Addressing the Impact of Solar Modulation Systematic Uncertainties on Cosmic-Ray Propagation Models

Abstract

We perform a comprehensive analysis of cosmic-ray propagation using the time-dependent AMS-02 flux measurements covering a full solar cycle, with particular emphasis on the role of solar modulation. We fit two representative Galactic propagation scenarios, convection- and re-acceleration-dominated models, in combination with three solar modulation prescriptions: the standard force-field approximation, an extended force-field model with a rigidity break, and the heliospheric propagation code $\texttt{HelMod}$. The inclusion of time-resolved antiproton data provides a unique probe of charge-sign-dependent modulation effects and low-energy systematics. We find that the force-field approximation can describe positively charged nuclei reasonably well outside the solar maximum in convection-dominated models, but fails during periods of high solar activity and for antiprotons at all times. In re-acceleration scenarios, strong degeneracies between solar modulation and low-energy propagation lead to unphysical results when simple modulation models are employed. Across all models, we identify systematic uncertainties of order 10-15% in the reconstructed local interstellar spectra and propagation parameters, driven by limitations in current solar modulation modelling. Compared to the percent level error of current measurements, these uncertainties significantly limit the precision of cosmic-ray studies. Future time-dependent measurements spanning a full 22-year solar cycle will be crucial to reduce these uncertainties.

Figures (21)

• Figure 1: The monthly-averaged number of sunspots SILSO_Sunspot_Number (top panel) and the cosmic-ray proton (orange circle markers) and antiproton (burgundy diamond markers) fluxes as measured by AMS-02 AMS:2025npjAMS:2025pgu (bottom panel). The cosmic-ray fluxes are shown for rigidities between 5 GV and 42 GV for each Bartels rotation from May 2011 to January 2021. The preMAX, MAX and postMAX periods indicate the separate fitting periods in our analysis. A larger number of sunspots indicates stronger solar activity, which is anti-correlated with the intensity of the cosmic-ray fluxes. Due to the time-lag of the propagation of the solar winds and magnetic field, the imprint of solar activity on the cosmic-ray fluxes is typically delayed by a few months to a year.
• Figure 2: The spectra for protons (left panel) and antiprotons (right panel) for the conv propagation model. In each plot, the LIS (dashed line) and modulated flux (solid) line are given for a different solar-modulation model: the force-field potential (orange), the extended force-field potential (burgundy) and the HelMod model (green). The residuals in each plot are compared to the 7-yr AMS-02 data.
• Figure 3: The cosmic-ray proton (orange circle markers) and antiproton (burgundy diamond markers) fluxes from AMS-02 AMS:2025npjAMS:2025pgu. The combined flux from Bartels rotation 2426 to 2560 is shown.
• Figure 4: The LIS spectra for protons (left panels) and antiprotons (right panels) using the force-field model (top panels) and extended force-field model (bottom panels) for solar modulation. The LISes are based on the conv propagation model.
• Figure 5: The LIS spectra for protons (left panels) and antiprotons (right panels) using the force-field model (top panels) and extended force-field model (bottom panels) for solar modulation. The LISes are based on the reacc propagation model.