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

The star formation efficiency per free-fall time ( ϵ 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 ff by mapping far-infrared (FIR) dust emission to infer gas surface densities (Σ gas ) and counting embedded protostars, assuming simplified lifetimes and masses. Using the fiducial starforge radiation–magnetohydrodynamics simulation of an M cl = 2 × 10 4 M ⊙ 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 ff − Σ 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 ff ∼ 1%–3% without requiring extreme initial conditions. We also find that ϵ 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 gas ≈ 2.3 M ⊙ 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 ff . Below the threshold, the discrepancies are primarily driven by star formation rate assumptions.