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Gaussian process representation of dispersion measure noise in pulsar wideband datasets

T0 review · 0 major / 7 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Wideband pulsar timing can now absorb Gaussian-process dispersion-measure noise through an analytically marginalized likelihood.

desk verdict Correct, clean derivation of a wideband DMGP likelihood; the DMX comparison is a nice practical bonus. read the letter →

arxiv 2505.05274 v2 pith:B24XOJER submitted 2025-05-08 astro-ph.IM astro-ph.HE

Abhimanyu Susobhanan , Rutger van Haasteren This is my paper · ORCID
classification astro-ph.IMastro-ph.HE
keywords pulsartimingdispersionmeasurenoisewidebandGaussianprocessBayesiananalysisarraysanalyticmarginalizationinterstellarmedium
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

This paper derives a closed-form likelihood for wideband pulsar timing, the paradigm in which each observation yields both a time of arrival and a dispersion measure (DM). It shows that when the timing model is linearized and the model parameters are given Gaussian priors, those parameters can be integrated out analytically, leaving a Gaussian likelihood whose covariance is the white-noise covariance plus a design-matrix projection of the prior covariance. Because the design matrix and prior covariance can encode any DM variation model, the result brings Gaussian-process models of stochastic DM variation into single-pulsar and pulsar-timing-array analyses. This matters because existing wideband analyses relied on piecewise-constant DMX bins or sampled many per-epoch parameters, whereas a Gaussian process captures long-timescale correlated DM variations with a spectral prior and keeps the computation analytically tractable.

What carries the argument

The central object is the analytically marginalized Gaussian likelihood identity: for a linear model $y = \bar{y} + M a$ with a zero-mean Gaussian prior $a \sim N(0, \Phi)$, the nuisance parameter $a$ can be integrated out exactly, leaving a Gaussian likelihood in $y$ with covariance $C = N + M \Phi M^{T}$. This identity carries the argument because it converts the choice of a DM variability model into a choice of design-matrix columns $M$ and prior covariance $\Phi$, so no per-epoch DM parameters need to be sampled.

What would settle it

Run the closed-form likelihood on a simulated wideband dataset in which the timing-model parameters are deliberately displaced far from their best-fit values, and compare its posterior with the full nonlinear posterior sampled directly; if the two disagree by more than the statistical uncertainty, the linearization premise fails. A similar comparison with a non-Gaussian prior on the parameter deviations would quantify how much the Gaussian-prior assumption costs.

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Extended reading notes

Core claim

Under the standard linearized wideband timing model $y = \bar{y} + M a$, with a zero-mean Gaussian prior on the parameter deviation vector $a$ with covariance $\Phi$, the paper derives the analytically marginalized likelihood $\Lambda \propto \exp(-\tfrac{1}{2} y^{T} C^{-1} y) / \sqrt{\det(2\pi C)}$, where $C = N + M \Phi M^{T}$. This expression has the same Gaussian form as the narrowband likelihood, so any DM variation model that can be written as design-matrix columns with Gaussian coefficients, including Fourier-basis Gaussian processes, DMX bins, constrained splines, and solar-wind models, can be included and marginalized analytically. The paper shows that a previously published wideband likelihood appears as the special case in which DMX and DMJUMP parameters are left unmarginalized, and that marginalizing those parameters brings it to the new form. A simulated dataset with injected spin noise and DM noise recovers the input parameters within $2\sigma$ uncertainties, and a comparison analysis with the DMX model finds that DMEFAC is underestimated because piecewise-constant DMX bins absorb short-timescale DM measurement noise.

Load-bearing premise

The derivation assumes the wideband residuals are exactly linear in the timing and noise parameter deviations, with a Gaussian prior on those deviations; when the timing solution is far from optimal or the priors are strongly non-Gaussian, the closed-form likelihood is only an approximation.

