Quantitative inference of the H₂ column densities from 3 mm molecular emission: case study towards Orion B^★

¹ Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, Allee Geoffroy Saint-Hilaire, 33615 Pessac, France
e-mail: pierre.gratier@u-bordeaux.fr
² IRAM, 300 rue de la Piscine, 38406 Saint Martin d’Hères, France
³ LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 75014 Paris, France
⁴ LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, 92190 Meudon, France
⁵ Aix-Marseille Univ, CNRS, Centrale Marseille, Institut Fresnel, Marseille, France
⁶ Chalmers University of Technology, Department of Space, Earth and Environment, 412 93 Gothenburg, Sweden
⁷ University of Toulouse, IRIT/INP-ENSEEIHT, CNRS, 2 rue Charles Camichel, BP 7122, 31071 Toulouse cedex 7, France
⁸ Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, GIPSA-Lab, Grenoble 38000, France
⁹ Univ. Lille, CNRS, Centrale Lille, UMR 9189 - CRIStAL, 59651 Villeneuve d’Ascq, France
¹⁰ Instituto de Física Fundamental (CSIC). Calle Serrano 121, 28006 Madrid, Spain
¹¹ Instituto de Astrofísica, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, 7820436 Macul, Santiago, Chile
¹² Institut de Recherche en Astrophysique et Planétologie (IRAP), Université Paul Sabatier, Toulouse cedex 4, France
¹³ Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris- Diderot, Sorbonne Paris Cité, Paris, France
¹⁴ National Radio Astronomy Observatory, 520 Edgemont Road, Charlottesville, VA, 22903, USA
¹⁵ School of Physics and Astronomy, Cardiff University, Queen’s buildings, Cardiff CF24 3AA, UK

Received: 3 March 2020
Accepted: 25 August 2020

Abstract

Context. Based on the finding that molecular hydrogen is unobservable in cold molecular clouds, the column density measurements of molecular gas currently rely either on dust emission observation in the far-infrared, which requires space telescopes, or on star counting, which is limited in angular resolution by the stellar density. The (sub)millimeter observations of numerous trace molecules can be effective using ground-based telescopes, but the relationship between the emission of one molecular line and the H₂ column density is non-linear and sensitive to excitation conditions, optical depths, and abundance variations due to the underlying physico- chemistry.

Aims. We aim to use multi-molecule line emission to infer the H₂ molecular column density from radio observations.

Methods. We propose a data-driven approach to determine the H₂ gas column densities from radio molecular line observations. We use supervised machine-learning methods (random forest) on wide-field hyperspectral IRAM-30m observations of the Orion B molecular cloud to train a predictor of the H₂ column density, using a limited set of molecular lines between 72 and 116 GHz as input, and the Herschel-based dust-derived column densities as “ground truth” output.

Results. For conditions similar to those of the Orion B molecular cloud, we obtained predictions of the H₂ column density within a typical factor of 1.2 from the Herschel-based column density estimates. A global analysis of the contributions of the different lines to the predictions show that the most important lines are ¹³CO(1–0), ¹²CO(1–0), C¹⁸O(1–0), and HCO⁺(1–0). A detailed analysis distinguishing between diffuse, translucent, filamentary, and dense core conditions show that the importance of these four lines depends on the regime, and that it is recommended that the N₂H⁺(1–0) and CH₃OH(2₀–1₀) lines be added for the prediction of the H₂ column density in dense core conditions.

Conclusions. This article opens a promising avenue for advancing direct inferencing of important physical parameters from the molecular line emission in the millimeter domain. The next step will be to attempt to infer several parameters simultaneously (e.g., the column density and far-UV illumination field) to further test the method.