Scrutinizing the impact of the solar modulation on AMS-02 antiproton excess

TL;DR

This work addresses whether solar modulation uncertainties can mimic or obscure a dark matter interpretation of the AMS-02 antiproton excess. It compares three solar-modulation schemes—from the simple force-field approximation to a full 3D Parker transport-based model—and evaluates DM signals via a profile likelihood analysis while treating AMS-02 systematics with both add-in-quadrature and nuisance-parameter approaches. The DM signal significance is highly model-dependent: it can reach around $2$–$4\sigma$ under the simple FFA with all CR data, but drops to $1\sigma$ or becomes insignificant under the CT-dependent FFA or 3D modulation, especially when using correlated-systematics treatment. The results emphasize the need for refined solar-modulation modeling and careful accounting of uncertainties to draw robust conclusions about DM from antiproton data, with DM interpretations remaining plausible only under specific, model-dependent conditions.

Abstract

This study examines the impact of solar modulation on the antiproton excess observed by AMS-02, which may indicate dark matter (DM) annihilation. We analyze three solar modulation models: the force-field approximation (FFA), a time-, charge-, and rigidity-dependent FFA, and a three-dimensional numerical simulation based on the Parker transport equation. Based on AMS-02 latest antiproton data (2025), our results show that the significance of the DM signal is sensitive to the chosen modulation model, with a 2$σ$ signal for the FFA (4$σ$ if including data from H, He, C, O, B/C, and B/O) and a reduced significance for more complex models. We also address systematic uncertainties using two methods: the add-in-quadrature method, which assumes uncorrelated uncertainties between energy bins, and the nuisance parameter method, which treats systematic uncertainties as nuisance parameters during the fitting process. Fitted to AMS-02 antiproton data, DM annihilation to the $b\bar{b}$ scenario with three different solar modulation models shows that the add-in-quadrature method causes overfitting, whereas the nuisance parameters approach leads to underfitting. Statistically, the signal region of the FFA model using the add-in-quadrature method is the most reliable. This work highlights the need for refined solar modulation models and a better treatment of uncertainties for a conclusive interpretation of the AMS-02 data.

Figures (9)

• Figure 1: The time dependence of HMF $|B_{\rm tot}|$ (upper panel), HCS tilt angle $\alpha$ (middle panel), and polarity $A$ (bottom panel). The HMF $|B_{\rm tot}(t)|$ and polarity $A(t)$ are adopted from https://izw1.caltech.edu/ACE/ASC/level2/lvl2DATA_MAG.html, while $\alpha(t)$ is adopted from http://wso.stanford.edu/Tilts.html. The time span covers the period from May 2011 to June 2022.
• Figure 2: The time dependence of different parameters, with $K_0$ in Eq. \ref{['eq:K-matrix']}, $\{a, b, R_k\}$ in Eq. \ref{['eq:K-parallel']}, and $K_{A0}$ in Eq. \ref{['eq:Vd']}, and the reduced $\chi^2$ for 79 BR cycles proton flux measured by AMS-02 2018PhRvL.121e1101A.
• Figure 3: Comparison of antiproton flux predictions from three solar modulation models with AMS-02 data. The three columns, from left to right, correspond to the FFA model, the CT-dependent FFA model, and the 3D numerical simulation approach. In each panel, the red lines indicate the background flux, with solid lines representing the TOA flux and dashed lines representing the LIS flux, calculated using the best-fit propagation parameters from Table \ref{['tab:Prior']}. The blue lines represent the additional flux from DM annihilation with a mass of 63 GeV, $b\bar{b}$ final states, and cross section of $1.5 \times 10^{-26}~\mathrm{cm^3/s}$. The lower subpanels display the residuals between the AMS-02 measurements and the background-only model.
• Figure 4: The $\delta\chi_{\bar{p}}^2$ map in the ($R$, residual flux) plane. Based on the best TOA spectra of background antiprotons obtained using different solar modulation models fitted to the experimental data, three residual plots were generated. From left to right, the solar modulation models used are: FFA, CT-dependent FFA, and 3D simulation. Each plot includes a curve representing the TOA of $\bar{p}$ produced by DM. The color map illustrates the $\chi_{\bar{p}}^2$ difference between scenarios with and without a signal at each rigidity bin.
• Figure 5: Contour plots of DM mass versus annihilation cross-section, using the simple FFA model (left panels), the CT-dependent FFA model (middle panels), and the 3D simulation approach (right panels) to account for solar modulation effects on CRs, respectively. The upper three panels show that $\delta\chi^2$ accounts solely antiproton experimental data (only $\bar{p}$ data), while the lower three panels combine data from antiprotons, protons, helium, and other CRs (all CR data). The solid and dashed lines represent the add-in-quadrature and nuisance parameter approaches for addressing systematic errors, respectively. Different colored contours from inner to outer represent the $1\sigma$ (blue), $2\sigma$ (red), $3\sigma$ (black), and $4\sigma$ (green) confidence regions for a $\chi^2$ distribution with 2 degree of freedom.