Editorial extensions

If this is right

  • Single-pulsar noise analysis of wideband data can now include Gaussian-process DM noise alongside the piecewise-constant DMX model, so long-timescale correlated DM variations are represented by a spectral prior instead of many per-epoch bins.
  • Wideband analyses no longer depend on infinitely wide improper priors on DMX parameters, making them usable when low-frequency or high-bandwidth observations leave individual DMs poorly constrained.
  • Pulsar timing array searches with wideband data can analytically marginalize DM variations, including Gaussian-process DM models, while looking for cross-pulsar correlated signals such as the nanohertz gravitational-wave background.
  • The likelihood evaluation cost is $O(N_{\mathrm{data}} p^{2})$, and for equivalent observations the narrowband likelihood is slower by a factor of $N_{\mathrm{subband}}/2$, so wideband Gaussian-process DM analyses are computationally cheaper as well as more general.
  • The same formalism covers piecewise-constant DMX, constrained spline, and solar-wind DM models as special cases, giving one unified likelihood for all common DM variability models.

Reading between the lines

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

  • The same $M \Phi M^{T}$ marginalization could be applied to other per-observation chromatic delays, such as scattering-variation delays, by adding design-matrix columns; the paper notes scattering is not yet well understood in wideband timing, but the mathematics does not depend on the physical origin of the delay.
  • The factorized form of the likelihood in Appendix B suggests a modular wideband pulsar-timing-array analysis in which DM residuals are modeled first and TOA residuals are then conditioned on the DM fit, which could simplify gravitational-wave searches.
  • A testable prediction follows from the simulation: on real wideband datasets with short-timescale DM fluctuations, DMX analyses will systematically underestimate DMEFAC relative to a Gaussian-process DM analysis, which can be checked with existing wideband pulsar data.
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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

0 major / 7 minor

Summary. The paper derives an analytically marginalized likelihood for wideband pulsar timing with arbitrary dispersion-measure (DM) variability models, including Gaussian-process (DMGP) models. Starting from a linearized wideband timing model y = ybar + M a and a Gaussian prior a ~ N(0, Phi), the authors marginalize over the parameter deviations to obtain Lambda = exp(-1/2 y^T C^{-1} y) / sqrt(det(2 pi C)) with C = N + M Phi M^T (Eqs. 17-18). The paper then derives a factorized ENTERPRISE-friendly form of this likelihood (Appendix B), compares it with the Alam et al. (2021) wideband likelihood (Appendix A), and derives a maximum-likelihood estimator for PINT (Appendix C). The method is demonstrated on a simulated 500-epoch dataset with injected spin and DM power-law noise; the posteriors recover the injected values, and a comparison with the DMX model shows a known bias in DMEFAC. Code and data are provided as supplementary material.

Significance. The central result, Eq. (17), is a clean and standard Gaussian marginalization. If it stands, it provides a general, computationally practical way to include DMGP, DMX, spline, and solar-wind DM models in wideband single-pulsar noise analysis and pulsar-timing-array analyses, removing the current DMX-only limitation in ENTERPRISE. The simulation validates the implementation, and the numerical equivalence check in Appendix B supports the factorized form. The paper also makes concrete contributions toward ENTERPRISE and PINT integration. The derivation is self-contained and builds on well-established PTA methods, and the released simulated dataset and notebook aid reproducibility. Overall, this is a useful methods paper for the pulsar-timing community, though a few presentation and consistency issues should be fixed.

