Notes on the formaldehyde masers

TL;DR

The paper addresses why 4.8 GHz H$_2$CO masers are rare and why 14.5 GHz masers are not detected by investigating free-free pumping in hyper-compact H II regions. It uses Cloudy to generate realistic free-free SEDs for different radial envelopes and feeds these into rate-equation calculations to assess inversion of the $1_{10}-1_{11}$ and $2_{11}-2_{12}$ transitions, including beaming and projection effects. The key findings show that under some conditions the $1_{10}-1_{11}$ line can be inverted while $2_{11}-2_{12}$ is not, that masers may arise in regions offset toward the H II region edge, and that attenuation by the molecular envelope can be substantial, potentially suppressing detectable maser emission. These results suggest that the observed scarcity arises from a combination of pumping efficiency, geometric projection, and envelope attenuation, with velocity offsets indicating association with rotating toroids or similar kinematic structures, shaping expectations for future observations.

Abstract

The questions of the rarity of the 4.8 GHz formaldehyde masers and the non-detection of 14.5 GHz formaldehyde masers are addressed from a theoretical point of view. The pumping free-free radiation fields were obtained using the photo-ionization code Cloudy to simulate hyper-compact HII regions. Implementation of these free-free radiation fields in solving the rate equations shows that the free-free radiation fields of some hyper-compact HII regions are ineffective to invert the 4.8 GHz transition. Investigation of the variation of the inversion of the 4.8 GHz and 14.5 GHz transitions with radial distance revealed that there are regions where only the 4.8 GHz transition is inverted. It is also shown that the projection of the masing region toward the edge of a hyper-compact may explain the non-detection of 14.5 GHz masers. The attenuation of the 4.8 GHz and 14.5 GHz masers in the molecular envelope is investigated. It is found that attenuation can be significant. Comparison of the velocities of the 4.8 GHz masers with the centre velocities of associated 4.8 GHz absorption features shows that the maser emission lies at the edge of the absorption features. This suggests that the masers may be associated with kinematic structures such as rotating toroids.

Figures (7)

• Figure 1: Comparison of the free-free SEDs used as examples. Filled black circles represent data for G24.78+0.08 A1 Cesaroni2019. The solid black line is the SED calculated with Cloudy and normalised to the data at 44 GHz. The dashed black line is the theoretical SED with $T_K = 10^4$K and EM = $1.3 \times 10^9\,\mathrm{pc\,cm^{-6}}$. The solid blue line is the SED calculated with Cloudy for the second example. The solid red line is a theoretical SED with $T_K = 10^4$K and EM = $3.9 \times 10^{10}\,\mathrm{pc\,cm^{-6}}$.
• Figure 2: Variation in $\tau_{4.8}$ and $\tau_{14.5}$ as a function of radial distance from the ionising star when the Cloudy SED for the hyper-compact HII region G24.78+0.08 A1 is used. The vertical dashed line represents the outer radius of the HII region. For case 1, $n_{H_2}(r_o) = 10^5~\mathrm{cm^{-3}}$ and $T_K(r_o) = 150$ K. For case 2, $n_{H_2}(r_o) = 7\times10^5~\mathrm{cm^{-3}}$ and $T_K(r_o) = 300$ K
• Figure 3: Variation in $\tau_{4.8}$ and $\tau_{14.5}$ as a function of radial distance from the ionising star when the Cloudy SED for the second example (blue line in Fig. \ref{['fig:g24spec']}) is used. Cases 1 and 2 correspond to those used in Fig. \ref{['fig:tauvsrg24']}
• Figure 4: Variation in $\tau_{4.8}$ as a function of radial distance from the ionising star when the Cloudy SED for the second example (blue line in Fig. \ref{['fig:g24spec']}) is used and when beaming is included.
• Figure 5: Variation in the free-free brightness temperature for G32.7441-0.0755 as derived from the publicly available CORNISH data. The vertical line represents the outer edge of the X-band emission estimated from the image in Yang2021.