On the "Hysteresis Effects" observed by AMS02 in Cosmic Ray Solar Modulations

The AMS02 collaboration has recently published high precision daily measurements of the spectra of cosmic ray protons, helium nuclei and electrons taken during a time interval of approximately 10 years from 2011 to 2020. Positron spectra averaged over distinct 27 days intervals have also been made public. The AMS02 collaboration has shown some intriguing "hysteresis" effects observed comparing the fluxes of protons and helium nuclei or protons and electrons. In this work we address the question of the origin of these effects. We find that the spectral distortions generated by propagation in the heliosphere are significantly different for particles with electric charge of opposite sign (an effect already well established), with different behaviour before and after the solar magnetic field polarity reversal at solar maximum. This results in hysteresis effects for the p/e comparison that follow the 22-year solar cycle. On the other hand particles with electric charge of the same sign suffer modulations that are approximately equal. The hysteresis effects observed for a helium/proton comparison can then be understood as the consequence of the fact that the two particles have interstellar spectra of different shape, and the approximately equal spectral distortions generated by propagation in the heliosphere have a rigidity dependence that is a function of time. These hysteresis effects can in fact be observed studying the time dependence of the shape of the spectra of a single particle type, and also generate short time loop-like structures in the hysteresis curves correlated with large solar activity events such as CME's. A description of solar modulations that includes these effects must go beyond the simple Force Field Approximation (FFA) model. A minimal, two-parameter generalization of the FFA model that gives a good description of the observations is presented.