SO Colloquium: TeV Halos and their connection to the Leptonic Cosmic Ray flux measured at the Earth

The origin and propagation of cosmic rays (CRs) is one of the most important questions in astroparticle physics nowadays. CRs generated by known sources also serve as background to those putatively generated by more exotic phenomena such as dark matter. Apart from the known electrons of primary origin and positrons of secondary one, pulsars and sources powered by them are one of the main candidates to contribute to the total amount of CR electrons and positrons. TeV halos are sources powered by a central pulsar whose electrons and positrons have escaped from the shock region dominated by the pulsar wind and are freely propagating into the interstellar medium. They have been postulated only a couple of years ago and up to date there are only two confirmed sources. In this talk, I will give a review of the current understanding of TeV halos, the observational status and their contribution to the CR sea in the Galaxy and the local measurements at the Earth.