The Rosetta Stone Project. II. The correlation between SFE and L/M indicator for the evolutionary stages of star-forming clumps in post-processed RMHD simulations

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-IR to radio wavelengths. Among them, the ratio between the bolometric luminosity and 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 have developed the Rosetta Stone project$\unicode{x2013}$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 perform multi-wavelength radiative transfer post-processing of RMHD simulations of the collapse of star-forming clumps fragmenting into protostars. We generate synthetic observations to obtain far-infrared emission from $70$ to $500\ \mu$m, as was done in the Hi-GAL survey and at $24\ \mu$m in the MIPSGAL survey, which are 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 has also been produced for the comparison with observational data. We have 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 $L/M\propto {\rm SFE}^{1.20^{+0.02}_{-0.03}}$. This correlation is independent of the mass of the clumps and the choice of initial conditions of the simulations in which they formed. (Abridged)