Modelling CO emission - II. The physical characteristics that determine the X factor in Galactic molecular clouds

Abstract

We investigate how the X factor, the ratio of H_2 column density (NH2) to\nvelocity-integrated CO intensity (W), is determined by the physical properties\nof gas in model molecular clouds (MCs). We perform radiative transfer\ncalculations on chemical-MHD models to compute X. Using integrated NH2 and W\nreproduces the limited range in X found in observations, resulting in a mean\nvalue X=2\\times10^20 s/cm^2/K^1/km^1 from the Galactic MC model. However, in\nlimited velocity intervals, X can take on a much larger range due to CO line\nsaturation. Thus, X strongly depends on both the range in gas velocities and\nvolume densities. The temperature (T) variations within individual MCs do not\nstrongly affect X, as dense gas contributes most to setting X. For fixed\nvelocity and density structure, gas with higher T has higher W, yielding X ~\nT^-1/2 for T~20-100 K. We demonstrate that the linewidth-size scaling relation\ndoes not influence the X factor - only the range in velocities is important.\nClouds with larger linewidths, regardless of the linewidth-size relation, have\na higher W, corresponding to a lower value of X, scaling roughly as X ~\nsigma^-1/2. The "mist" model, consisting of optically thick cloudlets with\nwell-separated velocities, does not accurately reflect the conditions in a\nturbulent MC. We propose that the observed cloud-average values of X ~ XGal is\nsimply a result of the limited range in NH2, temperatures, and velocities found\nin Galactic MCs - a ~constant value of X therefore does not require any\nlinewidth-size relation, or that MCs are virialized objects. Since gas\nproperties likely differ (slightly) between clouds, masses derived through a\nstandard X should only be considered as a rough first estimate. For\ntemperatures T~10-20 K, velocity dispersions ~1-6 km/s, and NH2~2-20\\times10^21\ncm^-2, we find cloud-averaged X ~ 2-4\\times10^20 s/cm^2/K^1/km^1 for\nSolar-metallicity models.\n