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Recent direct measurements of Galactic cosmic ray spectra byballoon/space-borne detectors reveal spectral hardenings of all major nucleusspecies at rigidities of a few hundred GV. The all-sky diffuse gamma-rayemissions measured by the Fermi Large Area Telescope also show spatialvariations of the intensities and spectral indices of cosmic rays. These newobservations challenge the traditional simple acceleration and/or propagationscenario of Galactic cosmic rays. In this work we propose a spatially-dependentdiffusion scenario to explain all these phenomena. The diffusion coefficient isassumed to be anti-correlated with the source distribution, which is a naturalexpectation from the charged particle transportation in turbulent magneticfield. The spatially-dependent diffusion model also gives a lower level ofanisotropies of cosmic rays, which are consistent with observations byunderground muons and air shower experiments. The spectral variations of cosmicrays across the Galaxy can be properly reproduced by this model.

physical review. d/physical review. d.

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