Qian Zhong

Extended $γ$-ray emission has been observed around several nearby pulsars and interpreted as inverse Compton radiation from relativistic electrons and positrons diffusing in the surrounding interstellar medium. In this work, we present a unified analysis of the TeV halos associated with the Geminga and Monogem pulsars, combining GeV--TeV $γ$-ray observations within a common physical framework. Assuming continuous injection of $e^\pm$ pairs from pulsar wind nebulae, we model the resulting $γ$-ray emission by accounting for particle diffusion and radiative energy losses. We find that the observed spectra of both Geminga and Monogem are well reproduced by the model, provided that particle transport in the vicinity of the pulsars is significantly suppressed with respect to the average Galactic diffusion. The injection spectra require cutoff energies of several tens of TeV, consistent with efficient acceleration in pulsar wind nebulae. Using the best-fit models inferred from the $γ$-ray data, we also evaluate the contribution of Geminga and Monogem to the local cosmic-ray positron flux measured by AMS-02. We find that the suppressed diffusion around the sources strongly limits the positron flux reaching the Earth, resulting in a subdominant contribution over the entire energy range probed by the experiment excect for the highest energy at around 1 TeV. Our results support an interpretation in which TeV halos trace regions of inhibited particle diffusion around pulsars, without implying a significant impact on the local cosmic-ray positron spectrum. This combined analysis highlights the importance of extended $γ$-ray observations for constraining particle transport in the vicinity of Galactic cosmic-ray sources.