Modeling CO Emission: II. The Physical Characteristics that Determine
  the X factor in Galactic Molecular Clouds
  We investigate how the X factor, the ratio of H_2 column density (NH2) to
velocity-integrated CO intensity (W), is determined by the physical properties
of gas in model molecular clouds (MCs). We perform radiative transfer
calculations on chemical-MHD models to compute X. Using integrated NH2 and W
reproduces the limited range in X found in observations, resulting in a mean
value X=2\times10^20 s/cm^2/K^1/km^1 from the Galactic MC model. However, in
limited velocity intervals, X can take on a much larger range due to CO line
saturation. Thus, X strongly depends on both the range in gas velocities and
volume densities. The temperature (T) variations within individual MCs do not
strongly affect X, as dense gas contributes most to setting X. For fixed
velocity and density structure, gas with higher T has higher W, yielding X ~
T^-1/2 for T~20-100 K. We demonstrate that the linewidth-size scaling relation
does not influence the X factor - only the range in velocities is important.
Clouds with larger linewidths, regardless of the linewidth-size relation, have
a higher W, corresponding to a lower value of X, scaling roughly as X ~
sigma^-1/2. The "mist" model, consisting of optically thick cloudlets with
well-separated velocities, does not accurately reflect the conditions in a
turbulent MC. We propose that the observed cloud-average values of X ~ XGal is
simply a result of the limited range in NH2, temperatures, and velocities found
in Galactic MCs - a ~constant value of X therefore does not require any
linewidth-size relation, or that MCs are virialized objects. Since gas
properties likely differ (slightly) between clouds, masses derived through a
standard X should only be considered as a rough first estimate. For
temperatures T~10-20 K, velocity dispersions ~1-6 km/s, and NH2~2-20\times10^21
cm^-2, we find cloud-averaged X ~ 2-4\times10^20 s/cm^2/K^1/km^1 for
Solar-metallicity models.
