Connecting Star Formation in the Milky Way and Nearby Galaxies -II. An Observationally Driven Analytical Model for Predicting Cloud-Scale Star Formation Rates

We construct a model by integrating observational constraints from the Milky Way and nearby galaxies to predict cloud-scale star formation rates (SFRs). In the model, we first estimate the initial total mass of clumps in a cloud based on the cloud mass, and then generate the initial clump population of the cloud using the initial clump mass function. Next, we model the star formation histories (SFHs) of the cloud to assign an age to each clump. We then sort out the intermediate-age clumps and calculate the total embedded cluster mass. Finally, we predict the SFR based on the duration of the embedded phase. The model-predicted SFR is broadly consistent with the observed SFR, supporting the plausibility of the model. The model primarily provides a theoretical framework that integrates a wide range of observational results, thereby clarifying the tasks for future observations.

💡 Research Summary

This paper presents an observationally driven analytical framework for predicting cloud‑scale star formation rates (SFRs) by explicitly linking the properties of molecular clouds to the clump (dense sub‑structure) population within them. The authors begin by compiling empirical relations derived from Milky Way surveys (ATLASGAL, Hi‑GAL) and high‑resolution CO observations of nearby galaxies. Two key scaling laws are adopted: (i) a log‑linear correlation between total clump mass and cloud mass (log M_clump,tot,obs = 0.75 log M_cloud − 0.56) and (ii) a near‑unity relation between cloud mass and observed SFR (log SFR_cloud,obs = 0.98 log M_cloud − 9.12). These relations allow the estimation of the initial total clump mass (including past, now‑dispersed clumps) for any given cloud mass.

The clump mass function (CLMF) is modeled as a single power law, ξ_clump(M) = k_clump M^‑β, with β ranging between –1.88 and –2.46 based on Hi‑GAL measurements. The lower mass cutoff is set to 5 M⊙, corresponding to the smallest observed stellar group, while the upper cutoff is effectively infinite (10⁹ M⊙) for the optimal‑sampling normalization. The normalization constant k_clump and the effective maximum mass M_max are solved simultaneously using mass‑conservation (∫M ξ dM = M_clump,tot) and the optimal‑sampling condition (∫_{10⁹ M⊙}^{M_max} ξ dM = 1).

Star formation histories (SFHs) are introduced to assign ages to individual clumps. Two families of SFH are explored: (a) a constant SFR, where clump ages t_b are drawn uniformly from