Estimating the dense gas mass of molecular clouds using spatially unresolved 3mm line observations

¹ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université Paul Sabatier, Toulouse cedex 4, France
² IRAM, 300 rue de la Piscine, 38406 Saint Martin d’Hères, France
³ LUX, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 75014 Paris, France
⁴ Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-Lab, Grenoble 38000, France
⁵ Univ. Lille, CNRS, Centrale Lille, UMR 9189 - CRIStAL, 59651 Villeneuve d’Ascq, France
⁶ LUX, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 92190 Meudon, France
⁷ Department of Earth, Environment, and Physics, Worcester State University, Worcester, MA 01602, USA
⁸ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA, 02138, USA
⁹ Department of Astronomy, University of Florida, PO Box 112055, Gainesville, FL 32611, USA
¹⁰ Instituto de Física Fundamental (CSIC). Calle Serrano 121, 28006 Madrid, Spain
¹¹ Université de Toulon, Aix Marseille Univ, CNRS, IM2NP, Toulon, France
¹² Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
¹³ Fakultät für Physik und Astronomie, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
¹⁴ National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
¹⁵ Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Allee Geoffroy Saint-Hilaire, 33615 Pessac, France
¹⁶ Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile
¹⁷ Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, Sorbonne Paris Cité, Paris, France
¹⁸ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
¹⁹ School of Physics and Astronomy, Cardiff University, Queen’s buildings, Cardiff CF24 3AA, UK

^★ Corresponding author: azakardjian@irap.omp.eu

Received: 11 April 2025
Accepted: 27 August 2025

Abstract

Context. Emission lines such as HCN(J = 1 → 0) are commonly used by extragalactic studies to trace high density molecular gas (n_H2 > ~ 10⁴ cm⁻³). Recent Milky Way studies have challenged their utility as unambiguous dense gas tracers, suggesting that a large fraction of their emission in nearby clouds is excited in low density gas.

Aims. We aim to develop a new method to infer the sub-beam probability density function (PDF) of H₂ column densities and the dense gas mass within molecular clouds using spatially unresolved observations of molecular emission lines in the 3 mm band.

Methods. We modelled spatially unresolved line integrated intensity measurements as the average of an emission function weighted by the sub-beam column density PDF. The emission function, which expresses the line integrated intensity as a function of the gas column density, is an empirical fit to high resolution (< 0.05 pc) multi-line observations of the Orion B molecular cloud. We assumed the column density PDF to be parametric, composed of a log-normal distribution at moderate column densities and a power-law distribution at higher column densities. To estimate the sub-beam column density PDF, we combined the emission model with a Bayesian inversion algorithm (implemented in the BEETROOTS code), which takes account of thermal noise and calibration errors.

Results. We validate our method by demonstrating that it recovers the true column density PDF of the Orion B cloud and reproduces the observed emission line integrated intensities within noise and calibration uncertainties. We applied the method to ¹²CO(J =1 → 0), ¹³CO(J =1 → 0), C¹⁸O(J =1 → 0), HCN(J =1 → 0), HCO⁺ ( J = 1 → 0) and N₂H⁺(J =1 → 0) observations of a 700 × 700 pc² field of view (FoV) in the nearby galaxy M51. On average, the model reproduces the observed intensities within 30%. The column density PDFs obtained for the spiral arm region within our test FoV are dominated by a power-law tail at high column densities, with slopes that are consistent with gravitational collapse. Outside the spiral arm, the column density PDFs are predominantly log-normal, consistent with supersonic isothermal turbulence setting the dynamical state of the molecular gas. We calculated the mass associated with the power-law tail of the column density PDFs and observe a strong, linear correlation between this mass and the 24 μm surface brightness.

Conclusions. Our method is a promising approach to infer the physical conditions within extragalactic molecular clouds using spectral line observations that are feasible with current millimetre facilities. Future work will extend the method to include additional physical parameters that are relevant for the dynamical state and star formation activity of molecular clouds.