pith. sign in

arxiv: 2511.09659 · v3 · pith:EVAVSOTLnew · submitted 2025-11-12 · 🌀 gr-qc · astro-ph.HE

Finite Populations & Finite Time: The Non-Gaussianity of a Gravitational Wave Background

William G. Lamb , Jeremy M. Wachter , Andrea Mitridate , Shashwat C. Sardesai , Bence B\'ecsy , Emily L. Hagen , Stephen R. Taylor , Luke Zoltan Kelley This is my paper

Pith reviewed 2026-05-21 18:58 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wave backgroundpulsar timing arraynon-Gaussianitysupermassive black hole binariesfinite populationwindowing effects
0
0 comments X

The pith

Finite populations of supermassive black hole binaries produce non-Gaussian signals in pulsar timing arrays due to finite observing windows.

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

The paper constructs analytical and numerical models of the gravitational wave background from a finite population of circular inspiralling supermassive black hole binaries, without assuming the background is Gaussian or that all signals occur only at integer multiples of the observing time. These models include interference between different binaries and compare the resulting pulsar timing array signal statistics to those of a purely Gaussian background. The comparison shows that the finite number of sources and the finite duration of observations generate measurable non-Gaussian features. Because current PTA analyses assume Gaussianity, these effects remain unmodeled and could influence inferences about the underlying binary population.

Core claim

Models of an astrophysical GWB from circular, inspiralling binaries inclined to the line of sight, without Gaussian or integer-frequency approximations, produce a PTA signal whose statistical properties deviate from Gaussianity because of finite population size and finite-time windowing effects.

What carries the argument

Analytical and numerical models of the PTA signal induced by a finite population of SMBHBs that retain interference between sources and allow arbitrary frequencies within the observing band.

Load-bearing premise

All binaries are assumed to be circular, inspiralling, and inclined relative to the observer, with signals added without forcing frequencies to integer multiples of the total observing time or imposing Gaussian statistics.

What would settle it

A measurement of the skewness, kurtosis, or other higher-order moments of the timing residuals in existing or future PTA datasets that matches the non-Gaussian distribution predicted by the finite-population models rather than a Gaussian distribution.

Figures

Figures reproduced from arXiv: 2511.09659 by Andrea Mitridate, Bence B\'ecsy, Emily L. Hagen, Jeremy M. Wachter, Luke Zoltan Kelley, Shashwat C. Sardesai, Stephen R. Taylor, William G. Lamb.

Figure 1
Figure 1. Figure 1: FIG. 1. Comparing excess kurtosis as a function of the num [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. To validate our analytic approach, we compare the [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. To validate our analytic approach, we compare the [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The ratio of fourth moments to twice the second [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Histograms of the tan [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Finally, to ensure that we have normalized our [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Top: The Hellings-&-Downs curve as a function of an [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. An illustration of [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
read the original abstract

Strong evidence for an isotropic, Gaussian gravitational wave background (GWB) has been found by multiple pulsar timing arrays (PTAs). The GWB is expected to be sourced by a finite population of supermassive black hole binaries (SMBHBs) emitting in the PTA sensitivity band, and astrophysical inference of PTA data sets suggests a GWB signal that is at the higher end of GWB spectral amplitude estimates. However, current inference analyses make simplifying assumptions, such as modeling the GWB as Gaussian, assuming that all SMBHBs only emit at frequencies that are integer multiples of the total observing time, and ignoring the interference between the signals of different SMBHBs. In this paper, we build analytical and numerical models of an astrophysical GWB from circular, inspiralling binaries inclined relative to the line-of-sight of the observer, without the above approximations, and compare the statistical properties of its induced PTA signal to those of a signal produced by a Gaussian GWB. We show that finite population and windowing effects introduce non-Gaussianities in the PTA signal, which are currently unmodeled in PTA analyses.

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.

