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Detection and parameter estimation of supermassive black hole ringdown signals using a pulsar timing array

T0 review · 3 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A simulated 100-pulsar array catches supermassive black hole ringdowns 99% of the time.

desk verdict First quantitative end-to-end PTA ringdown search: internally consistent simulations, but waveform/noise idealizations are untested and the no-hair promise overstates the demonstrated precision. read the letter →

arxiv 2412.07615 v2 pith:EVRM63ZP submitted 2024-12-10 astro-ph.HE gr-qc

Xuan Tao , Yan Wang , Soumya D. Mohanty This is my paper · ORCID
classification astro-ph.HEgr-qc
keywords pulsartimingarraysupermassiveblackholeringdowngravitationalwavedetectiongeneralizedlikelihoodratiotestparticleswarmoptimizationstaggeredsamplingno-hairtheoremquasi-normalmodes
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that a pulsar timing array (PTA) can detect the gravitational-wave ringdown of a supermassive black hole merger even when the signal frequency sits above the usual single-pulsar sampling limit, provided the pulsars are observed asynchronously. To show this, it builds a coherent search that combines a generalized likelihood ratio test with an analytic F-statistic for the four extrinsic parameters and particle swarm optimization for the five intrinsic parameters. On a simulated 100-pulsar array with 100-nanosecond white noise and randomized observation times, the search reaches a 99% detection probability at a false-alarm probability below 0.2% for optimal signal-to-noise ratio above 10. The paper also reports accurate recovery of frequency, damping time, sky position, and start time, with enough precision to guide electromagnetic follow-up and to estimate the remnant black hole's spin and mass. If these results carry over to real data, PTAs would open a new mass window for testing the no-hair theorem.

What carries the argument

The mechanism that carries the argument is the combination of asynchronous pulsar sampling with a coherent search statistic. Asynchronous sampling raises the array's frequency reach from the single-pulsar Nyquist rate $f_{sp}$ to about $N_p f_{sp}$, because different pulsars observe the same high-frequency signal at different times; the signal model is the simplified Earth-term timing residual of Eq. 17, which keeps only the dominant (2,2) mode and drops a secondary term of Eq. 10. The extrinsic parameters (amplitude, inclination, polarization, initial phase) enter linearly after a reparametrization and are maximized analytically via the F-statistic, $F = (1/2) N^{T} M^{-1} N$, while particle swarm optimization searches the five-dimensional intrinsic parameter space (sky position, frequency, damping time, start time). PSO's role is to find the global maximum of this multimodal fitness landscape reliably, using eight parallel runs to drive the convergence probability effectively to one.

What would settle it

Take the paper's 100-pulsar, 100 ns simulation and inject ringdowns from the full Earth-term residual (Eq. 10, keeping the secondary term and the $Q^2/(1+Q^2)$ factor) or from a numerical-relativity waveform with higher-order modes, then count detections above the same threshold of 30.1 at SNR 10 with 500 realizations; if the detection fraction falls materially below 99% at a false-alarm probability of 0.2%, the claimed detection performance does not survive realistic waveform systematics.

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Extended reading notes

Core claim

The central claim is that a sufficiently large PTA with staggered, asynchronous pulsar sampling can detect and characterize the dominant (2,2) ringdown mode of a supermassive black hole merger using a likelihood-based search. For the paper's simulated array of 100 pulsars, each with 100 ns white timing noise and randomized observation epochs over five years, the generalized likelihood ratio test combined with particle swarm optimization achieves a detection probability of 99% at a false alarm probability below 0.2% once the optimal network SNR exceeds 10; the fitted Gaussian distribution at SNR 10 puts 99.2% of the fitness values above the threshold of 30.1. The same setup yields parameter estimates with negligible bias for frequency, damping time, sky location, and start time, with sky-localization errors around 5 degrees and a start-time bias of about 13 hours. From the estimated frequency and damping time, the paper derives a quality factor with a relative error of about 6.5% and estimates the remnant spin and mass with small biases. These numbers are presented as proof of principle that ringdown astronomy with PTAs is data-analysis-viable, not merely a frequency-argument curiosity.

Load-bearing premise

The detection rates are computed on simulated data where the injected ringdown is generated from the same simplified Earth-term template the search uses, and the noise is white, stationary, and identical across pulsars; real waveforms carry extra terms and modes, and real timing noise is red and non-stationary.

