TeV halos around pulsars and prospects for next generation gamma ray observatories

The detection of extended very-high-energy (VHE, E > 0.1 TeV) gamma-ray emission surrounding the middle-aged pulsars Geminga and PSR B0656+14 by the HAWC Observatory in 2017 provided the first clear observational evidence for an extended inverse Compton component produced by electron-positron pairs diffusing away from pulsars, a component whose existence under conditions of suppressed diffusion had been anticipated theoretically. Such sources are now commonly referred to as TeV halos. These structures, now comprising two well-established halos and several candidates detected by HAWC, LHAASO, H.E.S.S., and Tibet AS γ , are understood to arise predominantly from inverse Compton (IC) scattering of interstellar radiation fields by relativistic electron-positron pairs that have escaped from their parent pulsar wind nebulae (PWNe) and diffuse through the surrounding interstellar medium (ISM). A defining observational characteristic of TeV halos is the strongly suppressed diffusion coefficient inferred within them, typically two orders of magnitude below the Galactic average, whose physical origin remains a subject of active debate. While purely leptonic models have been remarkably successful in reproducing the broadband spectral energy distributions and radial surface brightness profiles of known halos, the possible contribution of a hadronic component has also been discussed, particularly in light of LHAASO detections of ultra-high-energy (UHE, E > 100 TeV) emission from pulsar-associated sources. We show that, for middle-aged halo pulsars, the available pulsar potential and the rapid escape of energetic protons make a significant hadronic contribution unlikely, whereas PeV proton acceleration remains plausible in young, energetic pulsar wind nebulae. This review provides a comprehensive overview of the current observational landscape of TeV halos across the electromagnetic spectrum, from GeV energies probed by Fermi -LAT to the UHE domain accessed by LHAASO. We present the theoretical framework underpinning particle transport and emission in TeV halos, covering the standard two-zone diffusion model with isotropic and anisotropic diffusion scenarios, energy-dependent morphologies, and the role of self-generated turbulence. We critically examine the case for a lepto-hadronic interpretation, reviewing constraints from current gamma-ray and neutrino observations, including IceCube stacking analyses. We discuss the implications of TeV halos for the cosmic-ray positron excess measured by AMS-02 and DAMPE, the nature of particle escape from PWNe, and the transition from the nebular to the halo phase. Finally, we assess the transformative potential of next-generation observatories, the Cherenkov Telescope Array Observatory (CTAO), the Southern Wide-field Gamma-ray Observatory (SWGO), and upcoming neutrino telescopes, for resolving open questions through improved angular resolution, extended energy coverage, and Southern Hemisphere access to the inner Galaxy.