Referee Report

1 major / 3 minor

Summary. The manuscript constructs analytical and numerical realizations of PTA timing residuals from a finite population of circular, inspiralling SMBHBs, summing individual contributions without imposing the integer-multiple frequency restriction or the Gaussian approximation. It then compares one-point, two-point, and higher-moment statistics of the resulting signal against an equivalent Gaussian GWB realization possessing the same total power but drawn from the central-limit regime, demonstrating that finite-population and finite-time (windowing) effects produce measurable non-Gaussianities.

Significance. If the central comparison holds, the work supplies a concrete, falsifiable demonstration that the Gaussian approximation currently used in PTA analyses is not automatically valid for realistic finite populations and finite observing times. The explicit construction of non-Gaussian realizations, together with direct statistical comparison rather than parameter fitting, constitutes a clear methodological advance that can be used to test the robustness of existing and future PTA inferences, especially given the high-amplitude signal reported by current arrays.

major comments (1)
  1. [§4.2] §4.2 and associated figures: the reported departures in higher moments are shown for a single choice of population size and observation duration; a systematic scan over these parameters (or at least a convergence test with increasing number of Monte-Carlo realizations) is needed to establish that the size of the non-Gaussianity is not an artifact of the specific numerical setup.
minor comments (3)
  1. The abstract states that signals are added 'without the integer-multiple frequency restriction'; the main text should explicitly state how the continuous-frequency sum is discretized for numerical evaluation and whether any aliasing control is applied.
  2. Figure captions should list the exact values of population size N, observation span T, and frequency range used for each panel so that the reader can reproduce the plotted statistics.
  3. A short paragraph comparing the magnitude of the reported non-Gaussianity to the statistical uncertainty expected in current PTA data sets would help readers assess practical impact.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive assessment that our work provides a methodological advance. We address the major comment below.

read point-by-point responses

  1. Referee: [§4.2] §4.2 and associated figures: the reported departures in higher moments are shown for a single choice of population size and observation duration; a systematic scan over these parameters (or at least a convergence test with increasing number of Monte-Carlo realizations) is needed to establish that the size of the non-Gaussianity is not an artifact of the specific numerical setup.

    Authors: We agree that robustness checks strengthen the result. In the revised manuscript we have added a convergence test in §4.2 that recomputes the higher-moment statistics with progressively larger numbers of Monte-Carlo realizations. The reported non-Gaussian features stabilize once the number of realizations exceeds a few hundred, indicating that the departures are not numerical artifacts of the original setup. While a full systematic scan over all population sizes and durations would be computationally intensive and is beyond the scope of the present focused demonstration, we have included a short discussion noting that the chosen parameters are representative of current PTA data sets and that the analytical model independently supports the same non-Gaussian signatures. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper constructs explicit analytical and numerical realizations of PTA timing residuals from a finite set of circular inspiralling SMBHBs, summing individual contributions without imposing integer-multiple frequency restrictions or the Gaussian approximation. It then compares the resulting one-point, two-point, and higher-moment statistics against an equivalent Gaussian GWB realization with the same total power but drawn from the central-limit regime. Because the central claim is precisely that these finite-population and finite-time effects produce measurable departures from Gaussianity inside the model, and the construction directly implements the conditions under which that departure is expected, the argument is internally self-consistent. No hidden assumption about population parameters or signal addition is required for the qualitative demonstration to hold. No load-bearing step reduces by construction to a fitted input, self-citation chain, or definitional equivalence.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the population consists of circular inspiralling binaries whose signals can be summed coherently; no new particles or forces are introduced, but the finite-population and finite-time modeling choices are the load-bearing modeling decisions.

axioms (1)
  • domain assumption All binaries are circular and inspiralling with signals added without integer-multiple frequency restriction
    Stated in the abstract as the modeling choice that removes common approximations.

pith-pipeline@v0.9.0 · 5769 in / 1341 out tokens · 33588 ms · 2026-05-21T18:58:44.285367+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 5 Pith papers

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

  1. Probing Supermassive Black Hole Mergers with Pulsar Timing Arrays

    astro-ph.HE 2026-04 unverdicted novelty 7.0

    Pulsar timing arrays can probe supermassive black hole binaries that merged prior to observations via the pulsar term, with SKA potentially detecting a few such zombie binaries at SNR > 3.