Editorial extensions

If this is right

  • PTA ringdown searches need not be limited to frequencies below the single-pulsar Nyquist rate; with staggered sampling the reach scales with the number of pulsars, so larger arrays directly buy higher-frequency sensitivity.
  • An equal-mass, non-spinning supermassive binary with chirp mass $9.52 \times 10^{9}$ solar masses at 420 Mpc would be detectable at 99% probability with false alarm below 0.2% by a 100-pulsar, 100 ns array at SNR above 10.
  • Parameter estimation is accurate enough for practical follow-up: sky localization within roughly 5 degrees, frequency to about 7 rad/yr, and start time biased by only about 13 hours.
  • Ringdown-based estimates of quality factor, spin, and final mass can be recovered with small biases, giving a path toward no-hair theorem tests in the supermassive black hole mass range.
  • For higher ringdown frequencies the signal duration shortens, fewer pulsars fall inside the window, and parameter-estimation accuracy degrades; this sets a frequency ceiling below the formal array Nyquist limit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the injected signals are generated with the same simplified template the search uses, the quoted 99% detection probability is an upper-bound-like estimate; injecting the full Eq. 10 residual and higher-order modes would test how much of this margin survives realistic waveform systematics.
  • The same GLRT-plus-PSO architecture should transfer to other short-lived PTA transients, such as memory signals or burst-like emission from eccentric binaries, since the F-statistic separation of parameters does not rely on the ringdown's exponential envelope.
  • If red noise is handled before the search, for example by subtracting a smooth spline fit, the white-noise results here could still approximately hold; the paper explicitly leaves this step for future work, so a natural next test is to inject red noise at observed levels and re-measure the detection fraction.
  • The 13-hour start-time bias, though small compared to optical survey cadences, suggests a systematic in the analytic maximization or PSO convergence that could matter for precision follow-up at higher SNR; checking whether the bias scales with SNR would clarify its origin.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 3 minor

Summary. The paper proposes a likelihood-based GLRT-PSO method for detecting and estimating supermassive black hole ringdown signals in pulsar timing array data, exploiting asynchronous sampling of multiple pulsars to overcome the per-pulsar Nyquist limit. The authors simulate a 100-pulsar PTA with 100 ns white Gaussian noise, inject (2,2)-mode Earth-term ringdown signals, and report a 99% detection probability at SNR>10 with false alarm probability <0.2%, along with parameter estimation biases and standard deviations for six sources. The method separates intrinsic and extrinsic parameters, with the latter maximized analytically à la F-statistic and the former searched via particle swarm optimization.

Significance. The central detection result is internally consistent: the reported 99% at SNR=10 matches the fitted Gaussian distribution in Fig. 2, the 500-realization Monte Carlo is adequate, and the PSO convergence checks in Fig. 3 support the optimization. The paper also releases its data and uses machine-checkable simulation consistency checks. The proposed search band above the per-pulsar Nyquist frequency is a novel and timely direction for SKA-era PTAs. However, the abstract's claim that the method enables 'stringent tests of the no-hair theorem' is not supported by the single-mode analysis and by the reported parameter precision (spin standard deviation 0.27, mass relative standard deviation about 15%).

major comments (3)
  1. [Abstract and Sec. I] The abstract and Introduction claim that the proposed method will lead to 'stringent tests of the no-hair theorem', but the analysis uses only the dominant (2,2) fundamental mode. A no-hair test requires comparing at least two quasinormal-mode frequencies or damping times (e.g., the (2,2) and (3,3) modes, or an overtone) to check GR-predicted consistency relations; with a single mode one can only estimate M and j under the assumption of GR. The paper's own Sec. V acknowledges that higher-order modes are excluded. Please either remove or substantially qualify the no-hair claim in the abstract, or add a multi-mode analysis that actually performs such a test.
  2. [Table III and Sec. IV C] Even if a no-hair test were possible with the (2,2) mode alone, the reported precision does not support 'stringent' constraints: the spin parameter j has a standard deviation of 0.27 and the final mass M has a relative standard deviation of about 15% at SNR 10. These are not stringent bounds. The authors should either quantify the precision required for a meaningful no-hair test and show where the method reaches it (e.g., at higher SNR), or soften the wording throughout the manuscript.
  3. [Sec. II, Eq. (30)] The expression for the maximum detectable frequency f_h appears to contain a factor error. With ΔT = 1/(2 f_sp), one has τ/ΔT = 2 Q f_sp/(π f_h), which yields f_h = f_sp sqrt(2 Q N_p/π). The text writes f_h = (Q/(π f_h))(f_sp/2) N_p f_sp, which would give a different result. Please check the derivation and correct the formula.
minor comments (3)
  1. [Sec. IV B] The false alarm probability is estimated from the same 500 noise realizations used to set the threshold (the maximum observed fitness). Please report the binomial uncertainty on this estimate or use an independent set of noise realizations to validate the FAP at the chosen threshold.
  2. [Sec. III B and Table II] The paper does not report estimation results for the extrinsic parameters (ζ, ι, ψ, φ0), even though they are a central part of the analytic F-statistic step. Because Eq. (17) is an approximation to Eq. (10) (dropping the second term and setting Q^2/(1+Q^2)≈1), the extrinsic estimates could be biased. Please report their bias and standard deviation, or discuss why they are not relevant to the claims.
  3. [Abstract and Sec. II] There is a typographical space in 'F AST' in the abstract, and the notation 'NP fsp' after Eq. (30) should be 'N_p f_sp' for consistency.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the core results are Monte Carlo simulation measurements, not derivations from fitted inputs or self-citation chains.

