Gamma-ray observations of the Orion Molecular Clouds with the Fermi
  Large Area Telescope
  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 \sim100 MeV and
\sim100 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 \sim10% 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 (WCO) at a
1{\deg} \times1{\deg} pixel level. The correlation is found to be linear over a
WCO range of ~10 fold when divided in 3 regions, suggesting penetration of
nuclear CRs to most of the cloud volumes. The Wco-to-mass conversion factor,
Xco, is found to be \sim2.3\times10^20 cm-2(K km s-1)-1 for the high-longitude
part of Orion A (l > 212{\deg}), \sim1.7 times higher than \sim1.3 \times 10^20
found for the rest of Orion A and B. We interpret the apparent high Xco in the
high-longitude region of Orion A in the light of recent works proposing a
non-linear relation between H2 and CO densities in the diffuse molecular gas.
Wco decreases faster than the H2 column density in the region making the gas
"darker" to Wco.