minor comments (7)
  1. [Appendix C, Eq. (C2)] The covariance matrix after marginalizing over the correlated-noise amplitudes alpha with prior covariance Psi should be G = N + U Psi U^T, not G = N + U^T Psi^{-1} U as printed. The printed expression is dimensionally inconsistent (N is 2N_toa x 2N_toa while U^T Psi^{-1} U is n x n) and would propagate incorrectly into Eqs. (C3)-(C6). Please correct this.
  2. [Section 4 and Figure 1] The text in Section 4 states that all parameter estimates are consistent with the injected values within 2-sigma uncertainties, while the caption of Figure 1 says within 3-sigma uncertainties. Please make these statements consistent and verify which is correct.
  3. [Section 2, Eq. (2)] The Fourier/Taylor expansion for the rotational phase is written as a sum starting at j = 1, which omits the linear spin-frequency term F0 (tau_i - tau_0). Since Table 1 lists F0 as the spin frequency, the sum should start at j = 0 (or the indexing should be adjusted) to include the zeroth-order term.
  4. [Section 1] The Introduction says the linearization and analytic marginalization are described in Section 2, but these are actually presented in Section 3. Please correct the cross-reference.
  5. [Section 3, after Eq. (18)] The discussion of improper priors states that timing parameters have infinite diagonal elements in Phi. In the limit of infinite variance, C in Eq. (18) is not a finite matrix, and Eq. (17) is understood only as a limiting expression. Please state the limiting argument explicitly, for example by referring to a sequence of broad proper priors and noting that divergent constants cancel in the posterior for the noise parameters.
  6. [Section 4] The repeated analysis with a smaller number of harmonic bins is described only qualitatively ('EFAC and DMEFAC being overestimated'). Reporting the numerical values or a figure would make this robustness check reproducible and quantitative.
  7. [Appendix B, Eq. (B14a)] The quantity B G^T \bar L^{-1} delta is the posterior mean (or MAP under the prior B) of the dispersion parameters beta given the DM measurements, not the maximum-likelihood estimate. Please adjust the wording for accuracy.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: Eq. (17) is a standard analytic Gaussian marginalization, not an input recycled as a prediction.

full rationale

The paper's central result, Eq. (17), follows by direct analytic marginalization of the linearized wideband timing model (Eq. 10) under a conjugate Gaussian prior on parameter deviations (Eq. 14). The covariance matrix C = N + M Φ Mᵀ in Eq. (18) is obtained by standard Gaussian linear-model algebra; it is not defined in terms of any quantity fitted to the data whose prediction is then claimed. The DMGP model enters only through the design matrix M and the prior covariance Φ, which are model choices whose hyperparameters are the targets of inference, not inputs adjusted to force agreement with the data. The simulation in Section 4 uses injected parameter values and checks that the posteriors recover them, which is an external benchmark rather than a circular reuse of fitted outputs. Citations to prior work, including the authors' own Vela.jl and previous marginalization papers, are used for context and for standard spectral-model conventions; the marginalization itself is re-derived in the paper rather than imported as a black box. The linearization assumption in Eq. (10) is a stated approximation, not a circular step. No self-definitional, fitted-input-called-prediction, self-citation-load-bearing, uniqueness-imported, ansatz-smuggled, or renaming pattern is present.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The derivation is parameter-free in the sense that it holds for any prior covariance; the only hand-chosen number in the demonstration is the Fourier harmonic basis size, which the authors explicitly test. The axioms are the standard linearized-timing and Gaussian-process assumptions of pulsar timing, all clearly stated or cited. No invented entities are introduced.

free parameters (1)
  • Fourier harmonic basis size for spin/DM noise (N_harm linear bins plus sub-fundamental bins) = 124 bins (120 linear at f1 to 120f1 plus 4 log-spaced at f1/16 to f1/2)
    Chosen by hand in Section 4. The authors show that reducing this number biases white noise parameters, so the simulation result depends on this choice; the formal derivation is agnostic.
assumptions (4)
  • domain assumption Linearized timing model y = ȳ + M a
    Section 3, Eq. (10). The whole marginalization and the resulting covariance C = N + M Φ Mᵀ require Gaussian linearity; this is the standard pulsar timing approximation.
  • domain assumption Noise processes are stationary Gaussian processes represented by a finite Fourier series
    Section 3, Eq. (12). The paper's DMGP implementation relies on this spectral representation (Lentati et al. 2014). The formalism itself allows other bases.
  • domain assumption Conjugate Gaussian prior on parameter deviations; improper priors handled by limiting argument
    Section 3, Eqs. (13)-(16). Analytic marginalization is only exact for proper Gaussian priors; the unbounded priors for timing parameters are handled by the standard limiting procedure from van Haasteren et al. (2009), to which the paper defers.
  • domain assumption TOA-DM measurement covariance can be set to zero by fiducial frequency; Appendix B assumes exactly zero
    Section 2 and Appendix B. The main derivation can in principle include nonzero covariance, but the ENTERPRISE-friendly factorized likelihood assumes it vanishes.