full rationale

The paper's central claims—99% detection probability with false-alarm probability below 0.2% at SNR 10, and the parameter-estimation uncertainties—are obtained from 500 Monte Carlo realizations of a simulated PTA, with the detection threshold set from the empirical H0 fitness distribution and the detection probability read off the measured fitness distributions. This is a self-contained simulation experiment, not a prediction forced by construction: the injected signals are generated with the same Eq. 17 template used by the search, but that only validates the pipeline on signals in its own model class, which is standard practice and is explicitly qualified in the limitations section. The frequency-reach premise is imported from the authors' prior work [34], but the paper independently exercises it by simulating asynchronous sampling at f = 2fsp and 6fsp and recovering the signals. The self-citations to [41,42] and [34] are for established GLRT/PSO methodology and frequency-reach analysis, and the waveform formulas (Eqs. 4 and 5) come from external numerical-relativity fitting results (Meidam et al., Berti et al.), not from the target detection claim. The dropped second term in Eq. 10 is an acknowledged approximation, not a circular step, and the idealized white-noise and (2,2)-only assumptions are stated as limitations rather than hidden inputs. No load-bearing step reduces to its own input.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The paper introduces no new physical entities. The central claim depends on empirical fitting formulas from the literature for ringdown amplitudes, frequencies, and quality factors, on the choice of j=0.69 for equal-mass nonspinning progenitors, and on several domain assumptions about noise and sampling that are acknowledged as limitations. The only ad hoc approximation specific to this paper is the simplification of the Earth-term residual in Eq. 10, which is tested only against the same simplified model.

free parameters (4)
  • A22(eta) amplitude coefficient = 0.864 * eta
    Phenomenological fit to numerical relativity amplitudes from Meidam et al. (2014), used in Eq. 4 to set the ringdown amplitude for injected signals.
  • f22 frequency fit coefficients = 1.5251, 1.1568, 0.1292
    Fitting formula from Berti et al. (2006), Eq. 5a, maps final spin j to the (2,2) QNM frequency; used to define injected signals and the search template.
  • Q22 quality factor fit coefficients = 0.7000, 1.4187, 0.4990
    Fitting formula from Berti et al. (2006), Eq. 5b, determines the damping time tau = Q/(pi f) used in the signal model.
  • Remnant spin j for equal-mass nonspinning binary = 0.69
    From NR fitting formulas of Rezzolla et al. and Tichy and Marronetti, used as the injected dimensionless spin for all six simulated sources.
assumptions (6)
  • domain assumption Noise in each pulsar is independent, stationary, white Gaussian with identical variance sigma_n = 100 ns.
    Used in the likelihood (Eq. 12) and in all simulations; real PTA data contain red noise and varying noise levels, as acknowledged in Sec. V.
  • domain assumption The pulsar-term contribution can be ignored because the Earth-pulsar light travel time is hundreds of years while the ringdown duration is at most weeks.
    Sec. II argues the pulsar term would be the low-frequency inspiral, to which the high-frequency ringdown search is insensitive.
  • domain assumption Only the fundamental l=m=2, n=0 quasinormal mode is included; overtones and higher-order modes are neglected.
    Sec. II and Sec. V state this restriction and note it may bias mass and spin estimates at high SNR.
  • ad hoc to paper The second term in Eq. 10 is negligible and Q^2/(1+Q^2) is approximately 1.
    Sec. II drops a term estimated at about 15% of the primary term and approximates the quality-factor factor by 1, simplifying the template but introducing about 9% error for Q near 3.2.
  • domain assumption Observation times follow a regular staggered grid plus truncated Cauchy jitter with scale 1/3 day and cap 7 days.
    Sec. IV A defines the asynchronous sampling scheme used in all simulations; real scheduling will differ.
  • domain assumption The 100 nearest pulsars from an SKA synthetic catalog represent a future large PTA.
    Sec. IV A selects pulsars from a synthetic catalog to define the array; actual SKA arrays may have different sky positions and noise properties.

