Annu. Rev. Astron. Astrophys. 1992. 30: 575-611
Copyright © 1992 by . All rights reserved


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3. FREE-FREE EMISSION AND ABSORBTION

The thermal (free-free) radio luminosity of a normal galaxy indicates the total photoionization rate and hence the current number of the most massive short-lived stars. At low radio frequencies, free-free absorption affects both the thermal and synchrotron sources in normal galaxies, determining their radio spectra and limiting their maximum brightness temperatures to Tb ~ 10 5 K at GKz frequencies.

3.1 Basic Equations

The free-free absorption coefficient of an H II region is well approximated by

where ne is the electron density, Te the electron temperature, and the radio frequency expressed in the units indicated. The opacity = dl integrated along the line of sight is often written in terms of the emission measure EM ne2 dl (cm -6 pc). The free-free emission coefficient is = B , with B = 2kTe2/c2 at radio frequencies. At sufficiently high frequencies such that 1, the thermal spectral luminosity LT of an H II region photoionized by hot stars is proportional to the production rate Nuv of Lyman continuum photons and varies only weakly with Te (Rubin 1968). The value of Nuv can be estimated from

The inequality allows for possible absorption of Lyman continuum photons by dust. Values for the unknown Te range from 5 x 103 K to 104 K in our galaxy (Downes et al. 1980) and are thought to be comparable in other normal galaxies. The thermal luminosity of our galaxy is LT ~ 2.5 x 1020 W Hz-1 near = 1 GHz (Berkhuijsen 1984). The thermal luminosity LT = 4d2ST of M82 at distance d = 3.2 Mpc based on the thermal flux density ST ~ 0.7 Jy at 1 GHz (Figure 1) is LT ~ 1021 W Hz-1, indicating Nuv ~ 6 x 1053 s-1.

The thermal flux density ST may be compared with other measures of Nuv such as the (extinction corrected) H line flux F(H ). If N(He+) / N(H+)~ 0.08, then (Caplan & Deharveng 1986)

The ratios of other frequently observed optical and near-infrared recombination line fluxes to F(H ) are

These approximations, based on the tables of Hummer & Storey (1987), are good to ~1% for 102 cm-3 < ne < 104 cm-3 and 5 x 103 K < Te < 104 K. The flux F(Br ) ~ 2 x 10-11 erg cm-2 s-1 of M82 (Willner et al. 1977) is consistent with the observed thermal flux density, based on Equations 3 and 4b.

The merits of radio continuum and optical/infrared recombination lines for detecting H II regions, measuring extinction, and deriving Nuv were compared by Kennicutt & Pogge (1990). Radio observations are generally best for extremely luminous H II regions or compact starbursts with high dust extinction even at near-infrared wavelengths. However, care must be taken to avoid contamination by nonthermal emission in giant H II regions (Condon & Yin 1990, Viallefond 1991).

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