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

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6. Conclusions

We have demonstrated the importance of detailed calculations for thermal Gaunt factors of free-free emission. While the usual approximations in the radio and IR spectral bands are sufficient, there is a gap in frequencies where one has to rely on tabulated values or use a more sophisticated method as suggested here. For wavelength less than 100 µm free-bound transitions start to dominate over bremsstrahlung for [FORMULA] K. We have not gone beyond the standard formula for the free-bound transition but provide a short summary of that process. Despite their importance from the radio to NIR energy bands the total cooling of present day H II regions around massive stars is supported by line emission of heavier elements as is well known (Osterbrock 1989). We show that free-free, free-bound and subsequent bound-bound radiation can account for roughly 70% of the cooling. The first stars born out of primordial hydrogen and helium will produce H II regions, which expand into a surrounding medium still of primordial constituents. So the temperature in these first H II regions around massive stars will be determined by bremsstrahlung, recombination radiation and bound-bound transitions either as follow up to recombination to excited levels of hydrogen and helium or induced by collisions (see the compilation of Katz et al. 1996, for instance). During the expansion of the ionized region down to pressure balance with the surrounding medium or the end of the ionizing radiation, an ionization front will propagate and consume a large fraction of the ionizing photons. Assuming local ionization and thermal equilibrium inside the H II region, we derive temperatures ranging from [FORMULA] K in a dense inner He III region to an intermediate regime of [FORMULA] K for hot stars and a drop to [FORMULA] K for the main part of extended H II regions produced by all ionizing stars. The temperature drops to roughly [FORMULA] K as the ionization balance allows for a significant fraction of neutral hydrogen in the outermost parts. The evolution of an H II region to this stage takes approximately [FORMULA] years and has to be compared with the lifetime of the ionizing source.

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© European Southern Observatory (ESO) 2000

Online publication: April 17, 2000