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Nearby pulsars have been suggested as sources of $\sim$TeV $e^+/e^-$ CosmicRay (CR) excess on Earth. The High-Altitude Water Cherenkov Observatory (HAWC)detected extended TeV emission regions in the direction of two nearbymiddle-aged pulsars, Geminga and PSR B0656+14. By modeling the TeV emission asinverse Compton emission from electron-positron pairs diffusing in theinterstellar medium (ISM), the HAWC collaboration derives a diffusioncoefficient much smaller than the standard value in the vicinity of the twopulsars, which make them unlikely the origin of the positron excess. We proposethat the observed $\gamma$-ray emission originate from the relic pulsar windnebula. A two zone diffusion model with a slow diffusion in the nebula and afast diffusion in the ISM can explain the HAWC surface brightness profile andthe positron excess simultaneously. Inefficient diffusion in the $\gamma$-rayemission region surrounding a middle-aged pulsar maybe a common phenomenon thatcan be tested by future observation. The implied diffusion coefficient in theISM is smaller than the one suggested by the standard CR propagation model, butit is fully consistent with the predictions of the spiral arm model.

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