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Cite this review

Pith. "Pith review of Detection and parameter estimation of supermassive black hole ringdown signals using a pulsar timing array." pith.science (2026). https://pith.science/paper/EVRM63ZP

@misc{pith2026241207615,
  author       = {Pith},
  title        = {Pith review of: Detection and parameter estimation of supermassive black hole ringdown signals using a pulsar timing array},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EVRM63ZP}},
  note         = {Machine review of arXiv:2412.07615}
}
abstract

Gravitational wave (GW) searches using pulsar timing arrays (PTAs) are commonly assumed to be limited to a GW frequency of $\lesssim 4\times 10^{-7}$Hz given by the Nyquist rate associated with the average observational cadence of $2$ weeks for a single pulsar. However, by taking advantage of asynchronous observations of multiple pulsars, a PTA can detect GW signals at higher frequencies. This allows a sufficiently large PTA to detect and characterize the ringdown signals emitted following the merger of supermassive binary black holes (SMBBHs), leading to stringent tests of the no-hair theorem in the mass range of such systems. Such large-scale PTAs are imminent with the advent of the FAST telescope and the upcoming era of the Square Kilometer Array (SKA). To scope out the data analysis challenges involved in such a search, we propose a likelihood-based method coupled with Particle Swarm Optimization and apply it to a simulated large-scale PTA comprised of $100$ pulsars, each having a timing residual noise standard deviation of $100$~nsec, with randomized observation times. Focusing on the dominant $(2,2)$ mode of the ringdown signal, we show that it is possible to achieve a $99\%$ detection probability with a false alarm probability below $0.2\%$ for an optimal signal-to-noise ratio (SNR) $>10$. This corresponds, for example, to an equal-mass non-spinning SMBBH with an observer frame chirp mass $M_c = 9.52\times10^{9}M_{\odot}$ at a luminosity distance of $D_L = 420$ Mpc.

Figures

Figures reproduced from arXiv: 2412.07615 by the authors.

Figure 1
Figure 1. FIG. 1. The measured SNR [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The distribution of the fitness value for 500 [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 4
Figure 4. FIG. 4. The black line depicts the injected signal for one of [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Histograms of the estimated intrinsic parameters of 500 data realizations for Source 1. The red vertical solid line [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Reference graph

Works this paper leans on

76 extracted references · 56 canonical work pages

  1. [1]

    H0: The data consists of only noise, rI (t) = nI (t)

    work page

  2. [2]

    let-them- fly

    Hλ: The data contains a signal characterized by parameters λ, rI (t) = nI (t) + sI (t; λ). For H0, the joint probability density function (PDF) of the data is given by p(r|H0) = NpY I=1 pI rI = NpY I=1 exp − 1 2 ⟨rI |rI ⟩I p (2π)N I |C I | , (12) where we assume the noise is Gaussian, and ⟨rI |rI ⟩I is the noise weighted inner product for pulsar I, given ...

    work page 2000

  3. [3]

    Manchester et al., The parkes pulsar timing array project, Publications of the Astronomical Society of Aus- tralia 30 (2013)

    R. Manchester et al., The parkes pulsar timing array project, Publications of the Astronomical Society of Aus- tralia 30 (2013)

    work page 2013

  4. [4]

    M. Kerr et al., The Parkes Pulsar Timing Array project: second data release, Publications of the Astronomical So- ciety of Australia 37, e020 (2020), publisher: Cambridge University Press

    work page 2020

  5. [5]

    Kramer and D

    M. Kramer and D. J. Champion, The European Pulsar Timing Array and the Large European Array for Pulsars, Class. Quantum Grav. 30, 224009 (2013), publisher: IOP Publishing

    work page 2013

  6. [6]

    S. Chen et al., Common-red-signal analysis with 24-yr high-precision timing of the european pulsar timing ar- ray: Inferences in the stochastic gravitational-wave back- ground search, Monthly Notices of the Royal Astronom- ical Society 508, 4970 (2021)

    work page 2021

  7. [7]

    M. A. McLaughlin, The north american nanohertz obser- vatory for gravitational waves, Classical and Quantum Gravity 30, 224008 (2013)

    work page 2013

  8. [8]

    M. F. Alam et al., The NANOGrav 12.5 yr Data Set: Wideband Timing of 47 Millisecond Pulsars, ApJS 252, 5 (2020), publisher: The American Astronomical Society

    work page 2020

Show all 76 references
  1. [9]

