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A Gaussian-processes approach to fitting for time-variable spherical solar wind in pulsar timing data

Niţu, Iuliana C; Keith, Michael J; Tiburzi, Caterina; Brüggen, Marcus; Champion, David J; Chen, Siyuan; Cognard, Ismaël; Desvignes, Gregory; Dettmar, Ralf-Jürgen; Grießmeier, Jean-Mathias; Guillemot, Lucas; Guo, Yanjun; Hoeft, Matthias; Hu, Huanchen; Jang, Jiwoong; Janssen, Gemma H; Jawor, Jedrzej; Karuppusamy, Ramesh; Keane, Evan F; Kramer, Michael; Künsemöller, Jörn; Lackeos, Kristen; Liu, Kuo; Main, Robert A; McKee, James W; Porayko, Nataliya K; Shaifullah, Golam M; Theureau, Gilles; Vocks, Christian


Iuliana C Niţu

Michael J Keith

Caterina Tiburzi

Marcus Brüggen

David J Champion

Siyuan Chen

Ismaël Cognard

Gregory Desvignes

Ralf-Jürgen Dettmar

Jean-Mathias Grießmeier

Lucas Guillemot

Yanjun Guo

Matthias Hoeft

Huanchen Hu

Jiwoong Jang

Gemma H Janssen

Jedrzej Jawor

Ramesh Karuppusamy

Evan F Keane

Michael Kramer

Jörn Künsemöller

Kristen Lackeos

Kuo Liu

Robert A Main

Nataliya K Porayko

Golam M Shaifullah

Gilles Theureau

Christian Vocks


Propagation effects are one of the main sources of noise in high-precision pulsar timing. For pulsars below an ecliptic latitude of 5°, the ionized plasma in the solar wind can introduce dispersive delays of order 100 µs around solar conjunction at an observing frequency of 300 MHz. A common approach to mitigate this assumes a spherical solar wind with a time-constant amplitude. However, this has been shown to be insufficient to describe the solar wind. We present a linear, Gaussian-process piecewise Bayesian approach to fit a spherical solar wind of time-variable amplitude, which has been implemented in the pulsar software RUN_ENTERPRISE. Through simulations, we find that the current EPTA+InPTA data combination is not sensitive to such variations; however, solar wind variations will become important in the near future with the addition of new InPTA data and data collected with the low-frequency LOFAR telescope. We also compare our results for different high-precision timing data sets (EPTA+InPTA, PPTA, and LOFAR) of 3 ms pulsars (J0030+0451, J1022+1001, J2145−0450), and find that the solar-wind amplitudes are generally consistent for any individual pulsar, but they can vary from pulsar to pulsar. Finally, we compare our results with those of an independent method on the same LOFAR data of the three millisecond pulsars. We find that differences between the results of the two methods can be mainly attributed to the modelling of dispersion variations in the interstellar medium, rather than the solar wind modelling.


Niţu, I. C., Keith, M. J., Tiburzi, C., Brüggen, M., Champion, D. J., Chen, S., …Vocks, C. (2024). A Gaussian-processes approach to fitting for time-variable spherical solar wind in pulsar timing data. Monthly notices of the Royal Astronomical Society, 528(2), 3304-3319.

Journal Article Type Article
Acceptance Date Jan 17, 2024
Online Publication Date Jan 19, 2024
Publication Date Feb 1, 2024
Deposit Date Feb 9, 2024
Publicly Available Date Feb 13, 2024
Journal Monthly Notices of the Royal Astronomical Society
Print ISSN 0035-8711
Electronic ISSN 1365-2966
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 528
Issue 2
Pages 3304-3319
Keywords Methods: data analysis; Solar wind, pulsars: general; Pulsars: individual: PSR J0030+0451, PSR J1022+1001, PSR J2145–0450
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Copyright Statement
© 2024 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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