The Hysteresis Effects in Cosmic Ray-Solar Activity Relationships: Evidence for Non-Linear Coupling BetweenHeliospheric Modulation and Galactic Cosmic Ray Transport During Solar Magnetic Field Reversals

Abstract

We present comprehensive evidence for non-linear hysteresis effects in the relationship between solar activity and galactic cosmic ray (GCR) flux observed at Earth during the period 1980-2024, encompassing four complete solar magnetic field reversals. Analysis of neutron monitor data reveals systematic temporal delays and path-dependent responses in GCR modulation that cannot be explained by linear diffusion-convection models alone. During solar magnetic field reversals, we observe characteristic hysteresis loops in phase space plots of sunspot number versus cosmic ray intensity, with loop areas ranging from 1200 to 1800 arbitrary units across different solar cycles.

The hysteresis width, quantified as the temporal lag between solar activity changes and corresponding GCR flux variations, shows a systematic increase from 8 months in Solar Cycle 21 to 16 months in Solar Cycle 24, suggesting enhanced complexity in heliospheric magnetic structures. Wavelet coherence analysis demonstrates phase shifts between solar wind parameters and GCR flux that vary non-monotonically with heliospheric current sheet tilt angle, reaching maximum decorrelation at tilt angles of 60-70 degrees. These findings indicate that GCR transport through the heliosphere involves memory effects and multiple timescale dependencies that emerge from the interaction between particle drift patterns, turbulent diffusion, and the evolving topology of the heliospheric magnetic field.