The nearby Orion-Eridanus superbubble, which was blown by multiple supernovae several Myr ago, has likely produced cosmic rays. Its turbulent medium, still energised by massive stars, can impact cosmic-ray transport locally. The gamma rays produced in cosmic-ray interactions with interstellar gas were used to compare the GeV to TeV cosmic-ray spectrum in the superbubble and in other regions near the Sun. We used ten years of Fermi-LAT data in the 0.25-63 GeV energy range to study the closer (Eridanus) end of the superbubble. We modelled the spatial and spectral distributions of the gamma rays produced in the different gas phases of the clouds found in this direction. We found that the gamma-ray emissivity spectrum of the gas along the outer rim and in a shell inside the superbubble is consistent with the average spectrum measured in the solar neighbourhood. This result calls for a detailed assessment of the recent supernova rate and census of massive stellar winds in the superbubble in order to estimate the epoch and rate of cosmic-ray production and to constrain the transport conditions that can lead to such homogeneity and little re-acceleration. We also found significant evidence that a diffuse cloud lying outside the superbubble, at a height of 200-250 pc below the Galactic plane, is pervaded by a 34% lower cosmic-ray flux, but with the same particle energy distribution as the local one. Super-GeV cosmic rays should freely cross such a diffuse atomic cloud without significant loss or spectral distorsion. We tentatively propose that the cosmic-ray loss relates to the orientation of the magnetic field lines threading the cirrus, which point towards the halo according to the dust polarisation data. We gathered past and present emissivity measurements near the Sun to show how the local cosmic-ray flux decreases with Galactic height and to compare this trend with model predictions.
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