Notes on the formaldehyde masers

Context. The 4.8 GHz formaldehyde masers are rare when compared, for example, to the class II methanol masers, especially when both masers are associated with high-mass star-forming regions. Apart from the rarity of the masers, which has not yet been explained, the non-detection of associated 14.5 GHz masers is also still an outstanding question.Aims. The first aim of the present work is to investigate, from a theoretical point of view and with more realistic free-free spectral energy distributions (SEDs), whether there are physical conditions in the molecular envelope under which the 1_{10–111 transition is inverted but not the 211–212 transition. The possibility that the non-detection of 14.5 GHz masers is due to the masing region being projected towards the edge of a background hyper-compact H II region is also investigated. Since the 110–111 transition of ortho-H2CO is known to have an anti-inversion behaviour for typical conditions associated with high-mass star-forming regions, it is possible that attenuation affects the 4.8 and 14.5 GHz masers. The second aim is to estimate to what extent attenuation of the 4.8 and 14.5 GHz H2CO masers in the molecular envelope can explain the small number of detected H2CO masers.Methods. The photo-ionisation code Cloudy was used to calculate more realistic free-free SEDs for a given spectral type of the ionising star and different radial dependences of the initial H I distribution. The free-free SED obtained from the Cloudy simulation was used as the pumping radiation field in the statistical equilibrium calculations.Results. Using a fit from the Cloudy simulations to the observed free-free SED of the hyper-compact H II region G24.78+0.08 A1, it is found that while the 110–111 transition is weakly inverted, the 211–212 transition is not inverted. In this case, inversion of the 110–111 transition is dominated by collisions and the contribution of the free-free radiation field to the inversion is negligible. Analysis of the dependence of the inversion of the 110–111 and 211–212 transitions on distance into the molecular cloud suggests that there are regions in the circumstellar envelope where the 110–111 transition is inverted but not the 211–212 transition. The optical depths at 4.8 and 14.5 GHz were calculated for three different dependences of the abundance of o-H2CO on depth into the molecular cloud, which shows that significant attenuation of the maser emission is possible.Conclusions. Not all hyper-compact H II regions have free-free SEDs that are able to produce strong enough 4.8 GHz masers. Attenuation of the 4.8 GHz maser emission in the molecular envelope can be so significant that the 4.8 GHz maser emission is completely absorbed. Detection of the 14.5 GHz maser associated with the 4.8 GHz maser is not a requirement to prove the free-free pumping of the 4.8 GHz masers.}