Astronomy & Astrophysics A&A 666, A165 (2022) https://doi.org/10.1051/0004-6361/202039610 © N. Schneider et al. 2022 Understanding star formation in molecular clouds IV. Column density PDFs from quiescent to massive molecular clouds N. Schneider 1 , V. Ossenkopf-Okada 1 , S. Clarke 1,2 , R. S. Klessen 3 , S. Kabanovic 1 , T. Veltchev 4 , S. Bontemps 5 , S. Dib 5,6 , T. Csengeri 5 , C. Federrath 7 , J. Di Francesco 8,9 , F. Motte 10 , Ph. André 11 , D. Arzoumanian 12 , J. R. Beattie 7 , L. Bonne 5,13 , P. Didelon 11 , D. Elia 14 , V. Könyves 15 , A. Kritsuk 16 , B. Ladjelate 17 , Ph. Myers 18 , S. Pezzuto 14 , J. F. Robitaille 10 , A. Roy 5 , D. Seifried 1 , R. Simon 1 , J. Soler 6 , and D. Ward-Thompson 15 1 I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany e-mail: nschneid@ph1.uni-koeln.de 2 Academia Sinica, Institute of Astronomy and Astrophysics, Taipei, Taiwan 3 Institut für Theoretische Astrophysik, Zentrum für Astronomie, Universität Heidelberg, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany 4 Faculty of Physics, University of Sofia, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria 5 Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée G. Saint-Hilaire, 33615 Pessac, France 6 Max Planck Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany 7 Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia 8 Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada 9 NRC Herzberg Astronomy and Astrophysics, 5071 West Saanich Road, Victoria, BC V9E 2E7, Canada 10 Université Grenoble Alpes, CNRS, Institut de Planétologie et d’Astrophysique de Grenoble, 38000 Grenoble, France 11 Laboratoire AIM, CEA/DSM-CNRS-Université Paris Diderot, IRFU/SAP, CEA Saclay, 91191 Gif-sur-Yvette, France 12 Division of Science, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan 13 SOFIA Science Center, NASA Ames Research Center, Moffett Field, CA 94 045, USA 14 INAF – IAPS, via Fosso del Cavaliere, 100, 00133 Roma, Italy 15 University of Central Lancashire, Preston, Lancashire PR1 2HE, UK 16 Physics Dep. and CASS, University of California, San Diego, La Jolla, CA 92093-0424, USA 17 IRAM, Avda. Divina Pastora 7, Local 20, 18012 Granada, Spain 18 Center for Astrophysics, Harvard and Smithsonian, Cambridge, MA 02138, USA Received 7 October 2020 / Accepted 12 July 2022 ABSTRACT Probability distribution functions of the total hydrogen column density (N-PDFs) are a valuable tool for distinguishing between the various processes (turbulence, gravity, radiative feedback, magnetic fields) governing the morphological and dynamical structure of the interstellar medium. We present N-PDFs of 29 Galactic regions obtained from Herschel imaging at high angular resolution (18 ′′ ), covering diffuse and quiescent clouds, and those showing low-, intermediate-, and high-mass star formation (SF), and characterize the cloud structure using the Δ-variance tool. The N-PDFs show a large variety of morphologies. They are all double-log-normal at low column densities, and display one or two power law tails (PLTs) at higher column densities. For diffuse, quiescent, and low-mass SF clouds, we propose that the two log-normals arise from the atomic and molecular phase, respectively. For massive clouds, we suggest that the first log-normal is built up by turbulently mixed H 2 and the second one by compressed (via stellar feedback) molecular gas. Nearly all clouds have two PLTs with slopes consistent with self-gravity, where the second one can be flatter or steeper than the first one. A flatter PLT could be caused by stellar feedback or other physical processes that slow down collapse and reduce the flow of mass toward higher densities. The steeper slope could arise if the magnetic field is oriented perpendicular to the LOS column density distribution. The first deviation point (DP), where the N-PDF turns from log-normal into a PLT, shows a clustering around values of a visual extinction of A V (DP1) ∼ 2–5. The second DP, which defines the break between the two PLTs, varies strongly. In contrast, the width of the N-PDFs is the most stable parameter, with values of σ between ∼0.5 and 0.6. Using the Δ-variance tool, we observe that the A V value, where the slope changes between the first and second PLT, increases with the characteristic size scale in the Δ-variance spectrum. We conclude that at low column densities, atomic and molecular gas is turbulently mixed, while at high column densities, the gas is fully molecular and dominated by self-gravity. The best fitting model N-PDFs of molecular clouds is thus one with log-normal low column density distributions, followed by one or two PLTs. Key words. methods: statistical – ISM: clouds – dust, extinction – ISM: general – evolution – ISM: structure 1. Introduction Important tools for characterizing molecular clouds are probabil- ity distribution functions of density (ρ-PDF) and column density (N-PDF) because they can be directly linked to theories of the star formation process (e.g., Padoan et al. 1997, 2002; Vázquez- Semadeni & Garcia 2001; Hennebelle & Chabrier 2008, 2009; Federrath & Klessen 2012; Burkhart 2018). Numerical simula- tions that include or exclude particular physical processes (such as solenoidally or compressively driven turbulence, radiative A165, page 1 of 52 Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is published in open access under the Subscribe-to-Open model. Subscribe to A&A to support open access publication.