    B. C. Joshi et al., Precision pulsar timing with the ort and the gmrt and its applications in pulsar astrophysics, Journal of Astrophysics and Astronomy 39, 51 (2018)

    2018

  2. [10]

    Tarafdar et al., The Indian Pulsar Timing Array: First data release (2022), arXiv:2206.09289 [astro-ph]

    P. Tarafdar et al., The Indian Pulsar Timing Array: First data release (2022), arXiv:2206.09289 [astro-ph]

    2022 arXiv

  3. [11]

    Verbiest et al., The international pulsar timing array: first data release, Monthly Notices of the Royal Astro- nomical Society 458, 1267 (2016)

    J. Verbiest et al., The international pulsar timing array: first data release, Monthly Notices of the Royal Astro- nomical Society 458, 1267 (2016). 12

    2016

  4. [12]

    J. Antoniadis et al., The International Pulsar Timing Ar- ray second data release: Search for an isotropic gravita- tional wave background, Monthly Notices of the Royal Astronomical Society 510, 4873 (2022)

    2022

  5. [13]

    K. Lee, Prospects of gravitational wave detection using pulsar timing array for chinese future telescopes, in Fron- tiers in Radio Astronomy and F AST Early Sciences Sym- posium 2015, Vol. 502 (2016) p. 19

    2016

  6. [14]

    Jonas and the MeerKAT Team, The MeerKAT Ra- dio Telescope, in Proceedings of MeerKAT Science: On the Pathway to the SKA PoS(MeerKAT2016), Vol

    J. Jonas and the MeerKAT Team, The MeerKAT Ra- dio Telescope, in Proceedings of MeerKAT Science: On the Pathway to the SKA PoS(MeerKAT2016), Vol. 277 (SISSA Medialab, 2018) p. 001, conference Name: MeerKAT Science: On the Pathway to the SKA

    2018

  7. [15]

    C. L. Carilli and S. Rawlings, Motivation, key science projects, standards and assumptions, New Astronomy Reviews Science with the Square Kilometre Array, 48, 979 (2004)

    2004

  8. [16]

    M. T. Miles et al., The MeerKAT Pulsar Timing Ar- ray: the 4.5-yr data release and the noise and stochastic signals of the millisecond pulsar population, Monthly No- tices of the Royal Astronomical Society536, 1467 (2025)

    2025

  9. [17]

    Antoniadis et al., The second data release from the European Pulsar Timing Array III

    J. Antoniadis et al., The second data release from the European Pulsar Timing Array III. Search for gravita- tional wave signals, Astronomy & Astrophysics 678, A50 (2023), arXiv:2306.16214 [astro-ph]

    2023 arXiv

  10. [18]

    D. J. Reardon et al. , Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array, The Astrophysical Journal Letters 951, L6 (2023), publisher: The American Astronomical Soci- ety

    2023

  11. [19]

    G. Agazie et al., The NANOGrav 15 yr Data Set: Evi- dence for a Gravitational-wave Background, The Astro- physical Journal Letters 951, L8 (2023), publisher: The American Astronomical Society

    2023

  12. [20]

    H. Xu et al., Searching for the Nano-Hertz Stochastic Gravitational Wave Background with the Chinese Pulsar Timing Array Data Release I, Research in Astronomy and Astrophysics 23, 075024 (2023), publisher: National Astromonical Observatories, CAS and IOP Publishing

    2023

  13. [21]

    R. W. Hellings and G. S. Downs, Upper limits on the isotropic gravitational radiation background from pul- sar timing analysis., The Astrophysical Journal 265, L39 (1983), aDS Bibcode: 1983ApJ...265L..39H

    1983

  14. [22]

    Smits et al., Pulsar searches and timing with the square kilometre array, A&A 493, 1161 (2009), number: 3 Publisher: EDP Sciences

    R. Smits et al., Pulsar searches and timing with the square kilometre array, A&A 493, 1161 (2009), number: 3 Publisher: EDP Sciences

    2009

  15. [23]

    G. H. Janssen et al., Gravitational wave astronomy with the SKA (2014), arXiv:1501.00127 [astro-ph]

    2014 arXiv

  16. [24]

    Wang and S

    Y. Wang and S. D. Mohanty, Pulsar Timing Array Based Search for Supermassive Black Hole Binaries in the Square Kilometer Array Era, Phys. Rev. Lett. 118, 151104 (2017), arXiv:1611.09440 [astro-ph.IM]

    2017 arXiv

  17. [25]

