Synthetic CO emission and the X-CO factor of young molecular clouds: a convergence study

The properties of synthetic CO emission from 3D simulations of forming molecular clouds are studied within the SILCC-Zoom project. Since the time-scales of cloud evolution and molecule formation are comparable, the simulations include a live chemical network. Two sets of simulations with an increasing spatial resolution (dx = 3.9 pc to dx = 0.06 pc) are used to investigate the convergence of the synthetic CO emission, which is computed by post-processing the simulation data with the radmc-3d radiative transfer code. To determine the excitation conditions, it is necessary to include atomic hydrogen and helium alongside H-2, which increases the resulting CO emission by similar to 7-26 per cent. Combining the brightness temperature of (CO)-C-12 and (CO)-C-13, we compare different methods to estimate the excitation temperature, the optical depth of the CO line and hence, the CO column density. An intensity-weighted average excitation temperature results in the most accurate estimate of the total CO mass. When the pixel-based excitation temperature is used to calculate the CO mass, it is over-/underestimated at low/high CO column densities where the assumption that (CO)-C-12 is optically thick while (CO)-C-13 is optically thin is not valid. Further, in order to obtain a converged total CO luminosity and hence X-CO factor, the 3D simulation must have dx less than or similar to 0.1 pc. The X-CO evolves over time and differs for the two clouds; yet pronounced differences with numerical resolution are found. Since high column density regions with a visual extinction larger than 3 mag are not resolved for dx greater than or similar to 1 pc, in this case the H-2 mass and CO luminosity both differ significantly from the higher resolution results and the local X-CO is subject to strong noise. Our calculations suggest that synthetic CO emission maps are only converged for simulations with dx less than or similar to 0.1 pc.