Title:Pumping of the 4.8 GHz H$_{\text{2}}$CO masers and its implications for the periodic masers in G37.55+0.20

Abstract:Periodic or regular flaring of class II methanol masers in nine high mass star forming regions is now a well established phenomenon. Amongst the nine star forming regions, G37.55+0.20 is the only case at present where apart from the presence of a periodic class II methanol maser, correlated flaring of another masing species, formaldehyde in this case, has been detected. We perform numerical calculations to investigate under which conditions the 4.8 GHz transition of ortho-formaldehyde is inverted in order to address the question of the correlated flaring of the 6.7 GHz methanol and 4.8 GHz formaldehyde masers in G37.55+0.20. We developed a numerical code to study the population inversion of o-formaldehyde. Equilibrium solutions for the level populations are found by integrating the rate equations using Heun's method. It is found that collisional excitation with H$_2$ as well as radiative excitation by the free-free radio continuum radiation from a nearby ultra- or hyper-compact HII region can invert the 4.8 GHz transition. It is also found that radiative excitation by the dust infrared radiation field does not lead to an inversion of the 4.8 GHz transition. The 14.5 GHz and 28.9 GHz transitions are inverted only in the presence of the free-free continuum radiation field of a very compact HII region. Due to the different pumping mechanisms of the formaldehyde and methanol masers it is unlikely that the near simultaneous flaring of the methanol and formaldehyde masers in G37.55+0.20 is due to changes in the pumping of the masers.