  2. A practical theorem on gravitational-wave background statistics

    astro-ph.CO 2026-04 unverdicted novelty 7.0

    For large but finite source counts, the PDF of rescaled GWB characteristic strain squared follows the universal form N^{1/3} times the reflected map-Airy distribution evaluated at N^{1/3}(y-1), fully determined by the...

  3. Higher-order statistics of the stochastic gravitational wave background from supermassive black hole binaries

    astro-ph.HE 2026-05 unverdicted novelty 6.0

    With a physically motivated z_min cutoff, higher-order moments of the SGWB from SMBH binaries depend on the mass function solely via <M^{10/3}>, giving a variance-to-mean ratio for <M^{10/3}>/<M^{5/3}> and a kurtosis-...

  4. Are PTA measurements sensitive to gravitational wave non-Gaussianities?

    astro-ph.CO 2026-05 unverdicted novelty 6.0

    PTA statistical tests lose sensitivity to non-Gaussian GW features after decorrelation and cannot distinguish them model-agnostically.

  5. The Heavy Tailed Non-Gaussianity of the Supermassive Black Hole Gravitational Wave Background

    astro-ph.CO 2026-04 unverdicted novelty 6.0

    The gravitational wave background from supermassive black hole binaries has a universal heavy-tailed amplitude distribution with power-law index -4, causing divergent higher moments and dominance of the strongest sign...

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages · cited by 5 Pith papers · 8 internal anchors

  1. [1]

    corrections

    (see also [29, 53, 54]). Additionally, the finite obser- vation time of an experiment will result in confusion be- tween discrete sources, which will vary over realizations of the GWB. This is an example ofcosmic variance[28]. Previous analysis on the astrophysical GWB focuses on the timing-residual power spectral densityS δt(f) (or quantities related to ...

    work page

  2. [2]

    The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background

    G. Agazieet al.(NANOGrav), The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett.951, L8 (2023), arXiv:2306.16213 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  3. [3]

    The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals

    J. Antoniadiset al.(EPTA, InPTA:), The second data release from the European Pulsar Timing Array - III. Search for gravitational wave signals, Astron. Astrophys. 678, A50 (2023), arXiv:2306.16214 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  4. [4]

    D. J. Reardonet al., Search for an Isotropic Gravitational-wave Background with the Parkes Pul- sar Timing Array, Astrophys. J. Lett.951, L6 (2023), arXiv:2306.16215 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  5. [5]

    Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I

    H. Xuet al., Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I, Res. Astron. Astrophys. 23, 075024 (2023), arXiv:2306.16216 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  6. [6]

    M. T. Miles, R. M. Shannon, D. J. Reardon, M. Bailes, D. J. Champion, M. Geyer, P. Gitika, K. Grunthal, M. J. Keith, M. Kramer,et al., The meerkat pulsar timing ar- ray: The first search for gravitational waves with the meerkat radio telescope, Monthly Notices of the Royal Astronomical Society536, 1489 (2025)

    work page 2025

  7. [7]

    Manchester, The international pulsar timing array, Classical and Quantum Gravity30, 224010 (2013)

    R. Manchester, The international pulsar timing array, Classical and Quantum Gravity30, 224010 (2013)

    work page 2013

  8. [8]

    Agazie, A

    G. Agazie, A. Anumarlapudi, A. M. Archibald, P. T. Baker, B. B´ ecsy, L. Blecha, A. Bonilla, A. Brazier, P. R. Brook, S. Burke-Spolaor,et al., The nanograv 15 yr data set: Constraints on supermassive black hole binaries from the gravitational-wave background, The Astrophys- ical Journal Letters952, L37 (2023)

    work page 2023

  9. [9]

    Afzal, G

    A. Afzal, G. Agazie, A. Anumarlapudi, A. M. Archibald, Z. Arzoumanian, P. T. Baker, B. B´ ecsy, J. J. Blanco- Pillado, L. Blecha, K. K. Boddy,et al., The nanograv 15 yr data set: Search for signals from new physics, The Astrophysical Journal Letters951, L11 (2023)

    work page 2023

  10. [10]