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Cite this review

Pith. "Pith review of Gaussian process representation of dispersion measure noise in pulsar wideband datasets." pith.science (2026). https://pith.science/paper/B24XOJER

@misc{pith2026250505274,
  author       = {Pith},
  title        = {Pith review of: Gaussian process representation of dispersion measure noise in pulsar wideband datasets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B24XOJER}},
  note         = {Machine review of arXiv:2505.05274}
}
read the original abstract

The ionized interstellar medium disperses pulsar radio signals, resulting in a stochastic time-variable delay known as the dispersion measure (DM) noise. In the wideband paradigm of pulsar timing, we measure a DM together with a time of arrival from a pulsar observation to handle frequency-dependent profile evolution, interstellar scintillation, and radio frequency interference more robustly, and to reduce data volumes. In this paper, we derive a method to incorporate arbitrary models of DM variation, including Gaussian process models, in pulsar timing and noise analysis and pulsar timing array analysis. This generalizes the existing method for handling DM noise in wideband datasets.

Figures

Figures reproduced from arXiv: 2505.05274 by the authors.

Figure 1
Figure 1. Parameter estimation results for the simulation described in Section 4. The corner plots show the posterior samples, and the black lines represent the injected parameter values. The posterior distribution for the DMGP analysis is shown in red and the posterior distribution for the DMX analysis is shown in blue. The parameter estimates are consistent with the injected values within 3𝜎 uncertainties. The pre-fit and p… view at source ↗
Figure 2
Figure 2. The pre-fit and whitened time and DM residuals obtained from the simulation study described in Section 4 for the DMGP analysis. The colors indicate different observing frequencies. The whitened residuals are computed using equations (C5)–(C6). We see that the residuals have been effectively whitened. The three tracks seen in the top left panel correspond to three observing frequencies. They are not simply scaled cop… view at source ↗

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Forward citations

Cited by 2 Pith papers

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

  1. PSRDISP: A novel approach to modeling dispersive processes in single-pulsar noise analysis using epoch-wise dispersion measures

    astro-ph.IM 2026-07 unverdicted novelty 6.0 of 10

    PSRDISP is a Gaussian-process framework that fits dispersion-measure and solar-wind noise directly to epoch-wise dispersion measures, recovering injected signals in simulated pulsar data.

  2. Bayesian pulsar timing and noise analysis with Vela.jl: the wideband paradigm

    astro-ph.IM 2025-05 conditional novelty 6.0 of 10

    Vela.jl implements the first public, non-linear Bayesian wideband pulsar timing and noise analysis pipeline, demonstrated on NANOGrav wideband data for PSR J1923+2515.

Reference graph

Works this paper leans on

60 extracted references · 3 canonical work pages · cited by 2 Pith papers

  1. [1]

    Agazie G., et al., 2023, @doi [The Astrophysical Journal Letters] 10.3847/2041-8213/acda9a , https://ui.adsabs.harvard.edu/abs/2023ApJ...951L...9A 951, L9

    doi:10.3847/2041-8213/acda9a 2023

  2. [2]

    Agazie G., et al., 2024, @doi [The Astrophysical Journal] 10.3847/1538-4357/ad36be , https://ui.adsabs.harvard.edu/abs/2024ApJ...966..105A 966, 105

    doi:10.3847/1538-4357/ad36be 2024

  3. [3]

    F., et al., 2021, @doi [The Astrophysical Journals] 10.3847/1538-4365/abc6a1 , https://ui.adsabs.harvard.edu/abs/2021ApJS..252....5A 252, 5

