2012ApJS..203...13G

We analyze the collisional excitation of the 158 µm (1900.5 GHz) fine structure transition of ionized carbon in terms of line intensities produced by simple cloud models. The single C⁺ fine structure transition is a very important coolant of the atomic interstellar medium (ISM) and of photon-dominated regions in which carbon is partially or completely in ionized form. The [C II] line is widely used as a tracer of star formation in the Milky Way and other galaxies. Excitation of the [C II] fine structure transition can be via collisions with hydrogen molecules, atoms, and electrons. Analysis of [C II] observations is complicated by the fact that it is difficult to determine the optical depth of the line. We discuss the excitation of the [C II] line, deriving analytic results for several limiting cases and carry out numerical solutions using a large velocity gradient model for a more inclusive analysis. For antenna temperatures up to 1/3 of the brightness temperature of the gas kinetic temperature, the antenna temperature is linearly proportional to the column density of C⁺ irrespective of the optical depth of the transition. This is appropriately referred to as the effectively optically thin approximation. We review the critical densities for excitation of the [C II] line by various collision partners, briefly analyze C⁺ absorption, and conclude with a discussion of C⁺ cooling and how the considerations for line intensities affect the behavior of this important coolant of the ISM.