Studying the transport process of galactic cosmic rays (GCRs) in the heliosphere is crucial for understanding the space radiation environment in the inner heliosphere and large-scale heliospheric structures. Various numerical and theoretical studies, along with observational experiments, have demonstrated that GCR fluxes are modulated by the interplanetary magnetic field (IMF), which changes with solar activity cycle. However, there are still open questions on how different modulation processes, and their dependence on the IMF, impact the GCR propagation in the heliosphere. In particular, there are still uncertainties on how GCR time variations lag behind solar activity changes, referred to as GCR delay time in this study.
In this study, we parameterize the GCR delay time with respect to several solar activity indices and determine how this delay changes with GCR particle rigidity, aiming to establish a semi-quantitative relationship between the delay time and particle rigidity and to better understand the GCR transport processes in the heliosphere.
Employing multiple long-term high-energy particle observations, including particle detectors on board the Solar and Heliospheric Observatory (SOHO), the Interplanetary Monitoring Platform-8 (IMP-8), and the Alpha Magnetic Spectrometer (AMS-02), we innovatively apply information theory to analyze the GCR modulation processes and determine the delay time, using Monte Carlo methods to evaluate its uncertainty.
Consistent with previous findings, we confirm that qA<0 has a longer delay time than qA>0, where q is the GCR particle charge and A=±1 if the solar magnetic field is predominantly outward (inward) at the solar North pole. Using long-term GCR data collected since 1970, we examine the distribution of delay times for GCR protons and electrons in relation to the solar open magnetic flux, within a rigidity range from 0.3 GV to 10 GV. Utilizing a simple force field approximation and a particle diffusion approximation, we present an estimation formula for the delay time of GCR modulation.
We have examined the issue of the GCR modulation delay from the perspective of information theory, establishing a more natural connection between measurement uncertainty and delay time uncertainty through Monte Carlo methods. We present a novel method for calibrating the diffusion coefficient of GCRs in the heliosphere that does not depend on numerical models. Collectively, these findings will enhance our understanding of the transport processes of GCRs.