    Alam M. F., et al., 2021, @doi [The Astrophysical Journals] 10.3847/1538-4365/abc6a1 , https://ui.adsabs.harvard.edu/abs/2021ApJS..252....5A 252, 5

    doi:10.3847/1538-4365/abc6a1 2021

  4. [4]

    Arzoumanian Z., Brazier A., Burke-Spolaor S., Chamberlin S., Chatterjee S., et al., 2015, @doi [The Astrophysical Journal] 10.1088/0004-637X/813/1/65 , 813, 65

    doi:10.1088/0004-637x/813/1/65 2015

  5. [5]

    C., Hellings R

    Backer D. C., Hellings R. W., 1986, @doi [Annual Review of Astronomy and Astrophysics] 10.1146/annurev.aa.24.090186.002541 , https://ui.adsabs.harvard.edu/abs/1986ARA&A..24..537B 24, 537

    arXiv 1986

  6. [6]

    T., et al., 2020, @doi [Nature Astronomy] 10.1038/s41550-019-0880-2 , https://ui.adsabs.harvard.edu/abs/2020NatAs...4...72C 4, 72

    Cromartie H. T., et al., 2020, @doi [Nature Astronomy] 10.1038/s41550-019-0880-2 , https://ui.adsabs.harvard.edu/abs/2020NatAs...4...72C 4, 72

    doi:10.1038/s41550-019-0880-2 2020

  7. [7]

    Cury o M., et al., 2023, @doi [The Astrophysical Journal] 10.3847/1538-4357/aca535 , https://ui.adsabs.harvard.edu/abs/2023ApJ...944..128C 944, 128

    doi:10.3847/1538-4357/aca535 2023

  8. [8]

    Dai S., Johnston S., Kerr M., Berteaud J., Bhattacharyya B., Camilo F., Keane E., 2023, @doi [ ] 10.1093/mnras/stad704 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.521.2616D 521, 2616

    doi:10.1093/mnras/stad704 2023

Show all 60 references
  1. [9]

    Damour T., Deruelle N., 1986, Annales de L'Institut Henri Poincare Section (A) Physique Theorique, https://ui.adsabs.harvard.edu/abs/1986AIHPA..44..263D 44, 263

    1986

  2. [10]

    Y., et al., 2020, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202039517 , https://ui.adsabs.harvard.edu/abs/2020A&A...644A.153D 644, A153

    Donner J. Y., et al., 2020, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202039517 , https://ui.adsabs.harvard.edu/abs/2020A&A...644A.153D 644, A153

    2020 doi

  3. [12]

    A., Vallisneri M., Taylor S

    Ellis J. A., Vallisneri M., Taylor S. R., Baker P. T., 2020, ENTERPRISE: Enhanced Numerical Toolbox Enabling a Robust PulsaR Inference SuitE, Zenodo, @doi 10.5281/zenodo.4059815 , https://doi.org/10.5281/zenodo.4059815

    2020 doi

  4. [13]

    B., Wahlquist H

    Estabrook F. B., Wahlquist H. D., 1975, @doi [General Relativity and Gravitation] 10.1007/BF00762449 , 6, 439

    1975 doi

  5. [14]

    Foreman-Mackey D., 2016, @doi [The Journal of Open Source Software] 10.21105/joss.00024 , 1, 24

    2016 doi

  6. [15]

    W., Lang D., Goodman J., 2013, @doi [Publications of the Astronomical Society of the Pacific] 10.1086/670067 , https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F 125, 306

    Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, @doi [Publications of the Astronomical Society of the Pacific] 10.1086/670067 , https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F 125, 306

    2013 doi

  7. [16]

    S., Backer D

    Foster R. S., Backer D. C., 1990, @doi [The Astrophysical Journal] 10.1086/169195 , https://ui.adsabs.harvard.edu/abs/1990ApJ...361..300F 361, 300

