Measurements of the physical conditions in molecular clumps are key to our understanding of star formation. Formaldehyde (H_2_CO) is a molecule prevalent in these regions that can be used as diagnostic for the physical conditions in them. 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 lessen the discrepancy between the measurements between gas densities derived from molecular tracers and those derived of dust observations. The clumps have been 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{deg}<=l<=36{deg}, and the molecular cloud associated with the HII regions in the Lagoon nebula (M8). 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 reproduce the observed line intensities in the sources with volume densities n(H_2_)=5.4x10^4^-3.8x10^5^cm^-3^, gas kinetic temperatures Tgas=16-219K, and H_2_CO column densities N(H_2_CO)=6.0x10^12^-1.6x10^15^cm^-2^. The gas kinetic temperatures obtained from the non-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 overestimated by up to 0.5dex. The measured volume densities 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 to constrain the physical conditions in various phases of star formation more effectively.
Cone search capability for table J/A+A/708/A201/tablea (Overview of source list (tables A1-A4))
