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Connecting Star Formation in the Milky Way and Nearby Galaxies -II. An Analytical Model to Predict Cloud-Scale Star Formation Rate

J. W. Zhou, Sami Dib, Pavel Kroupa

TL;DR

This paper tackles predicting cloud-scale star formation rates from internal clump populations by integrating Milky Way correlations with a clump mass function and SFH-based aging. It builds an end-to-end analytic pipeline that estimates the initial total clump mass from cloud mass, populates clumps via a CMF whose slope depends on cloud SFR, assigns ages through SFH to identify clumps in the $2$–$5$ Myr embedded phase, and converts the resulting embedded-cluster mass to a cloud SFR using the embedded-phase duration $t_{\rm emb} \simeq 3$ Myr. To reconcile predictions across cloud masses, the authors introduce a smooth transition between high- and low-mass cloud regimes, improving the match to observed SFR across the mass spectrum. The results demonstrate robustness to SFH, CMF slope, and SFE assumptions, providing a physically grounded link between clump-scale physics and galaxy-scale star formation.

Abstract

We construct a model by integrating observational results from the Milky Way and nearby galaxies to predict cloud-scale star formation rate (SFR). 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 history (SFH) of the cloud to assign an age to each clump. We then identify the clumps with ages between 2 and 5 Myr 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 comparable to the observed SFR, demonstrating the validity of the model.

Connecting Star Formation in the Milky Way and Nearby Galaxies -II. An Analytical Model to Predict Cloud-Scale Star Formation Rate

TL;DR

This paper tackles predicting cloud-scale star formation rates from internal clump populations by integrating Milky Way correlations with a clump mass function and SFH-based aging. It builds an end-to-end analytic pipeline that estimates the initial total clump mass from cloud mass, populates clumps via a CMF whose slope depends on cloud SFR, assigns ages through SFH to identify clumps in the – Myr embedded phase, and converts the resulting embedded-cluster mass to a cloud SFR using the embedded-phase duration Myr. To reconcile predictions across cloud masses, the authors introduce a smooth transition between high- and low-mass cloud regimes, improving the match to observed SFR across the mass spectrum. The results demonstrate robustness to SFH, CMF slope, and SFE assumptions, providing a physically grounded link between clump-scale physics and galaxy-scale star formation.

Abstract

We construct a model by integrating observational results from the Milky Way and nearby galaxies to predict cloud-scale star formation rate (SFR). 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 history (SFH) of the cloud to assign an age to each clump. We then identify the clumps with ages between 2 and 5 Myr 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 comparable to the observed SFR, demonstrating the validity of the model.

Paper Structure

This paper contains 11 sections, 13 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Correlations from the Milky Way
  4. Clump mass function
  5. Initial total mass of clumps
  6. Star formation history
  7. Results and discussion
  8. Procedure and prediction
  9. Robustness
  10. Potential caveats
  11. Data availability

Figures (4)

  • Figure 1: Correlations between the total clump mass in a cloud ($M_{\mathrm{clump,tot,obs}}$), the cloud mass ($M_{\mathrm{cloud}}$) and the SFR of the cloud ($\mathrm{SFR}_{\mathrm{cloud,obs}}$) in the inner Milky Way. $r$ is the correlation coefficient.
  • Figure 2: Compare the observed SFR with the model-predicted SFR. (a) Based on equation.\ref{['Mcti']}; (b) Based on equation.\ref{['Mcto']}; (c) Based on equation.\ref{['Mctio']}. $r$ is the correlation coefficient.
  • Figure 3: Compare the observed SFR with the model-predicted SFR under 12 Gaussian star formation histories.
  • Figure 4: Comparison between the model-predicted SFR and observations under different star formation histories and parameter settings. (a) The black line represents the fit to the observed $\mathrm{SFR}_{\mathrm{cloud,obs}}$–$M_{\mathrm{cloud}}$ relation; (b) Same as Fig.\ref{['sfh']}, but for the flat star formation history; (c) and (d) Same as panel (b), but $\mathrm{SFE}_{\mathrm{clump}}$ and $\beta$ are constant.