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

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1. Introduction - The radio/IR emission from star-forming regions

Massive stars are preferentially formed in dense cores of molecular clouds. Photons emitted by the stars beyond the Lyman continuum (Lyc) limit ([FORMULA]Å) ionize the surrounding gas, which emits the absorbed energy as free-free, free-bound and - after recombination - as bound-bound emission. The recombined and still excited atoms decay to the ground state faster than they are reionized.

In this paper we present a calculation from first principles of the free-free emission for the case of a non-relativistic hydrogen gas, including recombination radiation. We compare the results with widely used analytical approximations for the low and the high frequency limits. Our results yield a consistent description of the Gaunt factor for the entire frequency range. In particular, the domain between the low and the high frequency approximations around [FORMULA]GHz is of interest for a comparison between free-free and dust emission from H II regions.

In describing H II regions it is usually assumed (but is correct only for electron densities [FORMULA]) that all Lyc-photons absorbed by the gas, [FORMULA], decay into Ly[FORMULA] photons ([FORMULA]) which eventually get absorbed by dust inside and surrounding the H II region. Stellar radiation [FORMULA] longward of the Lyc-limit


is absorbed by dust in the compact H II region (absorption optical depth [FORMULA]) and in the molecular cloud ([FORMULA]) or alternatively escapes to reach the observer. [FORMULA] is the column density of stars of a given spectral type i and [FORMULA] their radius. Free-free and free-bound emission


is absorbed by dust in the molecular cloud, where here and in the following ff+ implies the sum of free-free and free-bound transitions. We neglect absorption of ff+ emission by dust inside the H II region. Dust gets heated by absorption of direct and indirect stellar radiation to an average dust temperature [FORMULA] resulting in thermal emission from dust


Hence the total continuum emission of an HII region is


with [FORMULA] the Planck function and [FORMULA] the electron temperature in the ionized gas. The use of the Planck function for free-free emission is valid only for thermal electron distributions and must be replaced by a general source function otherwise. This is treated in Sect. 2. Typical parameters of H II regions are [FORMULA]K and [FORMULA]K. Stellar temperatures of ionizing stars (spectral type B0 and earlier) are [FORMULA]K producing an emission rate of ionizing photons [FORMULA]s-1 and luminosities [FORMULA]. Usually free-free emission dominates the radio spectrum ([FORMULA]Hz), dust emission the submm through MIR regime ([FORMULA]) and stellar and/or free-bound emission the NIR continuum ([FORMULA]). Dust ([FORMULA] K) affects the NIR spectrum mainly by absorption as shown in Eq. 4.

About thirty years ago it was realized that Eq. 4 - applied to the observed spectrum of planetary nebulae and compact H II regions - can be used to determine the stellar parameters [FORMULA] and [FORMULA] as well as the extinction of dust located in front of the ionizing stars. From the free-free flux density at a radio frequency where [FORMULA], one can predict [FORMULA] at NIR wavelengths and estimate with Eq. 4 dust absorption or stellar radiation. Willner et al. (1972) - using the Gaunt factor computed and tabulated by Karzas & Latter (1962) - applied this observing strategy to planetary nebulae and found in most cases excess emission at NIR wavelengths, which they attributed to very hot ([FORMULA]K) dust. Wynn-Williams et al. (1972) observed and compared the radio and MIR/NIR emission from compact H II regions located in the giant H II region W 3. They modeled the [FORMULA]m part of the spectrum with emission from 150 K dust mixed with the ionized gas, and explained a deficiency of the observed K-band ([FORMULA]m) flux density by dust absorption of up to [FORMULA]. Both investigations indicated that free-free and free-bound emission dominate the emission in the NIR regime. Only in one case was excess NIR emission observed and attributed to a point source, thought to be a heavily obscured O star.

In the following we consider the contribution of free-free and free-bound radiation from radio to NIR wavelengths emission. We compute the spectra of ionized gas in Sects. 2 and 3, and discuss its contribution to the spectrum and total luminosity of an H II region in Sect. 4. We find the most interesting application in metal-free H II regions which we treat in Sect. 5. We present our conclusions in Sect. 6.

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© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000