Diagnosing interstellar magnetic turbulence with TeV pulsar halos

Interstellar magnetic field is essential in various astrophysical phenomena and processes. Pulsar halos are a recently discovered class of TeV gamma-ray sources formed by escaping electrons/positrons from pulsars. The morphology of the halo is regulated by the diffusion of those escaping particles, and hence carry information of the interstellar magnetic field. We suggest that the morphology of TeV pulsar halos can be used as a novel probe of the properties of interstellar magnetic field around the pulsar, such as the Alfv\'{e}nic Mach number and the mean direction. We establish a theoretical relation between these quantities and the observational features of the halo's morphology based on the anisotropic diffusion model, and show that how X-ray observations of the pulsar halos can further improve the diagnosis of the magnetic field. Lastly, we try to apply our method to an observed pulsar halo candidate, HESS~J1809-193, as a practical example.