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Astron. Astrophys. 356, 1149-1156 (2000)

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3. Free-bound transitions

Free-bound transitions provide a considerable fraction to the NIR-emission of H II regions. Our aim is to recapitulate the existing theory and combine it with the free-free emission. We assume thermodynamic equilibrium, allowing Saha's equation to be used. From this, one obtains the Milne relation

[EQUATION]

Karzas & Latter (1962) obtained for hydrogenic atoms the cross section

[EQUATION]

with a Gaunt factor [FORMULA] depending on the radial and angular quantum numbers [FORMULA]. This Gaunt factor is usually of order unity. The number of emitted photons

[EQUATION]

times [FORMULA]d[FORMULA] integrated over the electron velocity distribution results in

[EQUATION]

[EQUATION]

which is the emissivity for radiative recombinations to states of radial quantum number n. The spectral emissivity for all recombinations is the sum over all transitions to ionization energies [FORMULA] less than the photon energy. So

[EQUATION]

is the free-bound emissivity for hydrogenic ions of charge Z. For the sake of convenience we use the approximation of Brussaard & van de Hulst (1962) to evaluate the sum in Eq. 32. The emission spectrum of free-free and free-bound transitions has been combined in Fig. 2. At NIR-frequencies the free-bound radiation dominates over free-free emission.

[FIGURE] Fig. 2. The spectrum of free-free and free-bound radiation (solid line), which has been scaled to unity for [FORMULA] GHz. We take [FORMULA] K. The dotted line represents the classical approximation by Oster (1961). The free-free emission alone is shown as dashed line. The low-energy limit of Menzel & Pekeris (1935) is shown as dashed-[FORMULA]dotted.

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© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000
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