We report on the gamma-ray observations of giant molecular clouds Orion A and B with the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope . The gamma-ray emission in the energy band between ∼100 MeV and ∼100 GeV is predicted to trace the gas mass distribution in the clouds through nuclear interactions between the Galactic cosmic rays (CRs) and interstellar gas. The gamma-ray production cross-section for the nuclear interaction is known to ∼10% precision which makes the LAT a powerful tool to measure the gas mass column density distribution of molecular clouds for a known CR intensity. We present here such distributions for Orion A and B, and correlate them with those of the velocity-integrated CO intensity ( W CO ) at a 1° × 1° pixel level. The correlation is found to be linear over a W CO range of ∼10-fold when divided in three regions, suggesting penetration of nuclear CRs to most of the cloud volumes. The W CO -to-mass conversion factor, X CO , is found to be ∼2.3 × 10 20 cm -2 (K km s −1 ) −1 for the high-longitude part of Orion A ( l > 212°), ∼1.7 times higher than ∼1.3 × 10 20 found for the rest of Orion A and B. We interpret the apparent high X CO in the high-longitude region of Orion A in the light of recent works proposing a nonlinear relation between H 2 and CO densities in the diffuse molecular gas. W CO decreases faster than the H 2 column density in the region making the gas "darker" to W CO .
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