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.
