Self-generated cosmic-ray confinement in TeV halos: Implications for TeV γ -ray emission and the positron excess

Recent observations have detected extended TeV γ -ray emission surrounding young and middle-aged pulsars. The morphology of these “TeV halos” requires cosmic-ray diffusion to be locally suppressed by a factor of ∼ 100 – 1000 compared to the typical interstellar medium. No model currently explains this suppression. We show that cosmic-ray self-confinement can significantly inhibit diffusion near pulsars. The steep cosmic-ray gradient generates Alfvén waves that resonantly scatter the same cosmic-ray population, suppressing diffusion within ∼ 20     pc of young pulsars ( ≲ 100     kyr ). In this model, TeV halos evolve through two phases, a growth phase where Alfvén waves are resonantly generated and cosmic-ray diffusion becomes increasingly suppressed, and a subsequent relaxation phase where the diffusion coefficient returns to the standard interstellar value. Intriguingly, cosmic rays are not strongly confined early in the TeV halo evolution, allowing a significant fraction of injected e ± to escape. If these e ± also escape from the surrounding supernova remnant, they would provide a natural explanation for the positron excess observed by PAMELA and AMS-02. Recently created TeV cosmic rays are confined in the TeV halo, matching observations by HAWC and H.E.S.S. While our default model relaxes too rapidly to explain the confinement of TeV cosmic rays around mature pulsars, such as Geminga, models utilizing a Kraichnan turbulence spectrum experience much slower relaxation. Thus, observations of TeV halos around mature pulsars may provide a probe into our understanding of interstellar turbulence.