Understanding the spectral hardenings and radial distribution of Galactic cosmic rays and Fermi diffuse gamma-rays with spatially-dependent propagation

Recent direct measurements of Galactic cosmic ray spectra by balloon/space-borne detectors reveal spectral hardenings of all major nucleus species at rigidities of a few hundred GV. The all-sky diffuse gamma-ray emissions measured by the Fermi Large Area Telescope also show spatial variations of the intensities and spectral indices of cosmic rays. These new observations challenge the traditional simple acceleration and/or propagation scenario of Galactic cosmic rays. In this work we propose a spatially-dependent diffusion scenario to explain all these phenomena. The diffusion coefficient is assumed to be anti-correlated with the source distribution, which is a natural expectation from the charged particle transportation in turbulent magnetic field. The spatially-dependent diffusion model also gives a lower level of anisotropies of cosmic rays, which are consistent with observations by underground muons and air shower experiments. The spectral variations of cosmic rays across the Galaxy can be properly reproduced by this model.