Constraining Anisotropic Diffusion between Geminga and Earth with the Cosmic-Ray Electron and Positron Spectrum

The gamma-ray halo around Geminga indicates significant suppression of cosmic-ray diffusion. One possible explanation for this phenomenon is the projection effect of slow diffusion perpendicular to the mean magnetic field (characterized by the diffusion coefficient D ⊥ ) within an anisotropic diffusion framework. In this scenario, the diffusion coefficient parallel to the mean field ( D ∥ ) can still be large, enabling electrons and positrons ( e ± ) produced by Geminga to efficiently travel to Earth along the magnetic field lines, possibly resulting in a detectable e ± flux. In this work, we first determine the basic parameters of the anisotropic model using the morphology and spectral measurements of the Geminga halo and then predict the flux of e ± produced by Geminga at the location of Earth. We find that the e − + e + spectrum of DAMPE can give crucial constraint on the anisotropic diffusion model: to ensure that the predicted spectrum does not exceed the measurements, the Alfvén Mach number of the turbulent magnetic field ( M A ) should not be less than 0.75, corresponding to D ∥ / D ⊥ ≲ 3 given that D ⊥ = D ∥ M A 4 . This implies that a significant suppression of D ∥ relative to the average value in the Galaxy may still be necessary. Furthermore, we find that under the anisotropic diffusion model, Geminga can produce a very sharp feature around 1 TeV in the e − + e + spectrum, which could naturally explain the peculiar 1.4 TeV excess tentatively observed by DAMPE.