Bridging Theory and Observation: Synthetic Far-infrared Insights into Star Formation Efficiency

Abstract

The star formation efficiency per free-fall time (${\epsilon }_{\mathrm{ff}}$) quantifies how efficiently giant molecular clouds (GMCs) convert gas into stars and is often observed to be orders of magnitude lower than expected for free-fall collapse. Observers typically estimate ${\epsilon }_{\mathrm{ff}}$ by mapping far-infrared (FIR) dust emission to infer gas surface densities (${\Sigma }_{\mathrm{gas}}$) and counting embedded protostars, assuming simplified lifetimes and masses. Using the fiducial STARFORGE radiation-magnetohydrodynamics simulation of an $M_{\mathrm{cl}}=2\times 10^4{M}_{\odot }$ GMC that self-consistently models star cluster formation and stellar feedback, we generate synthetic FIR observations and apply the same methodologies used in GMC surveys to investigate this discrepancy. We present the first ${\epsilon }_{\mathrm{ff}}-{\Sigma }_{\mathrm{gas}}$ analysis in a fully feedback-regulated GMC simulation that resolves the formation of stellar systems. Our synthetic measurements reproduce the low observationally inferred efficiencies, showing that feedback-regulated star formation naturally produces ${\epsilon }_{\mathrm{ff}}\sim 1-3\%$ without requiring extreme initial conditions. We also find that ${\epsilon }_{\mathrm{ff}}$ varies strongly over a GMC's lifetime, suggesting that much of the observed scatter reflects evolutionary sampling rather than intrinsic cloud-to-cloud differences. Finally, by comparing observational and simulation definitions, we show that methodological assumptions introduce systematic biases, with a transition near $\log {\Sigma }_{\mathrm{gas}}\approx 2.3M_{\odot }{\mathrm{pc}}^{-2}$ that depends on resolution. Above this threshold, the smoothing of dense structure increases both the inferred free-fall time and enclosed gas, with the latter dominating and suppressing ${\epsilon }_{\mathrm{ff}}$. Below the threshold, the discrepancies are primarily driven by star formation rate assumptions.

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