Two-zone diffusion of electrons and positrons from Geminga explains the positron anomaly

Abstract

The recent HAWC observations of very-high-energy $γ$-ray halo around Geminga and Monogem indicate a very slow diffusion of cosmic rays, which results in tiny contribution of positrons from these two pulsars to the local flux. This makes the cosmic positron excess anomaly observed by PAMELA and AMS-02 even more puzzling. However, from the Boron-to-Carbon ratio data one can infer that the average diffusion coefficient in the Galaxy should be much larger. In this work we propose a two-zone diffusion model that the diffusion is slow only in a small region around the source, outside of which the propagation is as fast as usual. We find that such a scenario can naturally explain the positron excess data with parameters even more reasonable than that in the conventional one-zone diffusion model. The reason is that during the life time of Geminga ($\sim 300$ kyr) the electrons/positrons have propagated too far away with a fast diffusion and lead to a low local flux. The slow diffusion region in the two-zone model helps to confine the electrons/positrons for a long time and lead to an enhancement of the local flux. So under the constraint of the HAWC observations, pulsars are still the probable origin of the cosmic-ray positron excess.