Gamma-ray haloes around pulsars as the key to understanding cosmic-ray transport in the Galaxy

Pulsars are factories of relativistic electrons and positrons that propagate away from the pulsar, eventually permeating our Galaxy. The acceleration and propagation of these cosmic particles are a matter of intense debate. In the last few years, we have had the opportunity to directly observe the injection of these particles into the interstellar medium through the discovery of gamma-ray haloes around pulsars. This new type of gamma-ray source is produced by electrons and positrons diffusing out of the pulsar wind nebula and scattering ambient photon fields to produce gamma rays. This correspondingly new field of study comes with a number of observations and constraints at different wavelengths and a variety of theoretical models that can explain the properties of these haloes. We examine the characteristics of the propagation of cosmic rays inferred from the observations of gamma-ray haloes and their local and global implications for particle transport within the Galaxy. We also discuss the prospects for observations of these sources with facilities such as the Large High Altitude Air Shower Observatory, the Cherenkov Telescope Array or the Southern Wide-field Gamma-ray Observatory in the near future. Our understanding of the relatively newly recognized phenomenon of haloes of gamma-ray emission around Galactic pulsars is summarized, from observational and theoretical perspectives, together with their implication for the acceleration of cosmic rays.