    1990 doi

  8. [17]

    H., Rickett B

    Hankins T. H., Rickett B. J., 1986, @doi [The Astrophysical Journal] 10.1086/164807 , https://ui.adsabs.harvard.edu/abs/1986ApJ...311..684H 311, 684

    1986 doi

  9. [18]

    R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , https://ui.adsabs.harvard.edu/abs/2020Natur.585..357H 585, 357

    Harris C. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , https://ui.adsabs.harvard.edu/abs/2020Natur.585..357H 585, 357

    2020 doi

  10. [19]

    S., et al., 2022, @doi [The Astrophysical Journal] 10.3847/1538-4357/ac5829 , 929, 39

    Hazboun J. S., et al., 2022, @doi [The Astrophysical Journal] 10.3847/1538-4357/ac5829 , 929, 39

    2022 doi

  11. [20]

    W., Downs G

    Hellings R. W., Downs G. S., 1983, @doi [The Astrophysical Journal] 10.1086/183954 , https://ui.adsabs.harvard.edu/abs/1983ApJ...265L..39H 265, L39

    1983 doi

  12. [21]

    A., Stinebring D

    Hemberger D. A., Stinebring D. R., 2008, @doi [The Astrophysical Journal] 10.1086/528985 , https://ui.adsabs.harvard.edu/abs/2008ApJ...674L..37H 674, L37

    2008 doi

  13. [22]

    B., Edwards R

    Hobbs G. B., Edwards R. T., Manchester R. N., 2006, @doi [Monthly Notices of the Royal Astronomical Society] 10.1111/j.1365-2966.2006.10302.x , https://ui.adsabs.harvard.edu/abs/2006MNRAS.369..655H 369, 655

    2006

  14. [23]

    D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    Hunter J. D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    2007 doi

  15. [24]

    Iraci F., et al., 2024, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202450740 , https://ui.adsabs.harvard.edu/abs/2024A&A...692A.170I 692, A170

    2024 doi

  16. [25]

    J., et al., 2024, @doi [ ] 10.3847/1538-4357/ad2930 , https://ui.adsabs.harvard.edu/abs/2024ApJ...964..179J 964, 179

    Jennings R. J., et al., 2024, @doi [ ] 10.3847/1538-4357/ad2930 , https://ui.adsabs.harvard.edu/abs/2024ApJ...964..179J 964, 179

    2024 doi

  17. [26]

    D., Meyers P

    Johnson A. D., Meyers P. M., Baker P. T., Cornish N. J., Hazboun J. S., et al., 2024, @doi [Physical Review D] 10.1103/PhysRevD.109.103012 , https://ui.adsabs.harvard.edu/abs/2024PhRvD.109j3012J 109, 103012

    2024 doi

  18. [27]

    J., et al., 2013, @doi [ ] 10.1093/mnras/sts486 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.429.2161K 429, 2161

    Keith M. J., et al., 2013, @doi [ ] 10.1093/mnras/sts486 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.429.2161K 429, 2161

    2013 doi

  19. [28]

    A., et al., 2021, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202140340 , https://ui.adsabs.harvard.edu/abs/2021A&A...651A...5K 651, A5

    Krishnakumar M. A., et al., 2021, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202140340 , https://ui.adsabs.harvard.edu/abs/2021A&A...651A...5K 651, A5

    2021 doi

  20. [29]

    Larsen B., et al., 2024, @doi [The Astrophysical Journal] 10.3847/1538-4357/ad5291 , https://ui.adsabs.harvard.edu/abs/2024ApJ...972...49L 972, 49

    2024 doi

  21. [30]

    P., Taylor S., Gair J., Balan S

    Lentati L., Alexander P., Hobson M. P., Taylor S., Gair J., Balan S. T., van Haasteren R., 2013, @doi [Physical Review D] 10.1103/PhysRevD.87.104021 , 87, 104021

    2013 doi

  22. [31]

