Positron flux and γ-ray emission from Geminga pulsar and pulsar wind nebula

Nearby pulsars have been suggested as sources of ∼TeV e⁺/e⁻ cosmic ray (CR) excess on the Earth. The High-Altitude Water Cherenkov Observatory (HAWC) detected extended TeV emission regions in the direction of two nearby middle-aged pulsars, Geminga and PSR B0656+14. By modelling the TeV emission as inverse Compton emission from electron-positron pairs diffusing in the interstellar medium (ISM), the HAWC collaboration derives a diffusion coefficient much smaller than the standard value in the vicinity of the two pulsars, which make them unlikely the origin of the positron excess. We propose that the observed γ-ray emission originate from the relic pulsar wind nebula. A two zone diffusion model with a slow diffusion in the nebula and a fast diffusion in the ISM can explain the HAWC surface-brightness profile and the positron excess simultaneously. Inefficient diffusion in the γ-ray emission region surrounding a middle-aged pulsar maybe a common phenomenon that can be tested by future observation. The implied diffusion coefficient in the ISM is smaller than the one suggested by the standard CR propagation model, but it is fully consistent with the predictions of the spiral arm model.