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

We investigate how the X factor, the ratio of the molecular hydrogen column density to velocity-integrated CO intensity (W), is determined by the physical properties of gas in model molecular clouds (MCs). The synthetic MCs are results of magnetohydrodynamic simulations, including a treatment of chemistry. We perform radiative transfer calculations to determine the emergent CO intensity, using the large velocity gradient approximation for estimating the CO population levels. In order to understand why observations generally find cloud-averaged values ofX=X_Gal~ 2 × 10²⁰cm^-2K^-1km^-1s, we focus on a model representing a typical Milky Way MC. Using globally integratedandWreproduces the limited range inXfound in observations and a mean valueX=X_Gal= 2.2 × 10²⁰cm^-2K^-1km^-1s. However, we show that when considering limited velocity intervals, X can take on a much larger range of values due to CO line saturation. Thus, the X factor strongly depends on both the range in gas velocities and the volume densities. The temperature variations within individual MCs do not strongly affectX, as dense gas contributes most to setting the X factor. For fixed velocity and density structure, gas with higher temperaturesThas higherW, yieldingX∝T^-1/2 forT~ 20-100K. We demonstrate that the linewidth-size scaling relationship does not influence the X factor - only therangein velocities is important. Clouds with larger linewidths σ, regardless of the linewidth-size relationship, have a higherW, corresponding to a lower value ofX, scaling roughly asX∝σ^-1/2. The 'mist' model, often invoked to explain a constantX_Gal 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-averaged values ofX~X_Gal are simply a result of the limited range in, temperatures and velocities found in Galactic MCs - a nearly constant value ofXtherefore does not require any linewidth-size relationship, or that MCs are virialized objects. Since gas properties likely differ (albeit even slightly) from cloud to cloud, masses derived through a standard value of the X factor should only be considered as a rough first estimate. For temperaturesT~ 10-20K, velocity dispersions σ~ 1-6kms^-1andcm^-2, we find cloud-averaged valuesX~ 2-4 × 10²⁰cm^-2K^-1km^-1s for solar-metallicity models.