  Theoretical and observational investigations have indicated that the
abundance of carbon monoxide (CO) is very sensitive to intrinsic properties of
the gaseous medium, such as density, metallicity, and the background UV field.
In order to accurately interpret CO observations, it is thus important to
understand how well CO traces the gas, which in molecular clouds (MCs) is
predominantly molecular hydrogen (H2). Recent hydrodynamic simulations by
Glover & Mac Low have explicitly followed the formation and destruction of
molecules in model MCs under varying conditions, confirming that CO formation
strongly depends on the cloud properties. Conversely, the H2 formation is
primarily determined by the age of the MC. We apply radiative transfer
calculations to these MC models in order to investigate the properties of CO
line emission. We focus on integrated CO (J=1-0) intensities emerging from
individual clouds, including its relationship to the total, H2, and CO column
densities, as well as the "X factor," the ratio of H2 column density to CO
intensity. Models with high CO abundances have a threshold CO intensity ~65 K
km/s at sufficiently large extinctions. Clouds with low CO abundances show no
such intensity thresholds. The distribution of H2 column densities are well
described as log-normal functions, though the distributions of CO intensities
and column densities are usually not log-normal. In general, the PDFs of the
integrated intensity do not follow the distribution functions of CO column
densities. In the model with Milky Way-like conditions, the X factor is in
agreement with the near constant value determined from observations. In clouds
with lower CO abundances the X factor can vary appreciably - sometimes by > 4
orders of magnitude. In models with high densities, the CO line is fully
saturated, so that the X factor is directly proportional to the molecular
column density.
