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

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 (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 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 ) that all Lyc-photons absorbed by the gas, , decay into Ly photons () which eventually get absorbed by dust inside and surrounding the H II region. Stellar radiation longward of the Lyc-limit

is absorbed by dust in the compact H II region (absorption optical depth ) and in the molecular cloud () or alternatively escapes to reach the observer. is the column density of stars of a given spectral type i and 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 resulting in thermal emission from dust

Hence the total continuum emission of an HII region is

with the Planck function and 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 K and K. Stellar temperatures of ionizing stars (spectral type B0 and earlier) are K producing an emission rate of ionizing photons s^-1 and luminosities . Usually free-free emission dominates the radio spectrum (Hz), dust emission the submm through MIR regime () and stellar and/or free-bound emission the NIR continuum (). Dust ( 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 and 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 , one can predict 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 (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 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 (m) flux density by dust absorption of up to . 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.

© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000
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