A momentum-regulated model for star formation efficiency in giant molecular clouds

We present a minimal analytic framework to investigate the star formation efficiency per free-fall time, ε_̊m ff, in giant molecular clouds (GMCs), focusing on the origin of the observed clustering around ε_ ̊m ff ∼ 0.01. We modeled the time evolution of the turbulent velocity dispersion through a momentum balance between stellar feedback and turbulent dissipation, and we show that this generically leads to a stable low-efficiency equilibrium with only weak dependence on global cloud properties. We extended the framework by including a phenomenological contribution from gravity-driven turbulence and find that both feedback- and gravity-driven motions converge to similar equilibrium states under typical GMC conditions. The efficiency can be expressed as the ratio between a gravitational velocity scale and an effective feedback velocity scale, providing a physically transparent interpretation of self-regulated star formation. The model provides a simple, physically motivated interpretation of observed gas--star formation scaling relations, including a Schmidt-like scaling at cloud scales and a Kennicutt-like scaling when averaged over cloud populations. Comparison with observed GMC properties shows agreement within a factor of a few and highlights the weak sensitivity of ε_̊m ff to cloud parameters. Despite its simplicity, the framework captures the leading-order interplay between turbulence, gravity, and feedback, and it provides a physically transparent explanation for the origin and robustness of low star formation efficiencies in GMCs.