    P., Feroz F., van Haasteren R., Lee K

    Lentati L., Alexander P., Hobson M. P., Feroz F., van Haasteren R., Lee K. J., Shannon R. M., 2014, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stt2122 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.437.3004L 437, 3004

    2014 doi

  23. [32]

    arXiv:1910.13970

    Lewis A., 2019, @doi [arXiv e-prints] 10.48550/arXiv.1910.13970 , https://ui.adsabs.harvard.edu/abs/2019arXiv191013970L p. arXiv:1910.13970

    2019 doi arXiv

  24. [33]

    Liu K., et al., 2014, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stu1420 , https://ui.adsabs.harvard.edu/abs/2014MNRAS.443.3752L 443, 3752

    2014 doi

  25. [34]

    R., Kramer M., 2012, Handbook of Pulsar Astronomy

    Lorimer D. R., Kramer M., 2012, Handbook of Pulsar Astronomy . Cambridge University Press

    2012

  26. [35]

    S., Archibald A., et al., 2021, @doi [The Astrophysical Journal] 10.3847/1538-4357/abe62f , https://ui.adsabs.harvard.edu/abs/2021ApJ...911...45L 911, 45

    Luo J., Ransom S., Demorest P., Ray P. S., Archibald A., et al., 2021, @doi [The Astrophysical Journal] 10.3847/1538-4357/abe62f , https://ui.adsabs.harvard.edu/abs/2021ApJ...911...45L 911, 45

    2021 doi

  27. [36]

    R., Cordes J

    Madison D. R., Cordes J. M., Arzoumanian Z., Chatterjee S., Crowter K., et al., 2019, @doi [The Astrophysical Journal] 10.3847/1538-4357/ab01fd , https://ui.adsabs.harvard.edu/abs/2019ApJ...872..150M 872, 150

    2019 doi

  28. [37]

    Nice D., et al., 2015, Tempo: Pulsar timing data analysis , Astrophysics Source Code Library, record ascl:1509.002

    2015

  29. [38]

    K., et al., 2023, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stad3122 , 527, 213

    Paladi A. K., et al., 2023, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stad3122 , 527, 213

    2023 doi

  30. [39]

    S., Folkner W

    Park R. S., Folkner W. M., Williams J. G., Boggs D. H., 2021, @doi [The Astronomical Journal] 10.3847/1538-3881/abd414 , 161, 105

    2021 doi

  31. [40]

    Parthasarathy A., et al., 2021, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stab037 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502..407P 502, 407

    2021 doi

  32. [41]

    T., 2019, @doi [The Astrophysical Journal] 10.3847/1538-4357/aaf6ef , 871, 34

    Pennucci T. T., 2019, @doi [The Astrophysical Journal] 10.3847/1538-4357/aaf6ef , 871, 34

    2019 doi

  33. [42]

    T., Demorest P

    Pennucci T. T., Demorest P. B., Ransom S. M., 2014, @doi [The Astrophysical Journal] 10.1088/0004-637X/790/2/93 , https://ui.adsabs.harvard.edu/abs/2014ApJ...790...93P 790, 93

    2014 doi

  34. [43]

    M., et al., 2014, @doi [ ] 10.1038/nature12917 , https://ui.adsabs.harvard.edu/abs/2014Natur.505..520R 505, 520

    Ransom S. M., et al., 2014, @doi [ ] 10.1038/nature12917 , https://ui.adsabs.harvard.edu/abs/2014Natur.505..520R 505, 520

    2014 doi

  35. [44]

    P., et al., 2013, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201322068 , https://ui.adsabs.harvard.edu/abs/2013A&A...558A..33A 558, A33

    Robitaille T. P., et al., 2013, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/201322068 , https://ui.adsabs.harvard.edu/abs/2013A&A...558A..33A 558, A33

    2013 doi

  36. [45]

    M., Cordes J

    Shannon R. M., Cordes J. M., 2010, @doi [The Astrophysical Journal] 10.1088/0004-637X/725/2/1607 , https://ui.adsabs.harvard.edu/abs/2010ApJ...725.1607S 725, 1607

