New insight from modelling galactic deuterons over changing solar activity

The interest in the origin and modulation of cosmic ray deuterons is expected to increase significantly now that observations from AMS-02 and PAMELA detectors have become available. These observations provide a useful tool with which a comprehensive description of the differences in the modulation of deuterons (D) and protons (p) can be made. Observations made by AMS-02 reveal the spectral shape and features of galactic D over the rigidity range 1.92–21.1 GV, whereas those from PAMELA are at a lower rigidity, from 0.75–2.5 GV. These observations provide interesting surprises leading to subsequent challenges to the established paradigm of the secondary origin of galactic D. In this study a comprehensive 3D numerical model and a set of diffusion and drift coefficients, previously applied to a number of cosmic ray nuclei, together with a newly estimated local interstellar spectrum (LIS) for D based on AMS-02 observations, are used to simulate the modulation of D from 2006 to 2014. These modelling results are compared to published D spectra and the corresponding D/p ratios made by PAMELA over the same period, thereby focussing on modulation during a so-called A < 0 solar magnetic field polarity cycle. A particular objective is to uncover how the D/p ratio evolves at different rigidities over changing solar activity. We find that from July 2006 until December 2009 the p spectra became softer than D spectra indicating that relatively more low rigidity p had reached Earth than D. As solar activity began to pick up after 2009, the contribution of adiabatic energy losses became increasingly evident at lower rigidities, with the modulated p spectra hardening more in comparison with D spectra based on the shapes of their respective LISs. Consequently, the time dependence of the D/p ratio is found to be significant at rigidities below 1 GV, and with a different time-trend than at higher rigidities. The numerical model computations display both qualitative and quantitative compatibility with the observed features of D spectra and D/p ratios from the PAMELA detector. © 2026 The Author(s). Published by Elsevier B.V. on behalf of COSPAR. This is an open access article under the CC BY-NC-ND license