Binary disruption during the early phase of open clusters

Abstract

The binary fraction in young open clusters exceeds that of field stars, making the study of binary dynamical evolution in clusters essential for understanding the origins and evolution of field binaries. Using N-body simulations based on Gaia DR3 open cluster observations and assuming a 100\% primordial binary fraction, we investigated the early evolution of binary survival fractions in open clusters. We find that binary disruption has two stages, an initial rapid decline followed by a slower decrease, well described by two piecewise linear functions. The early disruption rate, $k_1$, follows a power-law relation with the cluster's initial density ($ ρ_\mathrm{0} $), with an index of approximately 0.56, driven by the disruption of wide binaries via close encounters. The transition time between the two phases, $t_\mathrm{b}$, also exhibits a power-law dependence on $ρ_\mathrm{0}$ with an index of about -0.46. The disruption rate also depends on binary parameters: high-$q$ and wide binaries are disrupted faster, while the dependence on eccentricity $e$ is less clear, likely due to its strong evolution. We developed and publicly released a Python tool to predict binary survival fraction evolution based on $ρ_0$, $P$ and $q$. Additionally, we also investigate how open cluster binaries contribute to the field population, and find that the escaped stars have a systematically lower binary fraction, likely due to mass segregation. Both populations show similar distributions of $ P $ and $e$, but lower-$q$ systems preferentially remain bound within clusters, the origin of which remains uncertain.

Figures (15)

• Figure 1: Upper panel: Histogram of positional offsets between the normal-mass and massless sets after orbital traceback for all CM particles. The offsets are binned into 50 bins and shown by the blue histogram. The red curve represents a Gaussian fit to the distribution. The vertical dashed line marks the adopted positional offset threshold of $0.5^\circ$, corresponding to approximately the 98th percentile of the empirical distribution. Lower panel: Spatial distribution of CM particle positions after orbital traceback. Blue dots denote the coordinates of normal-mass CM particles, while red crosses indicate those of massless particles. Orange open circles and green open squares highlight outlier sources with positional offsets exceeding the adopted threshold ($0.5^\circ$), corresponding to the normal-mass and massless sets, respectively. Light gray lines connect the paired positions of the two mass sets.
• Figure 2: Comparison of projected half-number radius ($r_{50}$) between simulation and the 47-Hunt.2023 observed Catalog. The horizontal axis represents the radius containing 50% of members within the tidal radius ($r_{50}$) of the simulated clusters, and the vertical axis represents the corresponding $r_{50}$ in the 47-Hunt.2023 catalog. The red dashed line is a one-to-one reference line, where points closer to the line mean better agreement between simulated and observed $r_{50}$ values.
• Figure 3: Example of the evolution of the binary survival fraction (Eq. \ref{['eq:ft']}) for the cluster $\mathrm{NGC\_6416}$ (age 165 $\mathrm{Myr}$). The blue dashed curve shows the simulation data. The red solid line represents the piecewise linear fit described by Eq. \ref{['eq:func']}, with slopes $k_1$ and $k_2$ before and after turning point $t_{\mathrm b}$. The light blue point marks the $t_{\mathrm b}$.
• Figure 4: Relationship between fit parameters and $\rho_\mathrm{0}$ for all samples. The upper subplot shows the distribution of $k_1$ versus $\rho_\mathrm{0}$, and the bottom subplot shows the distribution of $k_2$ versus $\rho_\mathrm{0}$. The red dots represent the sample of $r_\mathrm{h,0}$ determined by the $M_0 - r_\mathrm{h,0}$ relationship from 60-Marks.2011. The blue, orange, and green dots correspond to samples with $r_\mathrm{h,0} = 0.5 \, \text{pc}$, $0.8 \, \text{pc}$, and $1.0 \, \text{pc}$, respectively.
• Figure 5: Fit results for the average value of $k_1$ at different densities. The dots represent the average $k_1$ of 15 randomized models for each cluster. Different colors correspond to clusters with different $r_{\mathrm{h},0}$ (1.0 pc, 0.8 pc, 0.5 pc, and 64-Marks.2012). The solid lines in the corresponding colors show the individual best-fitting results using Eq. \ref{['eq:coll_rate3']}. The purple dash line shows the result of fitting all $\overline{k_1}$ using Eq. \ref{['eq:all_k1_rho_fitting']}, and the black dash line shows the result of the re-fit of $\overline{k_1}$ after fixing the parameter $a$ in Eq. \ref{['eq:all_k1_rho_fitting']} to 0.5.