University of Oulu

Krivova, N. A.; Solanki, S. K.; Hofer, B.; Wu, C.-J.; Usoskin, I. G.; Cameron, R. (2021) Modelling the evolution of the Sun’s open and total magnetic flux. A&A, 50, A70 (2021),

Modelling the evolution of the Sun’s open and total magnetic flux

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Author: Krivova, N. A.1; Solanki, S. K.1,2; Hofer, B.1,3;
Organizations: 1Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, Göttingen, Germany
2School of Space Research, Kyung Hee University, Yongin, Gyeonggi-Do 446-701, Republic of Korea
3Institut für Astrophysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
4University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 1.2 MB)
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Language: English
Published: EDP Sciences, 2021
Publish Date: 2021-07-01


Solar activity in all its varied manifestations is driven by the magnetic field. Two global quantities are particularly important for many purposes, the Sun’s total and open magnetic flux, which can be computed from sunspot number records using models. Such sunspot-driven models, however, do not take into account the presence of magnetic flux during grand minima, such as the Maunder minimum. Here we present a major update of a widely used simple model, which now takes into account the observation that the distribution of all magnetic features on the Sun follows a single power law. The exponent of the power law changes over the solar cycle. This allows for the emergence of small-scale magnetic flux even when no sunspots have been present for multiple decades and leads to non-zero total and open magnetic flux also in the deepest grand minima, such as the Maunder minimum, thus overcoming a major shortcoming of the earlier models. The results of the updated model compare well with the available observations and reconstructions of the solar total and open magnetic flux. This opens up the possibility of improved reconstructions of the sunspot number from time series of the cosmogenic isotope production rate.

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Series: Astronomy and astrophysics
ISSN: 0004-6361
ISSN-E: 1432-0746
ISSN-L: 0004-6361
Volume: 650
Article number: A70
DOI: 10.1051/0004-6361/202140504
Type of Publication: A1 Journal article – refereed
Field of Science: 115 Astronomy and space science
Funding: N.A.K. and S.K.S. acknowledge support by the German Federal Ministry of Education and Research (Project No. 01LG1909C). S.K.S. received support from the Ministry of Education of Korea through the BK21 plus program of the National Research Foundation. B.H. was supported by the International Max-Planck Research School (IMPRS) for Solar System Science at the University of Göttingen. IU acknowledges a partial support from the Academy of Finland (Projects ESPERA no. 321882).
Academy of Finland Grant Number: 321882
Detailed Information: 321882 (Academy of Finland Funding decision)
Copyright information: © N. A. Krivova et al. 2021. Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Open Access funding provided by Max Planck Society.