Exploring the time variability of the solar wind using LOFAR pulsar data

¹ Physics, School of Natural Sciences, Ollscoil na Gaillimhe – University of Galway, University Road, Galway H91 TK33, Ireland
² Dipartimento di Fisica “G. Occhialini”, Universitá degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
³ INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
⁴ INAF – Osservatorio Astronomico di Cagliari, via della Scienza 5, 09047 Selargius, (CA), Italy
⁵ School of Physics, Trinity College Dublin, College Green, Dublin 2 D02 PN40, Ireland
⁶ Florida Space Institute, University of Central Florida, 12354 Research Parkway, Partnership 1 Building, Suite 214, Orlando, 32826-0650 FL, USA
⁷ Oregon State University, 1500 SW Jefferson Ave, Corvallis, OR 97331, USA
⁸ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁹ Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
¹⁰ National Centre for Radio Astrophysics, Pune University Campus Pune 411007, India
¹¹ Dipartimento di Fisica, Università di Cagliari, Cittadella Universitaria, I-09042 Monserrato, (CA), Italy
¹² LPC2E – Université d’Orléans/CNRS, 45071 Orléans Cedex 2, France
¹³ Observatoire Radioastronomique de Nançay (ORN), Observatoire de Paris, Université PSL, Univ Orléans, CNRS, 18330 Nançay, France
¹⁴ Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
¹⁵ Australia Telescope National Facility, CSIRO, Space and Astronomy, PO Box 76 Epping, NSW 1710, Australia
¹⁶ SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield SK11 9FT, United Kingdom
¹⁷ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
¹⁸ Leibniz Institute for Agricultural Engineering and Bioeconomy (ATB), Max-Eyth-Allee 100, 14469 Potsdam, Germany
¹⁹ University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
²⁰ Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany
²¹ Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), 44780 Bochum, Germany
²² Thüringer Landessternwarte Tautenburg, Sternwarte, 507778 Tautenburg, Germany
²³ Leibniz Institute of Astrophysics, An d. Sternwarte 16, 14482 Potsdam, Germany

^⋆ Corresponding author; saichaitus.99@gmail.com

Received: 10 May 2024
Accepted: 14 September 2024

Abstract

Context. High-precision pulsar timing is highly dependent on the precise and accurate modelling of any effects that can potentially impact the data. In particular, effects that contain stochastic elements contribute to some level of corruption and complexity in the analysis of pulsar-timing data. It has been shown that commonly used solar wind models do not accurately account for variability in the amplitude of the solar wind on both short and long timescales.

Aims. In this study, we test and validate a new, cutting-edge solar wind modelling method included in the enterprise software suite (widely used for pulsar noise analysis) through extended simulations. We use it to investigate temporal variability in LOFAR data. Our model testing scheme in itself provides an invaluable asset for pulsar timing array (PTA) experiments. Since, improperly accounting for the solar wind signature in pulsar data can induce false-positive signals, it is of fundamental importance to include in any such investigations.

Methods. We employed a Bayesian approach utilising a continuously varying Gaussian process to model the solar wind. It uses a spherical approximation that modulates the electron density. This method, which we refer to as a solar wind Gaussian process (SWGP), has been integrated into existing noise analysis software, specifically enterprise. Our Validation of this model was performed through simulations. We then conduct noise analysis on eight pulsars from the LOFAR dataset, with most pulsars having a time span of ∼11 years encompassing one full solar activity cycle. Furthermore, we derived the electron densities from the dispersion measure values obtained by the SWGP model.

Results. Our analysis reveals a strong correlation between the electron density at 1 AU and the ecliptic latitude (ELAT) of the pulsar. Pulsars with |ELAT|< 3° exhibit significantly higher average electron densities. Furthermore, we observed distinct temporal patterns in the electron densities in different pulsars. In particular, pulsars within |ELAT|< 3° exhibit similar temporal variations, while the electron densities of those outside this range correlate with the solar activity cycle. Notably, some pulsars exhibit sensitivity to the solar wind up to 45° away from the Sun in LOFAR data.

Conclusions. The continuous variability in electron density offered in this model represents a substantial improvement over previous models, that assume a single value for piece-wise bins of time. This advancement holds promise for solar wind modelling in future International Pulsar Timing Array (IPTA) data combinations.