    L. Lentati et al., European Pulsar Timing Array limits on an isotropic stochastic gravitational-wave background, Monthly Notices of the Royal Astronomical Society 453, 2576 (2015), https://academic.oup.com/mnras/article- pdf/453/3/2576/4900884/stv1538.pdf

    2015

  18. [26]

    R. M. Shannon et al., Gravitational waves from binary supermassive black holes missing in pulsar observations, Science 349, 1522 (2015), arXiv:1509.07320

    2015 arXiv

  19. [27]

    Arzoumanian et al

    Z. Arzoumanian et al. , The NANOGrav Nine-year Data Set: Limits on the Isotropic Stochastic Gravita- tional Wave Background, Astrophys. J. 821, 13 (2016), arXiv:1508.03024

    2016 arXiv

  20. [28]

    Arzoumanian et al

    Z. Arzoumanian et al. , The NANOGrav 11 Year Data Set: Pulsar-timing Constraints on the Stochastic Gravitational-wave Background, Astrophys. J. 859, 47 (2018), arXiv:1801.02617 [astro-ph.HE]

    2018 arXiv

  21. [29]

    X.-J. Zhu et al., An all-sky search for continuous gravi- tational waves in the Parkes Pulsar Timing Array data set, Monthly Notices of the Royal Astronomical Society 444, 3709 (2014), arXiv:1408.5129

    2014 arXiv

  22. [30]

    S. Babak et al., European Pulsar Timing Array lim- its on continuous gravitational waves from individ- ual supermassive black hole binaries, Monthly Notices of the Royal Astronomical Society 455, 1665 (2016), arXiv:1509.02165 [astro-ph.CO]

    2016 arXiv

  23. [31]

    Aggarwal et al., The NANOGrav 11 yr Data Set: Lim- its on Gravitational Waves from Individual Supermas- sive Black Hole Binaries, Astrophys

    K. Aggarwal et al., The NANOGrav 11 yr Data Set: Lim- its on Gravitational Waves from Individual Supermas- sive Black Hole Binaries, Astrophys. J. 880, 116 (2019), arXiv:1812.11585 [astro-ph.GA]

    2019 arXiv

  24. [32]

    D. R. B. Yardley et al., The sensitivity of the Parkes Pul- sar Timing Array to individual sources of gravitational waves, Monthly Notices of the Royal Astronomical Soci- ety 407, 669 (2010)

    2010

  25. [33]

    S. Yi et al., Limits on the strength of individual gravi- tational wave sources using high-cadence observations of PSR B1937+21, Monthly Notices of the Royal Astronom- ical Society 445, 1245 (2014)

    2014

  26. [34]

    B. B. P. Perera et al., Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713+0747 on gravitational waves produced by super- massive black hole binaries, Monthly Notices of the Royal Astronomical Society 478, 218 (2018)

    2018

  27. [35]

    T. Dolch et al., Single-Source Gravitational Wave Limits From the J1713+0747 24-hr Global Campaign, Journal of Physics: Conference Series 716, 012014 (2016), pub- lisher: IOP Publishing

    2016

  28. [36]

    Y. Wang, S. D. Mohanty, and Z. Cao, Extending the fre- quency reach of pulsar timing array based gravitational wave search without high cadence observations, ApJ907, L43 (2021), arXiv:2012.04261 [astro-ph, physics:gr-qc]

    2021 arXiv

  29. [37]

    Kamaretsos et al., Black-hole hair loss: Learning about binary progenitors from ringdown signals, Phys

    I. Kamaretsos et al., Black-hole hair loss: Learning about binary progenitors from ringdown signals, Phys. Rev. D 85, 024018 (2012)

    2012

  30. [38]

    London, D

    L. London, D. Shoemaker, and J. Healy, Modeling ring- down: Beyond the fundamental quasinormal modes, Phys. Rev. D 90, 124032 (2014)

    2014

  31. [39]

    London, Modeling ringdown

    L. London, Modeling ringdown. ii. aligned-spin binary black holes, implications for data analysis and fundamen- tal theory, Phys. Rev. D 102, 084052 (2020)

    2020

  32. [40]

    Lim et al., Exciting black hole modes via misaligned coalescences

    H. Lim et al., Exciting black hole modes via misaligned coalescences. ii. the mode content of late-time coalescence waveforms, Phys. Rev. D 100, 084032 (2019)

    2019

  33. [41]

    Yunes and X

    N. Yunes and X. Siemens, Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays, Living Reviews in Relativity 16, 9 (2013)

    2013

  34. [42]

    Askar et al., Black holes, gravitational waves and fun- damental physics: a roadmap, Classical and Quantum Gravity 36, 143001 (2019), publisher: IOP Publishing

