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Bayesian pulsar timing and noise analysis with vela.jl: The wideband paradigm

Phys. Rev. D 112, 063023 – Published 12 September, 2025

DOI: https://doi.org/10.1103/n3ck-lfdy

Abstract

vela.jl is a package for performing Bayesian pulsar timing and noise analysis written in julia and python. In the wideband paradigm of pulsar timing, simultaneous time of arrival and dispersion measure measurements are derived from a radio observation using frequency-resolved integrated pulse profiles and templates without splitting the observation into multiple frequency sub-bands. We describe the implementation of the wideband timing paradigm in vela.jl, and demonstrate its usage using the NANOGrav 12.5-year wideband data of PSR J1923+2515. vela.jl is the first software package to provide this functionality.

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References (61)

  1. D. R. Lorimer and M. Kramer, Handbook of Pulsar Astronomy (Cambridge University Press, Cambridge, United Kingdom, 2012).
  2. S. C. Susarla, A. Chalumeau, C. Tiburzi, E. F. Keane, J. P. W. Verbiest et al., Exploring the time variability of the solar wind using LOFAR pulsar data, Astron. Astrophys. 692, A18 (2024).
  3. G. Agazie, J. Antoniadis, A. Anumarlapudi, A. M. Archibald, P. Arumugam et al., Comparing recent pulsar timing array results on the nanohertz stochastic gravitational-wave background, Astrophys. J. 966, 105 (2024).
  4. G. B. Hobbs, R. T. Edwards, and R. N. Manchester, tempo2, A new pulsar-timing package—I. An overview, Mon. Not. R. Astron. Soc. 369, 655 (2006).
  5. R. T. Edwards, G. B. Hobbs, and R. N. Manchester, tempo2, A new pulsar timing package—II. The timing model and precision estimates, Mon. Not. R. Astron. Soc. 372, 1549 (2006).
  6. A. W. Hotan, W. van Straten, and R. N. Manchester, PSRCHIVE and PSRFITS: An open approach to radio pulsar data storage and analysis, Publ. Astron. Soc. Aust. 21, 302 (2004).
  7. J. H. Taylor, Pulsar timing and relativistic gravity, Phil. Trans. R. Soc. A 341, 117 (1992).
  8. P. Tarafdar, K. Nobleson, P. Rana, J. Singha, M. A. Krishnakumar et al., The Indian Pulsar Timing Array: First data release, Publ. Astron. Soc. Aust. 39, e053 (2022).
  9. P. B. Demorest, R. D. Ferdman, M. E. Gonzalez, D. Nice, S. Ransom et al., Limits on the stochastic gravitational wave background from the North American Nanohertz Observatory for gravitational waves, Astrophys. J. 762, 94 (2012).
  10. J. Wang, G. M. Shaifullah, J. P. W. Verbiest, C. Tiburzi, D. J. Champion et al., A comparative analysis of pulse time-of-arrival creation methods, Astron. Astrophys. 658, A181 (2022).
  11. G. Hobbs, R. N. Manchester, A. Dunning, A. Jameson, P. Roberts et al., An ultra-wide bandwidth (704 to 4 032 MHz) receiver for the Parkes radio telescope, Publ. Astron. Soc. Aust. 37, e012 (2020).
  12. H.-F. Liu, P. Jiang, C. He, F. Yang, H.-J. Liu et al., An ultra-wide bandwidth low-frequency radio astronomical cryogenic receiver for FAST telescope, Res. Astron. Astrophys. 22, 115016 (2022).
  13. R. S. Foster and D. C. Backer, Constructing a pulsar timing array, Astrophys. J. 361, 300 (1990).
  14. B. B. P. Perera, M. E. DeCesar, P. B. Demorest, M. Kerr, L. Lentati et al., The International Pulsar Timing Array: Second data release, Mon. Not. R. Astron. Soc. 490, 4666 (2019).
  15. T. H. Hankins and B. J. Rickett, Frequency dependence of pulsar profiles, Astrophys. J. 311, 684 (1986).
  16. D. A. Hemberger and D. R. Stinebring, Time variability of interstellar scattering and improvements to pulsar timing, Astrophys. J. 674, L37 (2008).
