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SILCC-Zoom: H$_2$ and CO-dark gas in molecular clouds -- The impact of feedback and magnetic fields

We analyse the CO-dark molecular gas content of simulated molecular clouds from the SILCC-Zoom project. The simulations reach a resolution of 0.1 pc and include H$_2$ and CO formation, radiative stellar feedback and magnetic fields. CO-dark gas is found in regions with local visual extinctions $A_\text{V, 3D} \sim$ 0.2 - 1.5, number densities of 10 - 10$^{3}$ cm$^{-3}$ and gas temperatures of few 10 K - 100 K. CO-bright gas is found at number densities above 300 cm$^{-3}$ and temperatures below 50 K. The CO-dark gas fractions range from 40% to 95% and scale inversely with the amount of well-shielded gas ($A_\text{V, 3D}$ $\gtrsim$ 1.5), which is smaller in magnetised molecular clouds. We show that the density, chemical abundances and $A_\text{V, 3D}$ along a given line-of-sight cannot be properly determined from projected quantities. As an example, pixels with a projected visual extinction of $A_\text{V, 2D} \simeq$ 2.5 - 5 can be both, CO-bright or CO-dark, which can be attributed to the presence or absence of strong density enhancements along the line-of-sight. By producing synthetic CO(1-0) emission maps of the simulations with RADMC-3D, we show that about 15 - 65\% of the H$_2$ is in regions with intensities below the detection limit. Our clouds have $X_\text{CO}$-factors around 1.5 $\times$ 10$^{20}$ cm$^{-2}$ (K km s$^{-1}$)$^{-1}$ with a spread of up to a factor $\sim$ 4, implying a similar uncertainty in the derived total H$_2$ masses and even worse for individual pixels. Based on our results, we suggest a new approach to determine the H$_2$ mass, which relies on the availability of CO(1-0) emission and $A_\text{V, 2D}$ maps. It reduces the uncertainty of the clouds' overall H$_2$ mass to a factor of $\lesssim$ 1.8 and for individual pixels, i.e. on sub-pc scales, to a factor of $\lesssim$ 3.