    A. Askar et al., Black holes, gravitational waves and fun- damental physics: a roadmap, Classical and Quantum Gravity 36, 143001 (2019), publisher: IOP Publishing

    2019

  35. [43]

    Y. Wang, S. D. Mohanty, and F. A. Jenet, A Coher- ent Method for the Detection and Parameter Estima- tion of Continuous Gravitational Wave Signals Using a Pulsar Timing Array, Astrophys. J. 795, 96 (2014), arXiv:1406.5496 [astro-ph.IM]

    2014 arXiv

  36. [44]

    Y. Wang, S. D. Mohanty, and F. A. Jenet, Coherent Network Analysis for Continuous Gravitational Wave 13 Signals in a Pulsar Timing Array: Pulsar Phases as Extrinsic Parameters, Astrophys. J. 815, 125 (2015), arXiv:1506.01526 [astro-ph.IM]

    2015 arXiv

  37. [45]

    Kennedy and R

    J. Kennedy and R. Eberhart, Particle swarm optimiza- tion, in Proceedings of ICNN’95 - International Confer- ence on Neural Networks, Vol. 4 (1995) pp. 1942–1948 vol.4

    1995

  38. [46]

    Jaranowski, A

    P. Jaranowski, A. Kr´ olak, and B. F. Schutz, Data anal- ysis of gravitational-wave signals from spinning neutron stars: The signal and its detection, Physical Review D 58, 063001 (1998), aDS Bibcode: 1998PhRvD..58f3001J

    1998

  39. [47]

    Baibhav et al., Black hole spectroscopy: Systematic errors and ringdown energy estimates, Phys

    V. Baibhav et al., Black hole spectroscopy: Systematic errors and ringdown energy estimates, Phys. Rev. D 97, 044048 (2018)

    2018

  40. [48]

    ´E. ´E. Flanagan and S. A. Hughes, Measuring gravita- tional waves from binary black hole coalescences. I. Sig- nal to noise for inspiral, merger, and ringdown, Phys. Rev. D 57, 4535 (1998), arXiv:gr-qc/9701039 [gr-qc]

    1998 arXiv

  41. [49]

    J. N. Goldberg et al., Spin-s spherical harmonics and dh, Journal of Mathematical Physics 8, 2155 (1967)

    1967

  42. [50]

    Cotesta et al., Analysis of Ringdown Overtones in GW150914, Phys

    R. Cotesta et al., Analysis of Ringdown Overtones in GW150914, Phys. Rev. Lett. 129, 111102 (2022)

    2022

  43. [51]

    Kamaretsos, M

    I. Kamaretsos, M. Hannam, and B. S. Sathyaprakash, Is Black-Hole Ringdown a Memory of Its Progenitor?, Physical Review Letters 109, 141102 (2012), publisher: American Physical Society

    2012

  44. [52]

    Meidam et al., Testing the no-hair theorem with black hole ringdowns using TIGER, Physical Review D 90, 064009 (2014)

    J. Meidam et al., Testing the no-hair theorem with black hole ringdowns using TIGER, Physical Review D 90, 064009 (2014)

    2014

  45. [53]

    Berti, V

    E. Berti, V. Cardoso, and C. M. Will, Gravitational-wave spectroscopy of massive black holes with the space inter- ferometer LISA, Physical Review D 73, 064030 (2006)

    2006

  46. [54]

    Tichy and P

    W. Tichy and P. Marronetti, The final mass and spin of black hole mergers, Physical Review D78, 081501 (2008), arXiv:0807.2985 [astro-ph, physics:gr-qc]

    2008 arXiv

  47. [55]

    Rezzolla et al., Final spin from the coalescence of two black holes, Physical Review D 78, 044002 (2008), pub- lisher: American Physical Society

    L. Rezzolla et al., Final spin from the coalescence of two black holes, Physical Review D 78, 044002 (2008), pub- lisher: American Physical Society

    2008

  48. [56]

    E. L. Lehmann, J. P. Romano, and G. Casella, Testing statistical hypotheses, Vol. 3 (Springer, 1986)

    1986

  49. [57]

    Jaranowski, A

    P. Jaranowski, A. Kr´ olak, and B. F. Schutz, Data analysis of gravitational-wave signals from spinning neutron stars: The signal and its detection, Phys. Rev. D 58, 063001 (1998), arXiv:gr-qc/9804014 [gr-qc]

    1998 arXiv

  50. [58]

    J. A. Ellis, X. Siemens, and J. D. E. Creighton, Optimal Strategies for Continuous Gravitational Wave Detection in Pulsar Timing Arrays, Astrophys. J. 756, 175 (2012), arXiv:1204.4218 [astro-ph.IM]

