On the accuracy of HI observations in molecular clouds -- More cold HI than thought?

We present a study of the cold atomic hydrogen (HI) content of molecular clouds simulated self-consistently within the SILCC-Zoom project. We produce synthetic observations of HI at 21 cm including HI self-absorption (HISA) and observational effects. We find that HI column densities, $N_\textrm{HI}$, of $\gtrsim$10$^{22}$ cm$^{-2}$ are frequently reached in molecular clouds and that the HI gas reaches temperatures as low as $\sim$10 K. We show that HISA observations tend to underestimate the amount of cold HI in molecular clouds by a factor of 3 - 10 and produce an artificial upper limit of observed $N_\textrm{HI}$ values around 10$^{21}$ cm$^{-2}$. Based on this, we argue that the cold HI mass in molecular clouds could be a factor of a few higher than previously estimated. Also $N_\textrm{HI}$-PDFs obtained from HISA observations might be subject to observational biases and should be considered with caution. The underestimation of cold HI in HISA observations is due to both the large HI temperature variations and the effect of noise in regions of high optical depth. We find optical depths of cold HI around 1 - 10 making optical depth corrections essential. We show that the high HI column densities ($\gtrsim$10$^{22}$ cm$^{-2}$) can in parts be attributed to the occurrence of up to 10 individual HI-H$_2$ transitions along the line of sight. However, also for a single HI-H$_2$ transition, $N_\textrm{HI}$ frequently exceeds a value of 10$^{21}$ cm$^{-2}$, thus challenging 1D, semi-analytical models. This can be attributed to non-equilibrium chemistry effects, which are included in our models, and the fact that HI-H$_2$ transition regions usually do not possess a 1D geometry. Finally, we show that the HI is moderately supersonic with Mach numbers of a few. The corresponding non-thermal velocity dispersion can be determined via HISA observations with an uncertainty of a factor of $\sim$2.