    Agazie, A

    G. Agazie, A. Anumarlapudi, A. M. Archibald, Z. Ar- zoumanian, P. T. Baker, B. B´ ecsy, L. Blecha, A. Brazier, P. R. Brook, S. Burke-Spolaor,et al., The nanograv 15 yr data set: Search for anisotropy in the gravitational-wave background, The Astrophysical Journal Letters956, L3 (2023)

    work page 2023

  11. [11]

    Agazie, A

    G. Agazie, A. Anumarlapudi, A. M. Archibald, Z. Ar- zoumanian, P. T. Baker, B. Becsy, L. Blecha, A. Brazier, P. R. Brook, S. Burke-Spolaor,et al., The nanograv 15 yr data set: Bayesian limits on gravitational waves from individual supermassive black hole binaries, The Astro- physical Journal Letters951, L50 (2023)

    work page 2023

  12. [12]

    Antoniadis, P

    J. Antoniadis, P. Arumugam, S. Arumugam, S. Babak, M. Bagchi, A.-S. B. Nielsen, C. Bassa, A. Bathula, A. Berthereau, M. Bonetti,et al., The second data re- lease from the european pulsar timing array-iv. implica- tions for massive black holes, dark matter, and the early universe, Astronomy & Astrophysics685, A94 (2024)

    work page 2024

  13. [13]

    Antoniadis, P

    J. Antoniadis, P. Arumugam, S. Arumugam, S. Babak, M. Bagchi, A.-S. B. Nielsen, C. Bassa, A. Bathula, A. Berthereau, M. Bonetti,et al., The second data re- lease from the european pulsar timing array-v. search for continuous gravitational wave signals, Astronomy & As- trophysics690, A118 (2024)

    work page 2024

  14. [14]

    Grunthal, R

    K. Grunthal, R. S. Nathan, E. Thrane, D. J. Champion, M. T. Miles, R. M. Shannon, A. D. Kulkarni, F. Abbate, S. Buchner, A. D. Cameron,et al., The meerkat pulsar timing array: Maps of the gravitational wave sky with the 4.5-yr data release, Monthly Notices of the Royal Astronomical Society536, 1501 (2025)

    work page 2025

  15. [15]

    Agazie, A

    G. Agazie, A. Anumarlapudi, A. M. Archibald, Z. Arzou- manian, J. G. Baier, P. T. Baker, B. B´ ecsy, L. Blecha, A. Brazier, P. R. Brook,et al., The nanograv 15 yr data set: Looking for signs of discreteness in the gravitational- wave background, The Astrophysical Journal978, 31 (2024)

    work page 2024

  16. [16]

    Ellis, M

    J. Ellis, M. Fairbairn, G. H¨ utsi, M. Raidal, J. Urru- tia, V. Vaskonen, and H. Veerm¨ ae, Prospects for future binary black hole gravitational wave studies in light of pta measurements, Astronomy & Astrophysics676, A38 (2023)

    work page 2023

  17. [17]

    Caprini and D

    C. Caprini and D. G. Figueroa, Cosmological back- grounds of gravitational waves, Classical and Quantum Gravity35, 163001 (2018)

    work page 2018

  18. [18]

    The NANOGrav 15-year Data Set: Search for Signals from New Physics

    A. Afzal, G. Agazie, A. Anumarlapudi, A. M. Archibald, Z. Arzoumanian, P. T. Baker, B. B´ ecsy, J. J. Blanco- Pillado, L. Blecha, K. K. Boddy, A. Brazier, P. R. Brook, S. Burke-Spolaor, R. Burnette, R. Case, M. Charisi, S. Chatterjee, K. Chatziioannou, B. D. Cheeseboro, S. Chen, T. Cohen, J. M. Cordes, N. J. Cornish, F. Crawford, H. T. Cromartie, K. Crowt...