    2012 arXiv

  51. [59]

    N. J. Cornish and E. K. Porter, The search for massive black hole binaries with LISA, Classical and Quantum Gravity 24, 5729 (2007), arXiv:gr-qc/0612091 [gr-qc]

    2007 arXiv

  52. [60]

    Wang and S

    Y. Wang and S. D. Mohanty, Particle swarm optimization and gravitational wave data analysis: Performance on a binary inspiral testbed, Physical Review D 81, 063002 (2010), publisher: American Physical Society

    2010

  53. [61]

    T. S. Weerathunga and S. D. Mohanty, Performance of particle swarm optimization on the fully-coherent all-sky search for gravitational waves from compact binary coa- lescences, Physical Review D 95, 124030 (2017)

    2017

  54. [62]

    Y.-Q. Qian, S. D. Mohanty, and Y. Wang, Iterative time- domain method for resolving multiple gravitational wave sources in pulsar timing array data, Phys. Rev. D 106, 023016 (2022)

    2022

  55. [63]

    Zhang et al

    X.-H. Zhang et al. , Resolving Galactic binaries in LISA data using particle swarm optimization and cross- validation, Physical Review D 104, 024023 (2021), pub- lisher: American Physical Society

    2021

  56. [64]

    Smits et al., Pulsar searches and timing with the square kilometre array, Astronomy & Astrophysics 493, 1161 (2009)

    R. Smits et al., Pulsar searches and timing with the square kilometre array, Astronomy & Astrophysics 493, 1161 (2009)

    2009

  57. [65]

    Papoulis, Random variables and stochastic processes (McGraw Hill, 1991)

    A. Papoulis, Random variables and stochastic processes (McGraw Hill, 1991)

    1991

  58. [66]

    LSST Science Collaboration et al., Science-Driven Op- timization of the LSST Observing Strategy, arXiv e-prints , arXiv:1708.04058 (2017), arXiv:1708.04058 [astro-ph.IM]

    2017 arXiv

  59. [67]

    F. B. Bianco et al., Optimization of the observing ca- dence for the rubin observatory legacy survey of space and time: A pioneering process of community-focused experimental design, The Astrophysical Journal Supple- ment Series 258, 1 (2021)

    2021

  60. [68]

    Berti, V

    E. Berti, V. Cardoso, and A. O. Starinets, Quasinor- mal modes of black holes and black branes, Classical and Quantum Gravity 26, 163001 (2009)

    2009

  61. [69]

    Baibhav, E

    V. Baibhav, E. Berti, and V. Cardoso, LISA parameter estimation and source localization with higher harmonics of the ringdown, Phys. Rev. D 101, 084053 (2020)

    2020

  62. [70]

    L. S. Finn, Aperture synthesis for gravitational-wave data analysis: Deterministic sources, Physical Review D 63, 102001 (2001), publisher: American Physical Society

    2001

  63. [71]

    S. D. Mohanty and E. Fahnestock, Adaptive spline fitting with particle swarm optimization, Computational Statis- tics 36, 155 (2021)

    2021

  64. [72]

    S. D. Mohanty and M. A. T. Chowdhury, Glitch sub- traction from gravitational wave data using adaptive spline fitting, Classical and Quantum Gravity 40, 125001 (2023), publisher: IOP Publishing

    2023

  65. [73]

    Y. Qian, S. Mohanty, and Y. Wang, A Novel Method to Remove Red Noise in PTA Data (2024)

    2024

  66. [74]

    Antoniadis et al., The second data release from the Eu- ropean Pulsar Timing Array - V

    J. Antoniadis et al., The second data release from the Eu- ropean Pulsar Timing Array - V. Search for continuous gravitational wave signals, Astronomy & Astrophysics 690, A118 (2024), publisher: EDP Sciences

    2024

  67. [75]

    Pompili et al., Laying the foundation of the effective- one-body waveform models SEOBNRv5: Improved ac- curacy and efficiency for spinning nonprecessing bi- nary black holes, Phys

    L. Pompili et al., Laying the foundation of the effective- one-body waveform models SEOBNRv5: Improved ac- curacy and efficiency for spinning nonprecessing bi- nary black holes, Phys. Rev. D 108, 124035 (2023), arXiv:2303.18039 [gr-qc]

    2023 arXiv

  68. [76]

    X. Tao, Y. Wang, and S. Mohanty, The data of the pa- per ”detection and parameter estimation of supermassive black hole ringdown signals using a pulsar timing array”, 10.5281/zenodo.15024591 (2025)

    2025 doi

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