Binary disruption during the early phase of open clusters

Binary disruption during the early phase of open clusters ZEPENG ZHENG ID, LONG WANG D, AND HOLGER BAUMGARDT ID

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 DR three open cluster observations and assuming a one hundred percent 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 one, follows a power-law relation with the cluster's initial density (po), with an index of approximately zero point five six, driven by the disruption of wide binaries via close encounters. The transition time between the two phases, tb, also exhibits a power-law dependence on po with an index of about negative zero point four six. 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 po, 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.

One. INTRODUCTION

Studies show that stars form in giant molecular clouds and are often assembled into star clusters. Over the past few decades, a large number of observations have shown that the fraction of binary and higher-order systems in star-forming regions as well as in young open clusters is very high. For example, G. Duchêne conducted a comprehensive study of low-mass binary stars in several star-forming regions and found a significant binary excess among Taurus members. Under the assumption that the period distribution of these stars is consistent with that of main-sequence binaries, up to ninety-five percent of stars are found in multiple star systems. M. S. Connelley et al. investigated the evolution of binary separation distributions for Class One Young Stellar Objects in star-forming regions such as Taurus, Ophiuchus and

Orion, and concluded that nearly all stars form in binary or multiple groups. During the Class Zero phase, the earliest, deeply embedded stage, many objects are part of non-hierarchical multiple systems. By the end of the Class One phase, when the protostar is more evolved with a less massive envelope, wide-separation binaries undergo significant disruption, leading to a significant decrease in binary frequency. This evolutionary trend in binary frequency was further validated by X. Chen et al. through a survey of Class Zero Young Stellar Objects. Without completeness corrections, the estimated binary fraction for Class Zero Young Stellar Objects is approximately sixty-four percent, roughly twice that of Class One Young Stellar Objects, indicating substantial binary disruption during the evolution from Class Zero to Class One Young Stellar Objects. H. Sana et al. found that over seventy percent of O-type stars in open clusters experience binary interactions. J. Donada et al. studied the binary fraction in two hundred two Galactic open clusters, finding that for high mass-ratio binary systems (q greater than zero point six), the binary fraction can reach up to eighty percent. M. C. Ramírez-Tannus et al. estimated the intrinsic binary fraction of the very young star cluster M seventeen to be eighty-seven percent.

In contrast, field stars exhibit a relatively lower binary proportion. For instance, A. Duquennoy & M. Mayor studied one hundred sixty-four solar-type stars in the solar neighborhood and found a multiple star fraction of forty-three percent. D. Raghavan et al. surveyed four hundred fifty-four stars within twenty-five parsecs of the Sun in the Hipparcos catalog and found a binary fraction of approximately thirty-three percent. G. Duchêne et al. conducted a survey of close visual binaries among members of the Orion Nebula Cluster with masses between zero point three solar masses and two point zero solar masses, finding that their companion star fraction is twice that of field stars.

Why do the binary fractions in star-forming regions and young open clusters differ so significantly from those of field stars? Understanding the binary fraction in star clusters and its evolutionary processes is crucial for addressing many important scientific questions. An important open question concerns the origin of binary systems among field stars. One hypothesis proposes that most field binaries originate from star clusters. Using N-body simulations, P. Kroupa showed that open clusters with a one hundred percent primordial binary fraction undergo rapid dynamical disruption, with the surviving binaries after cluster dissolution reproducing the observed properties of field binaries as found by A. Duquennoy & M. Mayor; M. Simon; C. Leinert et al.; A. Richichi et al. Later observations, such as D. Raghavan et al., further confirmed this picture. Building on this idea, M. Marks et al. developed a dynamical operator formalism to predict the binary evolution in clusters, and similar models have reproduced the binary properties observed in several young star-forming regions, such as Taurus, p Ophiuchus, and Chamaeleon. However, other observations reveal binary fractions that deviate from this model, leaving the formation pathway of field binaries still uncertain. Improved models for dynamical evolution of binary populations within clusters are therefore crucial for addressing this long-standing problem.

