Time Lag Between Cosmic-Ray and Solar Variability: Sunspot Numbers and Open Solar Magnetic Flux

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+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A+$\end{document} or negative A−\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$A-$\end{document} 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.