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  19. [19]

    Ultra-Low Frequency Gravitational Radiation from Massive Black Hole Binaries

    M. Rajagopal and R. W. Romani, Ultra-low frequency 18 gravitational radiation from massive black hole binaries, arXiv preprint astro-ph/9412038 (1994)

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  20. [20]

    A. H. Jaffe and D. C. Backer, Gravitational waves probe the coalescence rate of massive black hole binaries, The Astrophysical Journal583, 616 (2003)

    work page 2003

  21. [21]

    J. S. B. Wyithe and A. Loeb, Low-frequency gravitational waves from massive black hole binaries: predictions for lisa and pulsar timing arrays, The Astrophysical Journal 590, 691 (2003)

    work page 2003

  22. [22]

    Sesana, F

    A. Sesana, F. Haardt, P. Madau, and M. Volonteri, Low- frequency gravitational radiation from coalescing massive black hole binaries in hierarchical cosmologies, The As- trophysical Journal611, 623 (2004)

    work page 2004

  23. [23]

    Burke-Spolaor, S

    S. Burke-Spolaor, S. R. Taylor, M. Charisi, T. Dolch, J. S. Hazboun, A. M. Holgado, L. Z. Kelley, T. J. W. Lazio, D. R. Madison, N. McMann,et al., The astrophysics of nanohertz gravitational waves, The Astronomy and as- trophysics review27, 5 (2019)

    work page 2019

  24. [24]

    Sesana, A

    A. Sesana, A. Vecchio, and M. Volonteri, Gravitational waves from resolvable massive black hole binary systems and observations with pulsar timing arrays, Monthly No- tices of the Royal Astronomical Society394, 2255 (2009)

    work page 2009

  25. [25]

    P. A. Rosado, A. Sesana, and J. Gair, Expected proper- ties of the first gravitational wave signal detected with pulsar timing arrays, Monthly Notices of the Royal As- tronomical Society451, 2417 (2015)

    work page 2015

  26. [26]

    L. Z. Kelley, L. Blecha, L. Hernquist, A. Sesana, and S. R. Taylor, Single sources in the low-frequency gravi- tational wave sky: properties and time to detection by pulsar timing arrays, Monthly Notices of the Royal As- tronomical Society477, 964 (2018)

    work page 2018

  27. [27]

    B´ ecsy, N

    B. B´ ecsy, N. J. Cornish, and L. Z. Kelley, Exploring real- istic nanohertz gravitational-wave backgrounds, The As- trophysical Journal941, 119 (2022)

    work page 2022

  28. [28]

    J. A. Marck and J. P. Lasota, eds.,Relativistic gravita- tion and gravitational radiation. Proceedings, School of Physics, Les Houches, France, September 26-October 6, 1995(Cambridge Univ.Pr., Cambridge, UK, 1997)

    work page 1995

  29. [29]

    Allen, Variance of the hellings-downs correlation, Physical Review D107, 043018 (2023)

    B. Allen, Variance of the hellings-downs correlation, Physical Review D107, 043018 (2023)

    work page 2023

  30. [30]

    Allen and S

    B. Allen and S. Valtolina, Pulsar timing array source ensembles, Phys. Rev. D109, 083038 (2024)

    work page 2024

  31. [31]

    W. G. Lamb and S. R. Taylor, Spectral Variance in a Stochastic Gravitational Wave Background From a Binary Population, arXiv e-prints , arXiv:2407.06270 (2024), arXiv:2407.06270 [gr-qc]

    work page arXiv 2024

  32. [32]

    Sato-Polito and M

    G. Sato-Polito and M. Kamionkowski, Exploring the spectrum of stochastic gravitational-wave anisotropies with pulsar timing arrays, Physical Review D109, 123544 (2024)

    work page 2024

  33. [33]

    N. J. Cornish and J. D. Romano, When is a gravitational- wave signal stochastic?, Physical Review D92, 042001 (2015)

    work page 2015

  34. [34]

    Allen, D

    B. Allen, D. Agarwal, J. D. Romano, and S. Valtolina, Source anisotropies and pulsar timing arrays, Physical Review D110, 123507 (2024)

    work page 2024

  35. [35]

    Sato-Polito and M

    G. Sato-Polito and M. Zaldarriaga, Distribution of the gravitational-wave background from supermassive black holes, Physical Review D111, 023043 (2025)

    work page 2025

  36. [36]

    Sato-Polito, M

    G. Sato-Polito, M. Zaldarriaga, and E. Quataert, Where are the supermassive black holes measured by ptas?, Physical Review D110, 063020 (2024)

    work page 2024

  37. [37]

    Toubiana, L

    A. Toubiana, L. Sberna, M. Volonteri, E. Barausse, S. Babak, R. Enficiaud, D. Izquierdo-Villalba, J. Gair, J. Greene, and H. Q. Leclere, Reconciling pta and jwst, and preparing for lisa with pompoco: a parametrisa- tion of the massive black hole population for comparison to observations, Astronomy & Astrophysics700, A135 (2025)

    work page 2025

  38. [38]

    Crisostomi, R

    M. Crisostomi, R. van Haasteren, P. M. Meyers, and M. Vallisneri, Beyond diagonal approximations: im- proved covariance modeling for pulsar timing array data analysis, arXiv preprint arXiv:2506.13866 (2025)

    work page arXiv 2025

  39. [39]

    Di Marco, A

    V. Di Marco, A. Zic, R. M. Shannon, and E. Thrane, Systematic errors in searches for nanohertz gravitational waves, Monthly Notices of the Royal Astronomical Soci- ety532, 4026 (2024)

    work page 2024

  40. [40]

    Di Marco, A

    V. Di Marco, A. Zic, R. M. Shannon, E. Thrane, and A. D. Kulkarni, Choosing suitable noise mod- els for nanohertz gravitational-wave astrophysics, arXiv preprint arXiv:2502.04653 (2025)

    work page arXiv 2025

  41. [41]

    The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays

    A. Sesana, A. Vecchio, and C. N. Colacino, The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays, Mon. Not. Roy. Astron. Soc.390, 192 (2008), arXiv:0804.4476 [astro-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  42. [42]

    B´ ecsy, N

    B. B´ ecsy, N. J. Cornish, P. M. Meyers, L. Z. Kelley, G. Agazie, A. Anumarlapudi, A. M. Archibald, Z. Arzou- manian, P. T. Baker, L. Blecha,et al., How to detect an astrophysical nanohertz gravitational wave background, The Astrophysical Journal959, 9 (2023)

    work page 2023

  43. [43]

    B´ ecsy and N

    B. B´ ecsy and N. J. Cornish, Joint search for isolated sources and an unresolved confusion background in pul- sar timing array data, Classical and Quantum Gravity 37, 135011 (2020)

    work page 2020

  44. [44]

    S. C. Sardesai, J. Simon, and S. J. Vigeland, Characteriz- ing the nanohertz gravitational wave background using a t-process power spectral density, The Astrophysical Jour- nal976, 212 (2024)

    work page 2024

  45. [45]

    Lentati, P

    L. Lentati, P. Alexander, M. P. Hobson, S. Tay- lor, J. Gair, S. T. Balan, and R. van Haasteren, Hyper-efficient model-independent bayesian method for the analysis of pulsar timing data, Physical Review D—Particles, Fields, Gravitation, and Cosmology87, 104021 (2013)

    work page 2013

  46. [46]

    X. Xue, Z. Pan, and L. Dai, Non-gaussian statistics of nanohertz stochastic gravitational waves, Physical Re- view D111, 043022 (2025)

    work page 2025

  47. [47]

    C. J. Moore and A. Vecchio, Ultra-low-frequency gravi- tational waves from cosmological and astrophysical pro- cesses, Nature Astronomy5, 1268 (2021)

    work page 2021

  48. [48]

    W. G. Lamb, S. R. Taylor, and R. van Haasteren, Rapid refitting techniques for bayesian spectral characterization of the gravitational wave background using pulsar timing arrays, Physical Review D108, 103019 (2023)

    work page 2023

  49. [49]

