Are Pulsar Halos Truly symmetric? Insights from 3D Magnetic Turbulence Simulations

The diffuse gamma-ray emission from the Geminga halo has been suggested to exhibit asymmetric features, though the existence and origin of such asymmetry remain debated. We perform three-dimensional test-particle simulations of cosmic-ray (CR) electrons
propagating in turbulent magnetic fields characterized by Kolmogorov and Bohm spectra. Particle trajectories are computed under the Lorentz force, with radiative energy losses from synchrotron emission and inverse Compton scattering included self-consistently. We further incorporate a regular magnetic field component and explore different inclinations between the magnetic field direction and the line of sight, computing the resulting gamma-ray surface brightness and comparing it with HAWC observations. Our results constrain the magnetic coherence length to several parsecs and statistically favor the presence of a regular magnetic field in the Geminga region. Compared to Kolmogorov turbulence, Bohm turbulence produces more tangled magnetic field lines and a nearly isotropic CR distribution, failing to reproduce the observed halo morphology. The simulations indicate that filamentary substructures are intrinsically present within the Geminga halo. Although current very-highenergy instruments cannot resolve these internal asymmetries, projection effects do not erase them: even in the extreme case of a large coherence length combined with a strong regular field aligned with the line of sight, filamentary structures persist internally despite an apparently isotropic overall morphology.