A contribution of the HAWC observatory to the TeV era in the high energy gamma-ray astrophysics: The case of the TeV-halos

We present a short overview of the TeV-Halos objects as a discovery and a relevant contribution of the High Altitude Water Çerenkov (HAWC) observatory to TeV astrophysics. We discuss history, discovery, knowledge, and the next step through a new and more detailed analysis than the original study in 2017. TeV-Halos will contribute to resolving the problem of the local positron excess observed on the Earth. To clarify the latter, understanding the diffusion process is mandatory.