Gravitationally bound gas determines star formation in the Galaxy

¹ National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
² University of Chinese Academy of Sciences, Beijing 100049, China
³ School of Astronomy and Space Science, Nanjing University, Nanjing 210093, China
⁴ Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education, Nanjing 210093, China
⁵ Department of Astronomy, The University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712-1205, USA
⁶ Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, China
⁷ New Cornerstone Science Laboratory, Department of Astronomy, Tsinghua University, Beijing 100084, China
⁸ Zhejiang Lab, Hangzhou 311121, China
⁹ Physics Department, National Sun Yat-Sen University, Kaohsiung City 80424, Taiwan
¹⁰ Center of Astronomy and Gravitation, National Taiwan Normal University, Taipei 116, Taiwan
¹¹ School of Physical Science and Technology, Guangxi University, Nanning 530004, China
¹² Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA
¹³ Centre for Astrochemical Studies, Max-Planck-Institut für Extraterrestrische Physik, Gießenbachstraße 1, 85748 Garching, Germany
¹⁴ Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
¹⁵ Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing 210023, China

^★ Corresponding authors: sihanjiao@nao.cas.cn; jingwen@ucas.ac.cn

Received: 24 December 2024
Accepted: 19 June 2025

Abstract

Stars form from molecular gas under complex conditions influenced by multiple competing physical mechanisms, such as gravity, turbulence, and magnetic fields. However, accurately identifying the fraction of gas actively involved in star formation remains challenging. Using dust continuum observations from the Herschel Space Observatory, we derived column density maps and their associated probability distribution functions (N-PDFs). Assuming that the power-law component in the N-PDFs corresponds to gravitationally bound (and thus star-forming) gas, we analyzed a diverse sample of molecular clouds spanning a wide range of mass and turbulence conditions. This sample included 21 molecular clouds from the solar neighborhood (d < 500 pc) and 16 high-mass star-forming molecular clouds. For these two groups, we employed the counts of young stellar objects (YSOs) and mid to far-infrared luminosities as proxies for star formation rates (SFRs), respectively. Both groups revealed a tight linear correlation between the mass of the gravitationally bound gas and the SFR, suggesting a universally constant star formation efficiency in the gravitationally bound gas phase. The star-forming gas mass derived from threshold column densities (N_threshold) varies from cloud to cloud and is widely distributed over the range of ~1–17×10²¹ cm⁻² based on N-PDF analysis. However, in solar neighborhood clouds it is in rough consistency with the traditional approach using A_V≥ 8 mag. In contrast, in highly turbulent regions (e.g., the Galactic Central Molecular Zone) where the classical approach fails, the gravitationally bound gas mass and SFR still follow the same correlation as other high-mass star-forming regions in the Milky Way. Our findings also strongly support the interpretation that gas in the power-law component of the N-PDF is undergoing self-gravitational collapse to form stars.