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CO and [CII] line emission of molecular clouds -- the impact of stellar feedback and non-equilibrium chemistry

We analyse synthetic $^{12}$CO, $^{13}$CO, and [CII] emission maps of simulated molecular clouds of the SILCC-Zoom project, which include an on-the-fly evolution of H$_2$, CO, and C$^+$. We use simulations of hydrodynamical and magnetohydrodynamical clouds, both with and without stellar feedback. We introduce a novel post-processing of the C$^+$ abundance using CLOUDY, to account for further ionization states of carbon due to stellar radiation. We report the first self-consistent synthetic emission maps of [CII] in feedback bubbles, largely devoid of emission inside them, as recently found in observations. The C$^+$ mass is only poorly affected by stellar feedback but the [CII] luminosity increases by $50 - 85$ per cent compared to runs without feedback. Furthermore, we investigate the capability of the CO/[CII] line ratio as a tracer of the amount of H$_2$ in the clouds and their evolutionary stage. We obtain, for both $^{12}$CO and $^{13}$CO, no clear trend of the luminosity ratio, $L_\mathrm{CO}/L_\mathrm{[CII]}$. It can therefore \textit{not} be used as a reliable measure of the H$_2$ mass fraction. We note a monotonic relation between $L_\mathrm{CO}/L_\mathrm{[CII]}$ and the H$_2$ fraction when considering the ratio for individual pixels of our synthetic maps, but with large scatter. Moreover, we show that assuming chemical equilibrium results in an overestimation of H$_2$ and CO masses of up to 110 and 30 per cent, respectively, and in an underestimation of H and C$^+$ masses of 65 and 7 per cent, respectively. In consequence, $L_\mathrm{CO}$ would be overestimated by up to 50 per cent, and $L_\mathrm{C[II]}$ be underestimated by up to 35 per cent. Hence, the assumption of chemical equilibrium in molecular cloud simulations introduces intrinsic errors of a factor of up to $\sim2$ in chemical abundances, luminosities and luminosity ratios.