Bridging Theory and Observation: Synthetic Far-infrared Insights into Star Formation Efficiency
The star formation efficiency per free-fall time ($ε_{\rm ff}$) 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 $ε_{\rm ff}$ by mapping far-infrared (FIR) dust emission to infer gas surface densities ($Σ_{\rm gas}$) and counting embedded protostars, assuming simplified lifetimes and masses. Using the fiducial STARFORGE radiation-magnetohydrodynamics simulation of an $M_{\rm cl} = 2\times10^4 M_\odot$ 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 $ε_{\rm ff}-Σ_{\rm gas}$ 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 $ε_{\rm ff} \sim 1-3\%$ without requiring extreme initial conditions. We also find that $ε_{\rm ff}$ 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 $\log Σ_{\rm gas} \approx 2.3 M_\odot {\rm pc}^{-2}$ 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 $ε_{\rm ff}$. Below the threshold, the discrepancies are primarily driven by star formation rate assumptions.