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Context . Measurements of the physical conditions in molecular clumps are key to our understanding of star formation. Formaldehyde (H 2 CO) is a prevalent molecule in these regions, and it can be used as a diagnostic of the physical conditions. Aims . Here we explore a technique for determining the volume density and gas kinetic temperature in molecular clumps across various evolutionary phases and environments. The ground-state transition of H 2 CO has a critical density of n crit ∼ 10 4 cm −3 , allowing us to use this molecule as a densitometer at n ≤ 10 5 cm −3 and to lessen the discrepancy between the measurements between gas densities derived from molecular tracers and those derived from dust observations. Methods . The clumps in our study were observed with the IRAM 30-m telescope, marking the first extensive survey of the H 2 CO (1 0,1 − 0 0,0 ) line across a large sample of sources. These observations were complemented by the H 2 CO J = 3 − 2 lines, obtained using the APEX telescope. These clumps have been surveyed in three regions, the Cygnus-X giant molecular cloud complex, the GLOSTAR pilot region covering the Galactic plane at longitudes 28° ≤ l ≤ 36°, and the molecular cloud associated with the HII regions in the Lagoon nebula (M8). Results . We analyzed a total of 127 clumps, including 78 from Cygnus-X, 12 from the GLOSTAR pilot region, and 37 from M8. We derived the gas kinetic temperature, volume densities and H 2 CO column densities using radiative transfer modeling with pyradex+emcee in 102 clumps. We reproduced the observed line intensities in the sources with volume densities n (H 2 ) = 5.4 × 10 4 −3.8 × 10 5 cm −3 , gas kinetic temperatures T gas = 16−219 K, and H 2 CO column densities N (H 2 CO) = 6.0 × 10 12 −1.6 × 10 15 cm −2 . Conclusions . The gas kinetic temperatures obtained from the non-local thermodynamic equilibrium (LTE) modeling with pyradex+emcee agree well with the LTE gas kinetic temperature obtained from the ratio of H 2 CO (3 0,3 − 2 0,2 ) and H 2 CO (3 2,1 – 2 2,0 ) lines at densities n (H 2 ) ≤ 10 5.5 cm −3 . However, we find that, at higher densities, LTE temperatures derived from this ratio are over-estimated by up to 0.5 dex. The volume densities we measured are consistent with the volume densities obtained from dust continuum measurements, thereby probing the bulk of the gas. Furthermore, we find that the volume densities and dust temperatures increase with increasing evolutionary phase. The newly available ground-state transition of H 2 CO allows the physical conditions in various phases of star formation to be constrained more effectively.
Christensen et al. (Thu,) studied this question.