In star clusters, two main physical mechanisms determine the fate of binaries with different orbital separations: orbital decay and dynamical interactions. Orbital decay primarily affects short-period binaries embedded in the gaseous environment of star-forming clusters. These binaries experience gas-induced dynamical friction, gas accretion onto their envelopes, and disk interactions (if present). These processes reduce orbital energy and angular momentum, shrinking binary separation, occasionally resulting in mergers. In contrast, dynamical interactions mainly influence long-period binaries. Close encounters can perturb binary orbits, exchange components, or disrupt binaries. This process depends on the cluster's hard-soft boundary, where encounters disrupt soft binaries with low binding energies while hard binaries become more tightly bound. Together, these mechanisms preferentially disrupt short- and long-period binaries, leaving a surviving binary population dominated by intermediate-period systems.

mentum, shrinking binary separation, occasionally re- sulting in mergers. In contrast, dynamical interactions mainly influence long-period binaries. Close encoun- ters can perturb binary orbits, exchange components, or disrupt binaries (P. Kroupa 1995a). This process de- pends on the cluster's hard-soft boundary, where en- counters disrupt soft binaries with low binding energies while hard binaries become more tightly bound (D. C. Heggie 1975; J. G. Hills 1975). Together, these mech- anisms preferentially disrupt short- and long-period bi- naries, leaving a surviving binary population dominated by intermediate-period systems.

The evolution of the binary fraction is closely linked to cluster mass and density as shown in both observations and simulations. For example, A. Sollima et al. found an inverse correlation between the binary fraction in cluster cores and cluster mass when investigating open clusters in the Milky Way. Through a series of N-body simulations covering different initial cluster masses and half-mass radii, M. Marks et al. showed that star clusters with larger masses and smaller half-mass radii experience stronger binary disruption during their early evolutionary stages. Similarly, T. Kaczmarek performed N-body simulations of dense clusters containing different numbers of stars and found that systems with more stars-and thus higher initial mass and density-exhibit a faster decline in their binary fraction over time. More recently, J. Donada et al. measured the binary fractions of two hundred two open clusters using Gaia data. Although a clear dependence of the binary fraction on cluster mass was not firmly established, they found that massive clusters tend to have lower binary fractions, whereas low-mass clusters show a wider range of binary fractions, including cases with relatively high binary fraction.

Previous theoretical studies of binary dynamical evolution in open clusters face several limitations. Most rely on simplified analyses or restricted N-body simulations (e.g. no stellar evolution, limited primordial binary population and simplified Galactic potentials). These simplifications limit the ability to understand how binary evolution depends on cluster properties and orbital parameters such as period, mass ratio and eccentricity, as well as how binaries escape to the field.

Additionally, previous studies suffer from limited observational and theoretical samples of open clusters, which can introduce biases in the study of binary disruption. The recent release of Gaia DR three has provided a wealth of precise observational data for cluster studies. Notably, E. L. Hunt and S. Reffert constructed a catalog of seven thousand one hundred sixty-seven open clusters within the Milky Way based on Gaia DR three observations, offering a substantial sample for the study and simulation of open clusters. Therefore, in this work, we will utilize the open cluster catalog published by E. L. Hunt and S. Reffert (hereafter referred to as H twenty-three) to select a subset of valuable observed clusters for extensive N-body numerical simulations, thereby establishing a comprehensive simulation database. Based on this database, we systematically investigate how the binary survival fraction in different open clusters, as observed by Gaia, evolves over time, as well as its dependence on period, mass ratio, and initial density po, defined as the mean stellar mass density within the initial half-mass radius. We also explore the differences between binaries that escape clusters after tidal stripping and those that remain within clusters, providing theoretical support to address the inconsistencies between field and cluster binary populations.

In Section two, we introduce the N-body simulation program PETAR used for star cluster simulations, as well as the selection process for the simulated star cluster samples and the setup of initial conditions. In Section three, we analyze the evolution of the binary survival fraction in simulated star clusters over time, quantify the binary disruption process using equations, and examine the relationship between the binary survival fraction evolution and binary parameters such as mass ratio and period. Finally, we compare the binary survival fractions, period, mass ratio, eccentricity and mass inside and outside the tidal radius of the clusters. In Section four, we discuss the assumptions in our models, limitations and future improvements. Section five provides a summary of our work.