The most important external source of gas heating for opaque clouds is cosmic rays. Relativistic protons ionize H2, liberating electrons which then dissociate other, still intact molecules. The creation of ions within a cloud facilitates reactions that produce most molecules. One of these is OH, measurement of whose abundance allows one to determine empirically the cosmic-ray ionization rate.
Ultraviolet radiation is another source of thermal energy. The flux from field stars readily ionizes carbon in HI clouds. Again, it is the ejected electron that actually provides heating. The same radiation can also liberate electrons directly from the surfaces of dust grains. Those photons absorbed internally by the dust serve to raise its temperature to a value generally different from that of the gas. The ultraviolet radiation from a massive star can warm gas out to a great distance. Low-mass stars, on the other hand, provide heating through their X-rays. Here, the effect is more localized.
It is the minor constituents within a cloud, rather than the hydrogen itself, that emit energy into space. Hydrogen collides with O I and C II, exciting fine-structure levels that decay through far-infrared lines. The most important coolant in molecular clouds is CO. Photons from the lowest-lying rotational transitions become trapped inside the cloud, while those from higher levels escape from its surface. Finally, gas transfers energy by collisions to dust grains. These, in turn, radiate into the infrared continuum.
3 The average kinetic energy a molecule imparts to the grain surface is actually 2 kB Tg, since faster molecules, while rarer, hit more often. We ignore this correction, as well as the finite probability that molecules bounce instead of sticking to the grain.
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