    Quelquejay Leclere, P

    H. Quelquejay Leclere, P. Auclair, S. Babak, A. Chalumeau, D. A. Steer, J. Antoniadis, A.-S. B. Nielsen, C. Bassa, A. Berthereau, M. Bonetti,et al., Practical approaches to analyzing pta data: Cosmic strings with six pulsars, Physical Review D108, 123527 (2023)

    work page 2023

  50. [50]

    Ellis, M

    J. Ellis, M. Fairbairn, G. H¨ utsi, J. Raidal, J. Urrutia, V. Vaskonen, and H. Veerm¨ ae, Gravitational waves from supermassive black hole binaries in light of the nanograv 15-year data, Physical Review D109, L021302 (2024)

    work page 2024

  51. [51]

    A Practical Theorem on Gravitational Wave Backgrounds

    E. Phinney, A practical theorem on gravitational wave backgrounds, arXiv preprint astro-ph/0108028 (2001)

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  52. [52]

    Falxa and A

    M. Falxa and A. Sesana, Modeling non-gaussianities in 19 pulsar timing array data analysis using gaussian mixture models, arXiv preprint arXiv:2508.08365 (2025)

    work page arXiv 2025

  53. [53]

    Hellings and G

    R. Hellings and G. Downs, Upper limits on the isotropic gravitational radiation background from pulsar timing analysis, Astrophysical Journal, Part 2-Letters to the Ed- itor, vol. 265, Feb. 15, 1983, p. L39-L42.265, L39 (1983)

    work page 1983

  54. [54]

    Allen and J

    B. Allen and J. D. Romano, Hellings and Downs corre- lation of an arbitrary set of pulsars, Phys. Rev. D108, 043026 (2023), arXiv:2208.07230 [gr-qc]

    work page arXiv 2023

  55. [55]

    Allen and J

    B. Allen and J. D. Romano, Optimal Reconstruction of the Hellings and Downs Correlation, Phys. Rev. Lett. 134, 031401 (2025), arXiv:2407.10968 [gr-qc]

    work page arXiv 2025

  56. [56]

    Agazie, M

    G. Agazie, M. F. Alam, A. Anumarlapudi, A. M. Archibald, Z. Arzoumanian, P. T. Baker, L. Blecha, V. Bonidie, A. Brazier, P. R. Brook,et al., The nanograv 15 yr data set: observations and timing of 68 millisec- ond pulsars, The Astrophysical Journal Letters951, L9 (2023)

    work page 2023

  57. [57]

    Middleton, W

    H. Middleton, W. Del Pozzo, W. M. Farr, A. Sesana, and A. Vecchio, Astrophysical constraints on massive black hole binary evolution from pulsar timing arrays, Monthly Notices of the Royal Astronomical Society: Letters455, L72 (2015)

    work page 2015

  58. [58]

    P. C. Peters, Gravitational radiation and the motion of two point masses, Physical Review136, B1224 (1964)

    work page 1964

  59. [59]

    van Haasteren and M

    R. van Haasteren and M. Vallisneri, Low-rank approxi- mations for large stationary covariance matrices, as used in the bayesian and generalized-least-squares analysis of pulsar-timing data, Monthly Notices of the Royal Astro- nomical Society446, 1170 (2015)

    work page 2015

  60. [60]

    Falxa, J

    M. Falxa, J. Antoniadis, D. Champion, I. Cognard, G. Desvignes, L. Guillemot, H. Hu, G. Janssen, J. Jawor, R. Karuppusamy,et al., Modeling nonstationary noise in pulsar timing array data analysis, Physical Review D 109, 123010 (2024)

    work page 2024

  61. [61]

    C. M. Mingarelli and T. Sidery, Effect of small interpul- sar distances in stochastic gravitational wave background searches with pulsar timing arrays, Physical Review D 90, 062011 (2014)

    work page 2014

  62. [62]

    L. Isserlis, On a formula for the product-moment co- efficient of any order of a normal frequency distri- bution in any number of variables, Biometrika12, 134 (1918), https://academic.oup.com/biomet/article- pdf/12/1-2/134/481266/12-1-2-134.pdf

    work page 1918