Revisiting the formaldehyde masers

Centre for Space Research, North-West University, Potchefstroom 2520, South Africa
e-mail: johan.vanderwalt@nwu.ac.za

Received: 16 July 2021
Accepted: 30 November 2021

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.