Context. The Cygnus region hosts a giant molecular-cloud complex that actively forms massive stars. Interactions of cosmic rays with interstellar gas and radiation fields make it shine at γ-ray energies. Several γ-ray pulsars and other energetic sources are seen in this direction. Aims. In this paper we analyze the γ-ray emission measured by the Fermi Large Area Telescope (LAT) in the energy range from 100 MeV to 100 GeV in order to probe the gas and cosmic-ray content on the scale of the whole Cygnus complex. The γ-ray emission on the scale of the central massive stellar clusters and from individual sources is addressed elsewhere. Methods. The signal from bright pulsars is greatly reduced by selecting photons in their off-pulse phase intervals. We compare the diffuse γ-ray emission with interstellar gas maps derived from radio/mm-wave lines and visual extinction data. A general model of the region, including other pulsars and γ-ray sources, is sought. Results. The integral H i emissivity above 100 MeV averaged over the whole Cygnus complex amounts to [2.06 ± 0.11 (stat.) -0.84 +0.15(syst.)] × 10 -26 photons s -1 sr -1 H-atom -1, where the systematic error is dominated by the uncertainty on the H i opacity to calculate its column densities. The integral emissivity and its spectral energy distribution are both consistent within the systematics with LAT measurements in the interstellar space near the solar system. The average X CO = N(H 2)/W CO ratio is found to be [1.68 ± 0.05 (stat.) -0.10 +0.87(HI opacity)] × 10 20 molecules cm -2 (K km s -1) -1, consistent with other LAT measurements in the Local Arm. We detect significant γ-ray emission from dark neutral gas for a mass corresponding to ~40% of what is traced by CO. The total interstellar mass in the Cygnus complex inferred from its γ-ray emission amounts to 8 -1 +5 × 10 6 M ⊙ at a distance of 1.4 kpc. Conclusions. Despite the conspicuous star formation activity and high masses of the interstellar clouds, the cosmic-ray population in the Cygnus complex averaged over a few hundred parsecs is similar to that of the local interstellar space.
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