  17. G. Agazie, M. F. Alam, A. Anumarlapudi, A. M. Archibald, Z. Arzoumanian et al., The NANOGrav 15 yr data set: Observations and timing of 68 millisecond pulsars, Astrophys. J. 951, L9 (2023).
  18. T. T. Pennucci, P. B. Demorest, and S. M. Ransom, Elementary wideband timing of radio pulsars, Astrophys. J. 790, 93 (2014).
  19. K. Liu, G. Desvignes, I. Cognard, B. W. Stappers, J. P. W. Verbiest, K. J. Lee, D. J. Champion, M. Kramer, P. C. C. Freire, and R. Karuppusamy, Measuring pulse times of arrival from broad-band pulsar observations, Mon. Not. R. Astron. Soc. 443, 3752 (2014).
  20. T. T. Pennucci, Frequency-dependent template profiles for high-precision pulsar timing, Astrophys. J. 871, 34 (2019).
  21. A. K. Paladi, C. Dwivedi, P. Rana, K. Nobleson, A. Susobhanan et al., Multiband extension of the wideband timing technique, Mon. Not. R. Astron. Soc. 527, 213 (2023).
  22. M. A. Krishnakumar, D. Mitra, A. Naidu, B. C. Joshi, and P. K. Manoharan, Scatter broadening measurements of 124 pulsars at 327 MHz, Astrophys. J. 804, 23 (2015).
  23. J. E. Turner, D. R. Stinebring, M. A. McLaughlin, A. M. Archibald, T. Dolch, and R. S. Lynch, Scattering delay mitigation in high-accuracy pulsar timing: Cyclic spectroscopy techniques, Astrophys. J. 944, 191 (2023).
  24. O. Young and M. T. Lam, Redeveloping a clean deconvolution algorithm for scatter-broadened radio pulsar signals, Astrophys. J. 962, 131 (2024).
  25. D. Nice, P. Demorest, I. Stairs, R. Manchester, J. Taylor, W. Peters, J. Weisberg, A. Irwin, N. Wex, and Y. Huang, tempo: Pulsar timing data analysis, Astrophysics Source Code Library, record ascl:1509.002 (2015), https://ui.adsabs.harvard.edu/abs/2015ascl.soft09002N.
  26. J. Luo, S. Ransom, P. Demorest, P. S. Ray, A. Archibald et al., pint: A modern software package for pulsar timing, Astrophys. J. 911, 45 (2021).
  27. A. Susobhanan, D. L. Kaplan, A. M. Archibald, J. Luo, P. S. Ray et al., pint: Maximum-likelihood estimation of pulsar timing noise parameters, Astrophys. J. 971, 150 (2024).
  28. J. A. Ellis, M. Vallisneri, S. R. Taylor, and P. T. Baker, enterprise: Enhanced numerical toolbox enabling a robust pulsar inference suite, Zenodo (2020).
  29. A. D. Johnson, P. M. Meyers, P. T. Baker, N. J. Cornish, J. S. Hazboun et al., NANOGrav 15-year gravitational-wave background methods, Phys. Rev. D 109, 103012 (2024).
  30. L. Lentati, P. Alexander, M. P. Hobson, F. Feroz, R. van Haasteren, K. J. Lee, and R. M. Shannon, temponest: A Bayesian approach to pulsar timing analysis, Mon. Not. R. Astron. Soc. 437, 3004 (2014).
  31. M. F. Alam, Z. Arzoumanian, P. T. Baker, H. Blumer, K. E. Bohler et al., The NANOGrav 12.5 yr data set: Wideband timing of 47 millisecond pulsars, Astrophys. J. 252, 5 (2021).
  32. M. Curyło, T. T. Pennucci, M. Bailes, N. D. R. Bhat, A. D. Cameron et al., Wide-band timing of the parkes pulsar timing array UWL data, Astrophys. J. 944, 128 (2023).
  33. Z. Arzoumanian, A. Brazier, S. Burke-Spolaor, S. Chamberlin, S. Chatterjee et al., The NANOGrav nine-year data set: Observations, arrival time measurements, and analysis of 37 millisecond pulsars, Astrophys. J. 813, 65 (2015).
  34. A. Susobhanan and R. van Haasteren, Gaussian process representation of dispersion measure noise in pulsar wideband datasets, Mon. Not. R. Astron. Soc., staf1422 (2025).
  35. A. Susobhanan, Bayesian pulsar timing and noise analysis with vela.jl: An overview, Astrophys. J. 980, 165 (2025).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/n3ck-lfdy for a glossary of mathematical symbols used in this paper.
  37. T. Damour and N. Deruelle, General relativistic celestial mechanics of binary systems. II. The post-Newtonian timing formula, Ann. l’Inst. Henri Poincare Sect. A Phys. Theor. 44, 263 (1986).https://www.numdam.org/item/AIHPA_1986__44_3_263_0/
