The environment of TeV halo progenitors

TeV halos are extended very-high-energy gamma-ray sources found around some middle-aged pulsars. The emission extending over several tens of parsecs suggests an efficient confinement of the ultra-relativistic lepton pairs produced by pulsars in their vicinity. The exact physical mechanism responsible for this suppressed transport has not yet been identified. In some theoretical scenarios, pair confinement may be linked to the medium the pulsars are located in. We aim at understanding which type of medium pulsars are probing over their lifetime. We developed a model for the environment probed by moving pulsars, from their birth in the core-collapse explosion, where they receive a natal kick, until their entry into the interstellar medium at large. Ultimately, from a distribution of neutron star kick velocities, we assess in which medium pulsars are located as a function of time. We use this model to derive the statistical properties of a fully synthetic Galactic population, and then apply it to individual pulsars from the ATNF catalogue to assess the nature of the medium they are most likely to reside in. We show that pulsars escape into the ISM at around $200~\mathrm{kyr}$, significantly later than the values most commonly used in the literature. Pulsars that have a confirmed TeV halo have non negligible probabilities of still being in their parent environment.