2024MNRAS.534.1787V

We present new results of a numerical study of the pumping of 4.8 and 14.5 GHz maser of o-$\mathrm{H_2CO}$ in the presence of a free-free radiation field. It is shown that in the presence of a free-free radiation field inversion of not only the $1_{10}{\!-\!}1_{11}$, but also the $2_{11}{\!-\!}2_{12}$ and other doublet state transitions occur. Further results are presented to illustrate how, as a consequence of the pumping scheme, the inversion of the $1_{10}{\!-\!}1_{11}$ and $2_{11}{\!-\!}2_{12}$ transitions respond to the free-free radiation fields associated with H II regions with different emission measures and levels of geometric dilution with respect to the masing region. We also discuss the criticism raised in the past by various authors against the pumping of the 4.8 GHz $\mathrm{H_2CO}$ masers by a free-free radiation field. It is argued that the rarity of the $\mathrm{H_2CO}$ masers is not to be ascribed to the pumping scheme but to other factors such as, e.g. the evolution of the associated H II region or the chemical evolution of the star-forming region that determines the $\mathrm{H_2CO}$ abundance or a combination of both.