  38. D. C. Backer and R. W. Hellings, Pulsar timing and general relativity, Annu. Rev. Astron. Astrophys. 24, 537 (1986).
  39. F. B. Estabrook and H. D. Wahlquist, Response of Doppler spacecraft tracking to gravitational radiation, Gen. Relativ. Gravit. 6, 439 (1975).
  40. A. Parthasarathy, M. Bailes, R. M. Shannon, W. van Straten, S. Osłowski et al., Measurements of pulse jitter and single-pulse variability in millisecond pulsars using MeerKAT, Mon. Not. R. Astron. Soc. 502, 407 (2021).
  41. A. D. Kulkarni, R. M. Shannon, D. J. Reardon, M. T. Miles, M. Bailes, and M. Shamohammadi, An insight into chromatic behaviour of jitter in pulsars and its modelling: A case study of PSR J0437-4715, Mon. Not. R. Astron. Soc. 528, 3658 (2024).
  42. R. van Haasteren and M. Vallisneri, Low-rank approximations for large stationary covariance matrices, as used in the Bayesian and generalized-least-squares analysis of pulsar-timing data, Mon. Not. R. Astron. Soc. 446, 1170 (2014).
  43. R. van Haasteren and Y. Levin, Understanding and analysing time-correlated stochastic signals in pulsar timing, Mon. Not. R. Astron. Soc. 428, 1147 (2013).
  44. D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC hammer, Publ. Astron. Soc. Pac. 125, 306 (2013).
  45. R. S. Park, W. M. Folkner, J. G. Williams, and D. H. Boggs, The JPL planetary and lunar ephemerides DE440 and DE441, Astron. J. 161, 105 (2021).
  46. J. M. Yao, R. N. Manchester, and N. Wang, A new electron-density model for estimation of pulsar and FRB distances, Astrophys. J. 835, 29 (2017).
  47. P. Diaconis, The Markov Chain Monte Carlo revolution, Bull. Am. Math. Soc. 46, 179 (2009).https://www.ams.org/journals/bull/2009-46-02/S0273-0979-08-01238-X/
  48. G. Ashton et al., Nested sampling for physical scientists, Nat. Rev. Methods Primers 2, 39 (2022).
  49. H. J. Pletsch and C. J. Clark, Gamma-ray timing of redback PSR J2339-0533: Hints for gravitational quadrupole moment changes, Astrophys. J. 807, 18 (2015).
  50. N. Laal, W. G. Lamb, J. D. Romano, X. Siemens, S. R. Taylor, and R. van Haasteren, Exploring the capabilities of Gibbs sampling in pulsar timing arrays, Phys. Rev. D 108, 063008 (2023).
  51. S. Valtolina and R. van Haasteren, Regularizing the pulsar timing array likelihood: A path towards Fourier space, Phys. Rev. D 112, 043046 (2025).
  52. D. C. Price, C. Flynn, and A. Deller, A comparison of Galactic electron density models using pygedm, Publ. Astron. Soc. Aust. 38, e038 (2021).
  53. C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen et al., Array programming with numpy, Nature (London) 585, 357 (2020).
  54. T. P. Robitaille, E. J. Tollerud, P. Greenfield, M. Droettboom, E. Bray et al., astropy: A community python package for astronomy, Astron. Astrophys. 558, A33 (2013).
  55. J. D. Hunter, matplotlib: A 2d graphics environment, Comput. Sci. Eng. 9, 90 (2007).
  56. D. Foreman-Mackey, corner.py: Scatterplot matrices in python, J. Open Source Software 1, 24 (2016).
  57. J. Sarnoff et al., DoubleFloats, version 1.2.2, MIT, (2022), https://github.com/JuliaMath/DoubleFloats.jl.
  58. M. Besançon, T. Papamarkou, D. Anthoff, A. Arslan, S. Byrne, D. Lin, and J. Pearson, distributions.jl: Definition and modeling of probability distributions in the juliastats ecosystem, J. Stat. Software 98, 1 (2021).
  59. C. Rowley, pythoncall.jl: python and julia in harmony (2022), https://github.com/JuliaPy/PythonCall.jl.
  60. R. Finnegan, L. White et al., invenia/jlso.jl, Zenodo, 2022, https://doi.org/10.5281/zenodo.3992374.
  61. T. T. Pennucci et al., The NANOGrav 12.5-year wideband data set (version 12yv4), 10.5281/zenodo.4312887 (2020).

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