, 2417–2433

    2015

  25. [25]

    2013, Classical and Quantum Gravity, 30, 244009

    Sesana, A. 2013, Classical and Quantum Gravity, 30, 244009

    2013

  26. [26]

    Sesana, A., Vecchio, A., & Colacino, C. N. 2008, MNRAS, 390, 192

    2008

  27. [27]

    K., Falxa, M., et al

    Speri, L., Porayko, N. K., Falxa, M., et al. 2023, MNRAS, 518, 1802

    2023

  28. [28]

    C., Chalumeau, A., Tiburzi, C., et al

    Susarla, S. C., Chalumeau, A., Tiburzi, C., et al. 2024, A&A, 692, A18

    2024

  29. [29]

    2016, MNRAS, 455, 4339

    Tiburzi, C., Hobbs, G., Kerr, M., et al. 2016, MNRAS, 455, 4339

    2016

  30. [30]

    2020, libstempo: Python wrapper for Tempo2, Astrophysics Source Code Library, record ascl:2002.017

    Vallisneri, M. 2020, libstempo: Python wrapper for Tempo2, Astrophysics Source Code Library, record ascl:2002.017

    2020

  31. [31]

    2024, A&A, 683, A201 van Haasteren, R

    Valtolina, S., Shaifullah, G., Samajdar, A., & Sesana, A. 2024, A&A, 683, A201 van Haasteren, R. 2024, ApJS, 273, 23 van Haasteren, R. 2025, MNRAS, 537, L1 van Haasteren, R. & Vallisneri, M. 2014, Phys. Rev. D, 90, 104012

    2024

  32. [32]

    Verbiest, J. P. W., Lentati, L., Hobbs, G., et al. 2016, MNRAS, 458, 1267

    2016

  33. [33]

    Verbiest, J. P. W. & Shaifullah, G. M. 2018, Classical and Quantum Gravity, 35, 133001

    2018

  34. [34]

    J., Islo, K., Taylor, S

    Vigeland, S. J., Islo, K., Taylor, S. R., & Ellis, J. A. 2018, Phys. Rev. D, 98, 044003

    2018

  35. [35]

    Wyithe, J. S. B. & Loeb, A. 2003, ApJ, 590, 691

    2003

  36. [36]

    2023, Research in Astronomy and Astrophysics, 23, 075024 Article number, page 16 of 16

    Xu, H., Chen, S., Guo, Y ., et al. 2023, Research in Astronomy and Astrophysics, 23, 075024 Article number, page 16 of 16

    2023