Anisotropic Diffusion of $e^\pm$ in Pulsar Halos over Multiple Coherence of Magnetic Fields

Abstract

The slow particle diffusion in pulsar halos, inferred from TeV gamma-ray surface brightness profiles, is attributed to cross-field diffusion under the anisotropic diffusion model. This model assumes sub-Alfv\'enic interstellar turbulence in the surrounding medium of the pulsar and a rough alignment of the line-of-sight of observers towards the pulsars with the local mean magnetic field direction in the halo. In this model, the expected morphology of a pulsar halo is highly dependent on the properties of the interstellar magnetic field. We investigate the anisotropic diffusion of electron-positron pairs across multiple coherence of magnetic fields in pulsar halos in this work. We focus particularly on their influences on the predicted gamma-ray surface brightness profile and the asymmetry of the halo's morphology, as well as the observational expectations by the Large High Altitude Air Shower Observatory (LHAASO). Our results indicate that the requirement of a specific magnetic field geometry can be alleviated when accounting for a limited (and realistic) coherence length of the magnetic field in the model. Also, the halo's morphology may appear less asymmetric, especially after being smoothed by the point spread function of instruments. It largely relaxes the tension between the asymmetric morphology of halos predicted by the model and lack of apparent asymmetric halos detected so far. Our findings demonstrate the important influence of the coherence length of interstellar magnetic field on the distribution of particles around their accelerators, and the consequence on the measured source morphology.