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Anisotropic Cosmic Ray Diffusion and its Implications for Gamma-Ray Astronomy

Analyses of TeV-PeV cosmic ray (CR) diffusion around their sources usually assume either isotropic diffusion or anisotropic diffusion due to the regular Galactic magnetic field. We show that none of them are adequate on distances smaller than the maximal scale Lmax ~ 100 pc of fluctuations in the turbulent interstellar magnetic field. As a result, we predict anisotropic gamma-ray emissions around CR proton and electron sources, even for uniform densities of target gas. The centers of extended emission regions may have non-negligible offsets from their sources, leading to risks of misidentification. Gamma-rays from CR filaments have steeper energy spectra than those from surrounding regions. We point out that gamma-ray telescopes can be used in the future as a new way to probe and deduce the parameters of the interstellar magnetic field.