Slow diffusion around pulsar $\gamma$-ray halos and its impact on cosmic rays propagation

The diffusion coefficients around the pulsar $\gamma$-ray halos are highly suppressed compared with the value in the interstellar medium. It is suggested in the literature that the $\gamma$-ray halos can be explained by a ballistic-diffusive (BD) propagation without slow diffusion. However our calculation shows that the BD propagation can not account for the $\gamma$-ray halo profile well. Furthermore the transfer efficiency of the pulsar spin down energy to the high energy electrons and positrons is even larger than 1 in the BD scenario. Therefore slow diffusion is necessary to account for the pulsar $\gamma$-ray halos. Taking the slow diffusion into account the contribution of positron flux originated from nearby pulsars to the AMS-02 data is reexamined. We may also expect a slow diffusion disk of the Milky Way as many such slow diffusion regions exist. The positron contribution to the AMS-02 data from dark matter annihilation in the new propagation model is also reexamined. We find that the dark matter scenario satisfies all the $\gamma$-ray limits in the new propagation model.