We investigate how the X factor , the ratio of the molecular hydrogen column density ( N _ { H _ { 2 } } ) 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 magneto-hydrodynamic 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-average values of X = X _ { Gal } \sim 2 \times 10 ^ { 20 } cm ^ { -2 } K ^ { -1 } km ^ { -1 } s , we focus on a model representing a typical Milky Way MC .
Using globally integrated N _ { H _ { 2 } } and W reproduces the limited range in X found in observations and a mean value X = X _ { Gal } = 2.2 \times 10 ^ { 20 } cm ^ { -2 } K ^ { -1 } km ^ { -1 } s. 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 , as well as the volume densities .
The temperature variations within individual MCs do not strongly affect X , as dense gas contributes most to setting the X factor .
For fixed velocity and density structure , gas with higher temperatures T has higher W , yielding X \propto T ^ { -1 / 2 } for T \sim 20 - 100 K. We demonstrate that the linewidth-size scaling relationship does not influence the X factor - only the range in velocities is important .
Clouds with larger linewidths \sigma , regardless of the linewidth-size relationship , have a higher W , corresponding to a lower value of X , scaling roughly as X \propto \sigma ^ { -1 / 2 } .
The “ mist ” model , often invoked to explain a constant X _ { Gal } consisting of optically thick cloudlets with well-separated velocities , does not accurately reflect the conditions in a turbulent molecular cloud .
We propose that the observed cloud-average values of X \sim X _ { Gal } is simply a result of the limited range in N _ { H _ { 2 } } , temperatures , and velocities found in Galactic MCs - a nearly constant value of X therefore 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 temperatures T \sim 10 - 20 K , velocity dispersions \sigma \sim 1 - 6 km s ^ { -1 } , and N _ { H _ { 2 } } \sim 2 - 20 \times 10 ^ { 21 } cm ^ { -2 } , we find cloud-averaged values X \sim 2 - 4 \times 10 ^ { 20 } cm ^ { -2 } K ^ { -1 } km ^ { -1 } s for Solar-metallicity models .