Modelling charge-sign dependent modulation of cosmic rays in the heliosphere

Abstract

The solar minimum of cycle 23/24 has seen exceptionally quiet levels of solar activity and heliospheric modulation, which resulted in the highest cosmic ray (CR) spectrum ever recorded at Earth in December 2009 by the PAMELA detector. This solar minimum has been extensively observed by PAMELA in terms of CR intensities and presents a unique opportunity to study the heliosphere in light of CR modulation. A three-dimensional numerical model was used to simulate the transport and modulation of CRs, with the aim of reproducing a selection of PAMELA proton, electron and positron energy spectra, taken during the 2006 to 2009 minimum period. In doing so, various improvements were made to the model, such as using a new Smith-Bieber modification for the heliospheric magnetic field and utilizing the parallel computing capability of the graphics processing unit (GPU). New local interstellar proton, electron and positron spectra were also constructed using PAMELA, AMS-02 and Voyager 1 measurements as constraints over certain energy ranges, in addition to GALPROP solutions. A key objective of this study was to uncover and investigate the effects that drifts had on CRs, which present itself as charge-sign dependent modulation. Since the PAMELA and Ulysses missions overlapped between mid-2006 and mid-2009, simultaneous measurements from these were used to calculate the global radial and latitudinal gradients for protons in the inner heliosphere. Negative latitudinal gradients were found (-0.05±0.01 %/° at 1.63 GV), which is a consequence of charge-sign dependent modulation and indicative of the drift patterns experienced by positively charged CRs during an A < 0 solar polarity cycle. A comparative study revealed that the intensities of positively charged CRs increased significantly more from 2006 to 2009 than the negatively charged CR component - a result that can only be explained with drift theory. All of these characteristic signatures of charge-sign dependent modulation were reproduced through modelling, which subsequently facilitated a comprehensive study of drifts at energies beyond the observable ranges of PAMELA and AMS-02. In essence, this work provides substantial proof that all modulation processes played a role during the minimum period of cycle 23/24 and contributed to the observed energy spectra, including drifts.