Revisiting the formaldehyde masers

Abstract

Context. The 4.8 GHz formaldehyde (H2CO) masers are one of a number of rare types of molecular masers in the Galaxy. There still is not agreement on the mechanism responsible for the inversion of the 110−111 transition and the conditions under which an inversion can occur, and therefore how to interpret the masers. Aims. The aim of the present calculations is to explore a larger region of parameter space to improve on our previous calculations, thereby to better understand the range of physical conditions under which an inversion of the 110−111 transition occurs. We also aim to understand recently published results that H2CO masers are radiatively pumped. Methods. We solve the rate equations of the first 40 rotational levels of o-H2CO using a fourth-order Runge-Kutta method. We consider gas kinetic temperatures between 10 and 300 K, H2 densities between 104 and 106 cm−3, and a number of different dust temperatures and grey-body spectral energy density distributions. Results. We show that when using a black body radiation field the inversion of any transition will disappear as the kinetic temperature approaches the black-body radiation temperature since the system, consisting of the gas and radiation field, approaches thermodynamic equilibrium. Using a grey-body dust radiation field appropriate for Arp 220 we find that none of 110−111, 211−212, and 312−313 transitions are inverted for kinetic temperatures less than 100 K. Our calculations also show that in theory the 110−111 transition can be inverted over a large region of explored parameter space in the presence of an external far-infrared radiation field. Limiting the abundance of H2CO to less than 10−5, however, reduces the region where an inversion occurs to H2 densities ≳105 cm−3 and kinetic temperatures ≳100 K. We propose a pumping scheme for the H2CO masers which can explain why collisions play a central role in inverting the 110−111 transition, and therefore why an external radiation field alone does not lead to an inversion. Conclusions. Collisions are an essential mechanism for the inversion of the 110−111 transition. Our results suggest that 4.8 GHz H2CO megamasers are associated with hot and dense gas typical of high mass star forming regions rather than with cold material. Although limiting the H2CO abundance to less than 10−5 significantly reduces the region in parameter space where the 110−111 is inverted, it still is not clear whether this is the only reason why these masers are so rare.