The ultraviolet component of the radiation field is too weak at energies above 13.6 eV to significantly ionize the hydrogen or helium in molecular clouds. However, a number of heavier elements have lower ionization potentials. Of these, atomic carbon (C I) is the most abundant, with a number density relative to hydrogen of nC/nH = 3 x 10-4 (see Table 2.1). Any photon more energetic than 11.2 eV will eject an electron from C I. Since the kinetic energy of this electron quickly disperses to surrounding atoms through collisions, carbon ionization is an effective heating mechanism. The volumetric heating rate, which we denote as rCI, is then rci = Z(C I) nc AE(C I) . (7.15)
Here, Z(C I) is the ionization rate of a single carbon atom and AE(C I) the average energy of the ejected electron.
The evaluation of both Z(C I) and AE(C I) entails an integration over frequency of the radiation intensity Jv, weighted by the ionization cross section of C I. The result is that Z(C I) = 1 x 10-10 s-1 and AE(C I) = 1 eV. Substituting these values into equation (7.15)
along with the carbon abundance, yields
V103 cm-3 J
Note that our result implicitly assumes that carbon is still mostly in neutral form. In practice, the element can be largely ionized in cloud regions where the heating is significant, and one must reduce rCi appropriately.
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