    2010 doi

  37. [46]

    C., et al., 2024, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202450680 , https://ui.adsabs.harvard.edu/abs/2024A&A...692A..18S 692, A18

    Susarla S. C., et al., 2024, @doi [Astronomy & Astrophysics] 10.1051/0004-6361/202450680 , https://ui.adsabs.harvard.edu/abs/2024A&A...692A..18S 692, A18

    2024 doi

  38. [47]

    arXiv:2505.10141

    Susobhanan A., 2025a, @doi [arXiv e-prints] 10.48550/arXiv.2505.10141 , https://ui.adsabs.harvard.edu/abs/2025arXiv250510141S p. arXiv:2505.10141

    doi arXiv

  39. [48]

    Susobhanan A., 2025b, @doi [The Astrophysical Journal] 10.3847/1538-4357/adaaec , https://ui.adsabs.harvard.edu/abs/2025ApJ...980..165S 980, 165

    doi

  40. [49]

    Susobhanan A., et al., 2024, @doi [The Astrophysical Journal] 10.3847/1538-4357/ad59f7 , 971, 150

    2024 doi

  41. [50]

    M., et al., 2024, @doi [The Astrophysical Journal] 10.3847/1538-4357/ad28b2 , 966, 26

    Tan C. M., et al., 2024, @doi [The Astrophysical Journal] 10.3847/1538-4357/ad28b2 , 966, 26

    2024 doi

  42. [51]

    A., et al., 2022, @doi [Publications of the Astronomical Society of Australia] 10.1017/pasa.2022.46 , 39, e053

    Tarafdar P., Nobleson K., Rana P., Singha J., Krishnakumar M. A., et al., 2022, @doi [Publications of the Astronomical Society of Australia] 10.1017/pasa.2022.46 , 39, e053

    2022 doi

  43. [52]

    H., 1992, @doi [Philosophical Transactions of the Royal Society of London

    Taylor J. H., 1992, @doi [Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences] 10.1098/rsta.1992.0088 , 341, 117

    1992

  44. [53]

    Virtanen P., et al., 2020, @doi [Nature Methods] 10.1038/s41592-019-0686-2 , https://rdcu.be/b08Wh 17, 261

    2020 doi

  45. [54]

    P., Hobbs G

    You X. P., Hobbs G. B., Coles W. A., Manchester R. N., Han J. L., 2007, @doi [The Astrophysical Journal] 10.1086/522227 , 671, 907

    2007 doi

  46. [55]

    P., Coles W

    You X. P., Coles W. A., Hobbs G. B., Manchester R. N., 2012, @doi [Monthly Notices of the Royal Astronomical Society] 10.1111/j.1365-2966.2012.20688.x , 422, 1160

    2012

  47. [56]

    van Haasteren R., Levin Y., 2013, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/sts097 , https://ui.adsabs.harvard.edu/abs/2013MNRAS.428.1147V 428, 1147

    2013 doi

  48. [57]

    van Haasteren R., Vallisneri M., 2014a, @doi [Physical Review D] 10.1103/PhysRevD.90.104012 , https://ui.adsabs.harvard.edu/abs/2014PhRvD..90j4012V 90, 104012

    doi

  49. [58]

    van Haasteren R., Vallisneri M., 2014b, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stu2157 , 446, 1170

    doi

  50. [59]

    van Haasteren R., Levin Y., McDonald P., Lu T., 2009, @doi [Monthly Notices of the Royal Astronomical Society] 10.1111/j.1365-2966.2009.14590.x , https://ui.adsabs.harvard.edu/abs/2009MNRAS.395.1005V 395, 1005

    2009

  51. [60]

    van Haasteren R., et al., 2011, @doi [Monthly Notices of the Royal Astronomical Society] 10.1111/j.1365-2966.2011.18613.x , 414, 3117

    2011

  52. [61]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.