The Rosetta Stone Project

II. The correlation between star formation efficiency and L/M indicator for the evolutionary stages of star-forming clumps in post-processed radiative magnetohydrodynamics simulations

¹ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
² INAF – Istituto di Astrofisica e Planetologia Spaziali (INAF-IAPS), Via Fosso del Cavaliere 100, 00133 Roma, Italy
³ Alma Mater Studiorum Università di Bologna, Dipartimento di Fisica e Astronomia (DIFA), Via Gobetti 93/2, 40129 Bologna, Italy
⁴ INAF – Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy
⁵ Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy
⁶ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
⁷ Universität Heidelberg, Interdisziplinäres Zentrum für Wissenschaftliches Rechnen, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany
⁸ Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, U.S.A.
⁹ Radcliffe Institute for Advanced Studies at Harvard University, 10 Garden Street, Cambridge, MA 02138, U.S.A.
¹⁰ Jodrell Bank Centre for Astrophysics, Department of Physics & Astronomy, The University of Manchester, Oxford Road, Manchester M13 9PL, UK
¹¹ Physikalisches Institut der Universität zu Köln, Zülpicher Str. 77, 50937 Köln, Germany
¹² European Southern Observatory (ESO), Karl-Schwarzschild-Strasse 2, 85748 Garching bei Munchen, Germany

^★ Corresponding author: duy-tung.ngo@cea.fr

Received: 26 March 2025
Accepted: 3 July 2025

Abstract

Context. The evolution of massive star-forming clumps that are progenitors of high-mass young stellar objects are often classified based on a variety of observational indicators ranging from near-infrared to radio wavelengths. Among them, the ratio of the bolometric luminosity to the mass of their envelope, L/M, has been observationally diagnosed as a good indicator for the evolutionary classification of parsec-scale star-forming clumps in the Galaxy.

Aims. We developed the Rosetta Stone project – an end-to-end framework designed to enable an accurate comparison between simulations and observations for investigating the formation and evolution of massive clumps. In this study, we calibrate the L/M indicator in relation to the star formation efficiency (SFE) and the clump age, as derived from our suite of simulations.

Methods. We performed multi-wavelength radiative transfer post-processing of radiative magnetohydrodynamics (RMHD) simulations of the collapse of star-forming clumps fragmenting into protostars. We generated synthetic observations to obtain far-infrared emission from 70 to 500 µm, as was done in the Hi-GAL survey, and at 24 µm in the MIPSGAL survey, which were then used to build the spectral energy distributions (SEDs) and estimate the L/M parameter. An additional 1.3 mm wavelength in ALMA Band 6 was also produced for the comparison with observational data. We applied observational techniques – commonly employed by observers – to the synthetic data in order to derive the corresponding physical parameters.

Results. We find a correlation between L/M and the SFE, with a power-law form L/M ∝ SFE^1.20_−0.02^+0.02. This correlation is independent of the mass of the clumps and the choice of initial conditions of the simulations in which they formed. The relation between L/M and the ages of the clumps is instead mass-dependent, and can also be strongly influenced by the intensity of the magnetic fields.

Conclusions. Our results suggest that L/M is a reliable parameter for characterizing the overall evolutionary stage of a given starforming region. Its value can be directly compared with the star formation efficiency (SFE) parameter derived from simulations. However, to accurately infer the age of the observed clumps, it is essential to constrain their mass.