Statistical study for binary star evolution in dense embedded clusters

The dynamical evolution of binary populations in embedded star clusters shapes the statistical properties of binaries observed in the Galactic field. Accurately modelling this process requires resolving both the early cluster dynamics and binary interactions. We aim to characterize the early dynamical evolution of primordial binaries in embedded clusters and identify the key parameters that govern binary survival and disruption. We performed a set of direct N-body simulations starting from 100% primordial binaries in a time-varying gas potential of a gas-embedded cluster. To describe the evolution of binary orbital properties, we defined the empirical dynamical operators for the period, binding energy, and mass ratio. We then calibrated them across the simulated ensemble. The binding energy and orbital period evolve in a consistent, sigmoidal fashion. Their dynamical operators reveal that hard binaries heat the cluster and suppress wide binary formation, while a small residual population of soft binaries survives. The evolution of the mass-ratio distribution is less directly linked to dynamical processing and more shaped by internal processes such as stellar physics process in the pre-main sequence phase. High-q systems tend to be enhanced, while low-q systems are prone to disruption. Binary evolution in clusters is primarily governed by binding energy and orbital period. Our model displays an improvement over previous parameterizations of the dynamical operator by allowing for the existence of wide binaries and incorporating the embedded cluster phase. For individual clusters, direct N-body modelling remains the only reliable approach. On Galactic scales, population synthesis methods based on the stellar dynamical operator approach developed in this work remain essential.