ALMA-IMF

XIX. C¹⁸O (J = 2–1): Measurements of turbulence in 15 massive protoclusters

¹ Departamento de Astronomía, Universidad de Concepción, Casilla 160-C, Concepción, Chile
² Franco-Chilean Laboratory for Astronomy, IRL 3386, CNRS and Universidad de Chile, Santiago, Chile
³ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁴ Department of Astronomy, University of Florida, PO Box 112055, USA
⁵ Instituto de Radioastronomía y Astrofísica, Universidad Nacional Autónoma de México, Morelia, Michoacán 58089, Mexico
⁶ National Astronomical Observatory of Japan, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁷ Department of Astronomical Science, SOKENDAI (The Graduate University for Advanced Studies), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
⁸ S. N. Bose National center for Basic Sciences, Sector-III, Salt Lake, Kolkata 700106, India
⁹ Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
¹⁰ Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain
¹¹ Institut d’Estudis Espacials de Catalunya (IEEC), Esteve Terradas 1, Edifici RDIT, Ofic. 212 Parc Mediterrani de la Tecnologia (PMT) Campus del Baix LLobregat -– UPC 08860 Castelldefels (Barcelona), Catalonia, Spain
¹² Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, UMR 5804, 33615 Pessac, France
¹³ School of Physics and Astronomy, Yunnan University, Kunming, 650091, PR China
¹⁴ Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France
¹⁵ Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, 75005 Paris, France
¹⁶ Observatoire de Paris, PSL University, Sorbonne Université, LERMA, 75014 Paris, France
¹⁷ Instituto Argentino de Radioastronomía (CCT-La Plata, CONICET; UNLP; CICPBA), C.C. No. 5, 1894, Villa Elisa, Buenos Aires, Argentina
¹⁸ SKA Observatory, Jodrell Bank, Lower Withington, Macclesfield SK11 9FT, UK
¹⁹ Astronomy Department, Universidad de Chile, Casilla 36-D, Santiago, Chile
²⁰ Departments of Astronomy and Chemistry, University of Virginia, Charlottesville, VA 22904, USA

^★ Corresponding author: atanuphysics15@gmail.com

Received: 20 January 2025
Accepted: 8 August 2025

Abstract

ALMA-IMF is a Large Program of the Atacama Large Millimeter/submillimeter Array (ALMA) that aims to determine the origin of the core mass function (CMF) of 15 massive Galactic protoclusters (~1.0–25.0 × 10³ M_⊙ within ~2.5 × 2.5 pc²) located toward the Galactic plane. In addition, the objective of the program is to obtain a thorough understanding of their physical and kinematic properties. Here we study the turbulence in these protoclusters with the C¹⁸O (2–1) emission line using the sonic Mach number analysis (M_s) and the size-linewidth relation. The probability distribution functions (PDFs) for M_s show a similar pattern, exhibiting no clear trend associated with evolutionary stage, peaking in the range between 4 and 7, and then extending to ~25. Such values of M_s indicate that the turbulence in the density regime traced by the C¹⁸O line inside the protoclusters is supersonic in nature. In addition, we compared the non-thermal velocity dispersions (σ_nth,C¹⁸O) obtained from the C¹⁸O (2–1) line with the non-thermal line widths (σ_{nth, DCN}) of the cores obtained from the DCN (3–2) line. We observed that, on average, the non-thermal linewidth in cores is half that of the gas surrounding them. This suggests that turbulence diminishes at smaller scales or dissipates at the periphery of the cores. Furthermore, we examined the size-linewidth relation for the structures we extracted from the position-position-velocity C¹⁸O (2–1) line emission cube with the dendrogram algorithm. The power-law index (p) obtained from the size-linewidth relation is between 0.41 and 0.64, steeper than the Kolmogorov law of turbulence, as expected for compressible media. In conclusion, this work is one of the first to carry out a statistical study of turbulence for embedded massive protoclusters.