The energy difference between the 3P1 and 3P2 levels of OI is 2.0 x 10"2 eV, corresponding to a temperature Ta of 230 K. The upper level can be collisionally excited in the warmer regions of a molecular cloud and decays with an associated A-value of 9.0 x 10"5 s"1. Note that all the downward fine-structure transitions are "forbidden" by the electric-dipole selection rules of quantum mechanics and therefore occur through slower magnetic dipole interactions. For the 3P1 ^ 3P2 transition of O I, the emitted spectral line is symbolized [O I] 63 pm, where the braces denote a forbidden transition. Except in the very densest cloud regions, this far-infrared radiation readily escapes and provides an important source of cooling. The deexcitation rate 7ui from hydrogen impact has the value 4 x 10"11 cm3 s"1 at the temperatures of interest (Tg < 40 K), so that ncrit = 2 x 106 cm"3. We may therefore evaluate AOi, the volumetric cooling rate, from the subcritical expression, equation (7.24). Using a number density of oxygen relative to hydrogen of 4 x 10"4 (Table 2.1) and noting that the degeneracy of each J-state is 2 J +1, we find
This expression would need to be modified in denser regions, where much of the oxygen is in CO or grain mantles. In such locales, however, other cooling mechanisms dominate (Chapter 8).
Fine-structure cooling is also available from carbon, which has an elemental abundance comparable to oxygen. As we have seen, atomic carbon can be readily ionized by the ultraviolet component of the interstellar radiation field, so that it is actually C II that provides most of the cooling. The ion has only one p-electron, and the spin-orbit interaction splits its ground state into 2P3/2 and 2P1/2 levels. Figure 7.8 shows that, in this case, the energy ordering is normal, i. e., the 2P1/2 level is actually the ground state. The energy difference between the levels is 7.93 x 10"3 eV, corresponding to a Ta of 92 K and a photon wavelength of 158 pm.
The appropriate value of 7ul is now 6 x 10"10 cm3 s"1, and Aul is 2.4 x 10"6 s"1. Thus, the critical density is only 3 x 103 cm"3, a value often reached in molecular clouds. However, most of the carbon is locked into CO at higher density, so that the subcritical cooling rate is still appropriate. We find
Ac"=3 x 10-9 (ïoÎIf3)2 exp (-^r) • <7-27)
Both Equations (7.26) and (7.27) have assumed that promotion to upper fine-structure levels occurs only through impact with ambient hydrogen atoms. In fact, the levels are much more easily excited by free electrons. It is only because the fractional ionization throughout quiescent molecular clouds is very low that we may safely ignore the electronic contribution.
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