Gas phase Elemental abundances in Molecular cloudS (GEMS)

VIII. Unlocking the CS chemistry: The CH + S → CS + H and C₂ + S → CS + C reactions

¹ Laboratory for Astrophysics, Leiden Observatory, Leiden University, PO Box 9513, 2300-RA, Leiden, The Netherlands
² Instituto de Física Fundamental (IFF-CSIC), C.S.I.C., Serrano 123, 28006 Madrid, Spain
e-mail: octavio.roncero@csic.es
³ University of Firat, Department of Physics, 23169 Elazig, Turkey
⁴ Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun, Grudziadzka 5, 87-100 Torun, Poland
⁵ Université Paris-Saclay, CEA, AIM, Département d’Astrophysique (DAp), 91191 Gif-sur-Yvette, France
⁶ Observatorio Astronómico Nacional (IGN), c/ Alfonso XII 3, 28014 Madrid, Spain
⁷ Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France
⁸ Institut des Sciences Moléculaires (ISM), CNRS, Univ. Bordeaux, 351 cours de la Libération, 33400 Talence, France
⁹ Sorbonne Université, Observatoire de Paris, Univerité PSL, CNRS, LERMA, 92190 Meudon, France
¹⁰ Centre for Astrochemical Studies, Max-Planck-Institute for Extraterrestrial Physics, Giessenbachstrasse 1, 85748 Garching, Germany
¹¹ Institut de Planétologie et d’Astrophysique de Grenoble (IPAG), Université Grenoble Alpes, CNRS, 38000 Grenoble, France
¹² Institut de Radioastronomie Millimétrique (IRAM), 300 Rue de la Piscine, 38406 Saint-Martin-d’Hères, France

Received: 22 May 2023
Accepted: 29 June 2023

Abstract

Context. Carbon monosulphide (CS) is among the few sulphur-bearing species that have been widely observed in all environments, including in the most extreme, such as diffuse clouds. Moreover, CS has been widely used as a tracer of the gas density in the interstellar medium in our Galaxy and external galaxies. Therefore, a complete understanding of its chemistry in all environments is of paramount importance for the study of interstellar matter.

Aims. Our group is revising the rates of the main formation and destruction mechanisms of CS. In particular, we focus on those involving open-shell species for which the classical capture model might not be sufficiently accurate. In this paper, we revise the rates of reactions CH + S → CS + H and C₂ + S → CS + C. These reactions are important CS formation routes in some environments such as dark and diffuse warm gas.

Methods. We performed ab initio calculations to characterize the main features of all the electronic states correlating to the open shell reactants. For CH+S, we calculated the full potential energy surfaces (PESs) for the lowest doublet states and the reaction rate constant with a quasi-classical method. For C₂+S, the reaction can only take place through the three lower triplet states, which all present deep insertion wells. A detailed study of the long-range interactions for these triplet states allowed us to apply a statistic adiabatic method to determine the rate constants.

Results. Our detailed theoretical study of the CH + S → CS + H reaction shows that its rate is nearly independent of the temperature in a range of 10–500 K, with an almost constant value of 5.5 × 10⁻¹¹ cm³ s⁻¹ at temperatures above 100 K. This is a factor of about 2–3 lower than the value obtained with the capture model. The rate of the reaction C₂ + S → CS + C does depend on the temperature, and takes values close to 2.0 × 10⁻¹⁰ cm³ s⁻¹ at low temperatures, which increase to ~ 5.0 × 10⁻¹⁰ cm³ s⁻¹ for temperatures higher than 200 K. In this case, our detailed modeling - taking into account the electronic and spin states – provides a rate that is higher than the one currently used by factor of approximately 2.

Conclusions. These reactions were selected based on their inclusion of open-shell species with many degenerate electronic states, and, unexpectedly, the results obtained in the present detailed calculations provide values that differ by a factor of about 2–3 from the simpler classical capture method. We updated the sulphur network with these new rates and compare our results in the prototypical case of TMC1 (CP). We find a reasonable agreement between model predictions and observations with a sulphur depletion factor of 20 relative to the sulphur cosmic abundance. However, it is not possible to fit the abundances of all sulphur-bearing molecules better than a factor of 10 at the same chemical time.