  Relating the observed CO emission from giant molecular clouds (GMCs) to the
underlying H2 column density is a long-standing problem in astrophysics. While
the Galactic CO-H2 conversion factor (Xco) appears to be reasonably constant,
observations indicate that Xco may be depressed in high-surface density
starburst environments. Using a multi-scale approach, we investigate the
dependence of Xco on the galactic environment in numerical simulations of disc
galaxies and galaxy mergers. Xco is proportional to the GMC surface density
divided by the integrated CO intensity, Wco, and Wco is related to the kinetic
temperature and velocity dispersion in the cloud. In disc galaxies (except
within the central ~ kpc), the galactic environment is largely unimportant in
setting the physical properties of GMCs provided they are gravitationally
bound. The temperatures are roughly constant at ~10 K due to the balance of CO
cooling and cosmic ray heating, giving a nearly constant CO-H2 conversion
factor in discs. In mergers, the velocity dispersion of the gas rises
dramatically during coalescence. The gas temperature also rises as it couples
well to the warm (~50 K) dust at high densities (n > 10^4 cm^-3). The rise in
velocity dispersion and temperature combine to offset the rise in surface
density in mergers, causing Xco to drop by a factor of ~2-10 compared to the
disc simulation. This model predicts that high-resolution ALMA observations of
nearby ULIRGs should show velocity dispersions of ~10-100 km/s, and brightness
temperatures comparable to the dust temperatures.
