Synthetic [C II] emission maps of a simulated molecular cloud in formation

The C⁺ ion is an important coolant of interstellar gas, and so the [C II] fine structure line is frequently observed in the interstellar medium. However, the physical and chemical properties of the [C II]-emitting gas are still unclear. We carry out non-LTE (local thermal equilibrium) radiative transfer simulations with RADMC-3D to study the [C II] line emission from a young, turbulent molecular cloud before the onset of star formation, using data from the SILCC-Zoom project. The [C II] emission is optically thick over 40 per cent of the observable area with I_{[C II]} > 0.5 K km s^-1. To determine the physical properties of the [C II] emitting gas, we treat the [C II] emission as optically thin. We find that the [C II] emission originates primarily from cold, moderate density gas (40 ≲ T ≲ 65 K and 50 ≲ n ≲ 440 cm^-3), composed mainly of atomic hydrogen and with an effective visual extinction between ∼0.50 and ∼0.91. Gas dominated by molecular hydrogen contributes only ≲20 per cent of the total [C II] line emission. Thus, [C II] is not a good tracer for CO-dark H₂ at this early phase in the cloud's lifetime. We also find that the total gas, H and C⁺ column densities are all correlated with the integrated [C II] line emission, with power law slopes ranging from 0.5 to 0.7. Further, the median ratio between the total column density and the [C II] line emission is Y_{C II} ≈ 1.1 × 10²¹ cm^-2 (K km s^-1)^-1, and Y_{C II}} scales with I_{[C II]}^{-0.3}. We expect Y_{C II} to change in environments with a lower or higher radiation field than simulated here.