Formaldehyde as a densitometer and thermometer in Cygnus-X, the GLOSTAR pilot region, and M8

Utilizing the H₂CO ground-state transition

¹ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
² Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany
³ Max Planck Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁴ Purple Mountain Observatory, and Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, 10 Yuanhua Road, Nanjing 210023, PR China

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 10 November 2025
Accepted: 19 February 2026

Abstract

Context. Measurements of the physical conditions in molecular clumps are key to our understanding of star formation. Formaldehyde (H₂CO) 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 H₂CO has a critical density of n_crit ∼ 10⁴ cm⁻³, allowing us to use this molecule as a densitometer at n ≤ 10⁵ cm⁻³and 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 H₂CO (1_0,1 − 0_0,0) line across a large sample of sources. These observations were complemented by the H₂CO 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 H₂CO 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(H₂) = 5.4 × 10⁴−3.8 × 10⁵ cm⁻³, gas kinetic temperatures T_gas = 16−219 K, and H₂CO column densities N(H₂CO) = 6.0 × 10¹² −1.6 × 10¹⁵ 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 H₂CO (3_0,3 − 2_0,2) and H₂CO (3_2,1 – 2_2,0) lines at densities n(H₂) ≤ 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 H₂CO allows the physical conditions in various phases of star formation to be constrained more effectively.