Statistical study for binary star evolution in dense embedded clusters

TL;DR

This study uses direct $N$-body simulations with the PeTar code to quantify how deeply embedded cluster dynamics reshape primordial binary populations during the first 0.6 Myr. By introducing empirical dynamical operators for $E_{ m b}$ and $P$, the authors show that disruption dominates early evolution, while hard binaries heat the cluster and suppress formation of wide pairs; mass-ratio evolution remains primarily governed by pre-main-sequence processes. The analysis highlights that binding energy and orbital period encode the essential dynamical information needed for population synthesis on Galactic scales, whereas the mass-ratio distribution is only weakly affected by dynamics. The embedded gas potential markedly increases encounter rates, influencing the inferred cluster-density mapping relative to previous gas-free models, and suggesting that population-synthesis frameworks should account for gas-embedded phases to accurately predict field binary properties.

Abstract

Context: 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 early cluster dynamics and binary interactions. Aims: 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. Methods: We perform 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 define empirical dynamical operators for period, binding energy, and mass ratio, and calibrate them across the simulated ensemble. Results: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. Conclusions: The binary evolution in clusters is primarily governed by binding energy and orbital period. Our model improves 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 here remain essential.

Figures (16)

• Figure 1: Histogram of the crossing time, $t_{\rm cr}$ (panel a) and the half-mass relaxation time $t_{\rm rh}$ (panel b), for all model clusters in the sample.
• Figure 2: Time evolution of global cluster properties: (a) half-mass radius $R_{\rm h,m}$; (b) half-number radius $R_{\rm h,n}$; (c) (one-dimensional) velocity dispersion within $R_{\rm h,m}$, $\sigma_{\rm cl}$; (d) binary fraction. Black lines show the median; dark and light grey areas mark the 16th–84th (68%) and 2.5th–97.5th (95%) percentiles, respectively.
• Figure 3: (a) BDF of the absolute value of binding energy $E_{\rm b}$ at 0 Myr (solid) and 0.6 Myr (dashed). For all samples the same binning is used; curves show the median across all realizations. (b) Dynamical operator $\Omega_{E_{\rm b}}$ as defined from the $N$-body data. Black dots indicate the median values, with error bars marking the 16th–84th percentiles. The solid grey line shows the median fit of Equation \ref{['eq:OmegaEb']}.
• Figure 4: Histogram of the survival fraction of binaries at 0.6 Myr for all model clusters. The survival fraction is defined as the number of binaries present at both 0 and 0.6 Myr, divided by the total number of binaries.
• Figure 5: (a) Empirical PDFs of the absolute value of the binding energy $E_{\rm b}$ for surviving binaries at 0 Myr (solid) and 0.6 Myr (dashed). The same binning is applied to all models, and the plotted histograms show, for each bin, the median value across all clusters. The two distributions are nearly indistinguishable. (b) Histogram of quantile shifts (Equation \ref{['eq:quantileshift']}, see text for definition), where the bar heights represent the median values across all clusters.