We analyze the collisional excitation of the 158 micron (1900.5 GHz) fine structure transition of ionized carbon (C+) 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 and of photon dominated regions in which carbon is partially or completely in ionized form. The [CII] line is widely used as a tracer of star formation in the Milky Way and other galaxies. Excitation of the [CII] fine structure transition can be via collisions with hydrogen molecules, atoms, and electrons. Velocity-resolved observations of [CII] have become possible with the HIFI instrument on Herschel and the GREAT instrument on SOFIA. Analysis of these observations is complicated by the fact that it is difficult to determine the optical depth of the [CII] line due to the relative weakness and blending of the components of the analogous transition of 13C$+. We discuss the excitation and radiative transition of the [CII] line, deriving analytic results for several limiting cases and carry out numerical solutions using a large velocity gradient model for a more inclusive analysis. We show that 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, which can be referred to as the effectively optically thin (EOT) approximation. We review the critical densities for excitation of the [CII] line by various collision partners. We 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.
(Abridged) The 30 Dor region in the Large Magellanic Cloud (LMC) is the most vigorous star-forming region in the Local Group. Star formation in this region is taking place in low-metallicity molecular gas that is exposed to an extreme far--ultraviole
t (FUV) radiation field powered by the massive compact star cluster R136. We used the NANTEN2 telescope to obtain high-angular resolution observations of the 12CO 4-3, 7-6, and 13CO 4-3 rotational lines and [CI] 3P1-3P0 and 3P2-3P1 fine-structure submillimeter transitions in 30Dor-10, the brightest CO and FIR-emitting cloud at the center of the 30Dor region. We derived the properties of the low-metallicity molecular gas using an excitation/radiative transfer code and found a self-consistent solution of the chemistry and thermal balance of the gas in the framework of a clumpy cloud PDR model. We compared the derived properties with those in the N159W region, which is exposed to a more moderate far-ultraviolet radiation field compared with 30Dor-10, but has similar metallicity. We also combined our CO detections with previously observed low-J CO transitions to derive the CO spectral-line energy distribution in 30Dor-10 and N159W. The separate excitation analysis of the submm CO lines and the neutral carbon fine structure lines shows that the mid-J CO and [CI]-emitting gas in the 30Dor-10 region has a temperature of about 160 K and a H2 density of about 10^4 cm^-3. We find that the molecular gas in 30Dor-10 is warmer and has a lower beam filling factor compared to that of N159W, which might be a result of the effect of a strong FUV radiation field heating and disrupting the low--metallicity molecular gas. We use a clumpy PDR model (including the [CII] line intensity reported in the literature) to constrain the FUV intensity to about chi_0 ~ 3100 and an average total H density of the clump ensemble of about 10^5 cm^-3 in 30Dor-10.
