University of Oulu

Koldobskiy, S.A., Kähkönen, R., Hofer, B. et al. Time Lag Between Cosmic-Ray and Solar Variability: Sunspot Numbers and Open Solar Magnetic Flux. Sol Phys 297, 38 (2022).

Time lag between cosmic-ray and solar variability : sunspot numbers and open solar magnetic flux

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Author: Koldobskiy, Sergey A.1,2; Kähkönen, Riikka1; Hofer, Bernhard3;
Organizations: 1University of Oulu, Oulu, Finland
2National Research Nuclear University MEPhI, Moscow, Russia
3Max Planck Institute for Solar System Research, Göttingen, Germany
4Ioffe Physical-Technical Institute, St. Petersburg, Russia
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 3.3 MB)
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Language: English
Published: Springer Nature, 2022
Publish Date: 2022-04-26


Solar magnetic activity drives the dominant 11-year cyclic variability of different space environmental indices, but they can be delayed with respect to the original variations due to the different physical processes involved. Here, we analyzed the pairwise time lags between three global solar and heliospheric indices: sunspot numbers (SSN), representing the solar surface magnetic activity, the open solar flux (OSF), representing the heliospheric magnetic variability, and the galactic cosmic-ray (GCR) intensity near Earth, using the standard cross-correlation and the more detailed wavelet-coherence methods. All the three indices appear highly coherent at a timescale longer than a few years with persistent high coherence at the timescale of the 11-year solar cycle. The GCR variability is delayed with respect to the inverted SSN by about eight 27-day Bartels rotations on average, but the delay varies greatly with the 22-year cycle, being shorter or longer around positive A+ or negative A− solar polarity epochs, respectively. The 22-year cyclicity of the time lag is determined by the global heliospheric drift effects, in agreement with theoretical models. The OSF lags by about one year behind SSN, and is likely determined by a combination of the short lifetime of active regions and a longer (≈3 years) transport time of the surface magnetic field to the poles. GCRs covary nearly in antiphase with the OSF, also depicting a strong 22-year cycle in the delay, confirming that the OSF is a good index of the heliospheric modulation of GCRs. This provides an important observational constraint for solar and heliospheric physics.

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Series: Solar physics
ISSN: 0038-0938
ISSN-E: 1573-093X
ISSN-L: 0038-0938
Volume: 297
Article number: 38
DOI: 10.1007/s11207-022-01970-1
Type of Publication: A1 Journal article – refereed
Field of Science: 115 Astronomy and space science
Funding: This work was partly supported by the Academy of Finland (projects ESPERA No. 321882 and QUASARE No. 330064), University of Oulu (Project SARPEDON), and the Russian Science Foundation (RSF Project No. 20-72-10170). Open Access funding provided by University of Oulu including Oulu University Hospital.
Academy of Finland Grant Number: 321882
Detailed Information: 321882 (Academy of Finland Funding decision)
330064 (Academy of Finland Funding decision)
Copyright information: © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit