Evolution Of Star Clusters Research Articles

A Systematic Analysis of Star Cluster Disruption by Tidal Shocks. II. Predicting Star Cluster Dissolution Rates from a Time-series Analysis of Their Tidal Histories

Most of the dynamical mass loss from star clusters is thought to be caused by the time variability of the tidal field (“tidal shocks”). Systematic studies of tidal shocks have been hampered by the fact that each tidal history is unique, implying both a reproducibility and a generalization problem. Here we address these issues by investigating how star cluster evolution depends on the statistical properties of its tidal history. We run a large suite of direct N-body simulations of clusters with tidal histories generated from power spectra of a given slope and with different normalizations, which determine the timescales and amplitudes of the shocks, respectively. At fixed normalization (i.e., the same median tidal field strength), the dissolution timescale is nearly independent of the power spectrum slope. However, the dispersion in dissolution timescales, obtained by repeating simulations for different realizations of statistically identical tidal histories, increases with the power spectrum slope. This result means that clusters experiencing high-frequency shocks have more similar mass-loss histories than clusters experiencing low-frequency shocks. The density–mass relationship of the simulated clusters follows a power law with slope between 1.08 and 1.45, except for the lowest normalizations (for which clusters effectively evolve in a static tidal field). Our findings suggest that star cluster evolution can be described statistically from a time-series analysis of its tidal history, which is an important simplification for describing the evolution of the star cluster population during galaxy formation and evolution.

The formation and evolution of dark star clusters – II. The impact of primordial mass segregation

ABSTRACT We investigate the impact of primordial mass segregation on the formation and evolution of dark star clusters (DSCs). Considering a wide range of initial conditions, we conducted N-body simulations of globular clusters (GCs) around the Milky Way. In particular, we assume a canonical initial mass function for all GCs without natal kicks for supernova remnants, namely neutron stars or black holes. Our results demonstrate that clusters with larger degrees of primordial mass segregation reach their DSC phase earlier and spend a larger fraction of their dissolution time in such a phase, compared to clusters without mass segregation. In primordially segregated clusters, the maximum Galactocentric distance that the clusters can have to enter the DSC phase is almost twice that of the clusters without primordial mass segregation. Primordially segregated clusters evolve with a higher number of stellar mass black holes, accelerating energy creation in their central regions and consequently increasing evaporation rates and cluster sizes during dark phases. The simulations reveal that aggregating heavy components at the centre doubles the time spent in the dark phase. Additionally, the study identifies potential links between simulated dark clusters and initial conditions of Milky Way GCs, suggesting some may transition to dark phases before dissolution. Higher primordial mass segregation coefficients amplify the average binary black hole formation rate by 2.5 times, raising higher expectations for gravitational-wave emissions.

Evolution of Star Clusters within Galaxies Using Self-consistent Hybrid Hydro/N-body Simulations

We introduce a GPU-accelerated hybrid hydro/N-body code (Enzo-N) designed to address the challenges of concurrently simulating star clusters and their parent galaxies. This task has been exceedingly challenging, primarily due to the considerable computational time required, which stems from the substantial scale difference between galaxies (∼0.1 Mpc) and star clusters (∼parsecs). Yet, this significant scale separation means that particles within star clusters perceive those outside the star cluster in a semistationary state. By leveraging this aspect, we integrate a direct N-body code (Nbody6++GPU) into a cosmological (magneto)hydrodynamic code (Enzo) through utilization of the semistationary background acceleration approximation. We solve the dynamics of particles within star clusters using a direct N-body solver with regularization for few-body interactions, while evolving particles outside—dark matter, gas, and stars—using a particle-mesh gravity solver and hydrodynamic methods. We demonstrate that Enzo-N successfully simulates the coevolution of star clusters and their parent galaxies, capturing phenomena such as core collapse of the star cluster and tidal stripping due to galactic tides. This comprehensive framework opens up new possibilities for studying the evolution of star clusters within galaxies, offering insights that were previously inaccessible.

FRACTAL DIMENSION OF STAR CLUSTERS

Quantitative analysis of the structure of star clusters is crucial for understanding their formation and evolution. In this article, we explore the application of fractal dimension analysis to study the evolution of star clusters, also fractal dimension, a concept from fractal geometry, provides a quantitative measure of the complexity and self-similarity of geometric objects. By considering star clusters as complex networks, we employ the box covering method to calculate their fractal dimension. Our methodology combines the well-established Minimum Spanning Tree (MST) and Box-Covering (BC) methods and using these methods, the fractal structure of the clusters was determined. It was revealed that star clusters disintegrate at a fractal dimension of 1.3 and obey a power law. It should be noted that the obtained result was compared with the results of the McLuster.

Great Balls of FIRE

Context. Despite the nearly hundred gravitational-wave detections reported by the LIGO-Virgo-KAGRA Collaboration, the question of the cosmological origin of merging binary black holes (BBHs) remains open. The two main formation channels generally considered are from isolated field binaries or via dynamical assembly in dense star clusters. Aims. Here we focus on understanding the dynamical formation of merging BBHs within massive clusters in galaxies of different masses. Methods. To this end, we applied a new framework to consistently model the formation and evolution of massive star clusters in zoom-in cosmological simulations of galaxies. Each simulation, taken from the FIRE project, provides a realistic star formation environment, with a unique star formation history, that hosts realistic giant molecular clouds that constitute the birthplace of star clusters. Combined with the code for star cluster evolution CMC, we are able to produce populations of dynamically formed merging BBHs across cosmic time in different environments. Results. As the most massive star clusters preferentially form in dense massive clouds of gas, we find that, despite their low metallicities favouring the creation of black holes, low-mass galaxies contain few massive clusters and therefore make a limited contribution to the global production of dynamically formed merging BBHs. Furthermore, we find that massive clusters can host hierarchical BBH mergers with clear, identifiable physical properties. Looking at the evolution of the BBH merger rate in different galaxies, we find strong correlations between BBH mergers and the most extreme episodes of star formation. Finally, we discuss the implications for future LIGO-Virgo-KAGRA gravitational wave observations.

The impact of a top-heavy IMF on the formation and evolution of dark star clusters

ABSTRACT The Spitzer instability leads to the formation of a black hole subsystem (BHSub) at the centre of a star cluster providing energy to luminous stars (LSs) and increasing their rate of evaporation. When the self-depletion time of the BHSub exceeds the evaporation time of the LSs, a dark star cluster (DSC) will appear. Using the nbody7 code, we performed a comprehensive set of direct N-body simulations over a wide range of initial conditions to study the pure effect of the top-heaviness of the initial mass function (IMF) on the formation of the DSC phase. In the Galactic tidal field, top-heavy IMFs lead to the fast evaporation of LSs and the formation of DSCs. Therefore, DSCs can be present even in the outer region of the Milky Way (MW). To successfully transition to the DSC phase, the MW Globular Clusters (GCs) must possess an initial black hole (BH) mass fraction of $\widetilde {\mathit {M}}_\mathrm{BH}(0)\gt 0.05$. For star clusters with $\widetilde {\mathit {M}}_\mathrm{BH}(0)\gt 0.08$, the DSC phase will be created for any given initial density of the cluster and Galactocentric distance. The duration of the cluster’s lifetime spent in the DSC phase shows a negative (positive) correlation with the initial density, and Galactocentric distance of the star cluster if $\widetilde {\mathit {M}}_\mathrm{BH}(0)\le 0.12$ ($\widetilde {\mathit {M}}_\mathrm{BH}(0)\ge 0.15$). Considering the canonical IMF, it is unlikely for any MW GCs to enter the DSC phase. We discuss the BH retention fraction in view of the observed properties of the GCs of the MW.

Is the RSGC4 (Alicante 8) Cluster a Real Star Cluster? Peculiar Radial Velocities of Red Supergiant Stars

Young massive star clusters, like the six red supergiant clusters in the Scutum complex, provide valuable insights into star formation and galaxy structures. We investigated the high-resolution near-infrared spectra of 60 RSG candidates in these clusters using the Immersion Grating Infrared Spectrograph. Among the candidates in RSGC4, we found significant scattering in radial velocity (−64 to 115 km s−1), unlike other clusters with velocities of ∼100 km s−1. Most candidates in RSGC4 have Q GK s values larger than 1.7, suggesting that they could be early AGB stars. Four candidates in RSGC4 exhibit infrared excess and distinct absorption features absent in other candidates. Two of these stars exhibit absorption lines resembling those of D-type symbiotic stars, showing radial velocity changes in multiepoch observations. Analysis of relative proper motions revealed no runaway/walkaway stars in RSGC4. The dynamic properties of RSGC4 and RSGC1 differ from the disklike motions of other clusters: RSGC4 has low normalized horizontal action J hor = J ϕ /J tot and vertical action J ver = (J z − J R)/J tot values and high eccentricities, while RSGC1 has vertical motions with high J ver values and inclinations. We propose that RSGC4 may not be a genuine star cluster but rather a composite of RSGs and AGB stars distributed along the line of sight at similar distances, possibly originating from various environments. Our results suggest a complex and hierarchical secular evolution of star clusters in the Scutum complex, emphasizing the importance of considering factors beyond density crowding when identifying star clusters in the bulge regions.

Young, wild, and free: The early expansion of star clusters

Early expansion plays a fundamental role in the dynamical evolution of young star clusters. However, until very recently most of our understanding of cluster expansion was based only on indirect evidence or on statistically limited samples of clusters. Here we present a comprehensive kinematic analysis of virtually all known young Galactic clusters (t < 300 Myr) based on the improved astrometric quality of the Gaia DR3 data. Such a large sample provides an unprecedented opportunity to robustly constrain the fraction of clusters and the timescale during which expansion has a prominent impact on the overall kinematics. We find that a remarkable fraction (up to 80%) of clusters younger than ∼30 Myr is currently experiencing significant expansion, whereas older systems are mostly compatible with equilibrium configurations. We observe a trend in which the expansion speed increases with the cluster-centric distance, suggesting that clusters undergoing expansion will likely lose a fraction of their present-day mass. Also, most young expanding clusters are extended, possibly due to the expansion itself. A comparison with a set of N-body simulations of young star clusters shows that the observed expansion pattern is in general qualitative agreement with that found for systems undergoing violent relaxation and evolving toward a final virial equilibrium state. However, we also note that additional processes likely associated with residual gas expulsion and mass loss due to stellar evolution likely also play a key role in driving the observed expansion.

Star-forming environments in smoothed particle magnetohydrodynamics simulations II: re-simulating isolated clumps to determine equivalence of extracted clumps and parent simulations

ABSTRACT What is the numerical reproducibility of a stellar system (including its discs) when evolving only a subset of (partially-evolved) smoothed particle hydrodynamics (SPH) particles? To investigate this, we modelled the evolution of 29 star-forming clumps that were extracted from our previous simulations that investigated the formation and early evolution of low-mass star clusters. These clumps were evolved using a three-dimensional smoothed particle radiation magnetohydrodynamics code, where we included or excluded non-ideal magnetohydrodynamics to match the cluster simulation. While star formation proceeded as expected, we were unable to identically reproduce any of the systems present at the end of the cluster simulations. However, the final distributions of stellar mass, stellar system mass, disc mass, and disc radii were reproduced statistically; unfortunately, the distribution of average magnetic field strengths in the discs was not reproduced statistically, but this may be a result of our updated algorithms governing the evolution of the magnetic field. Therefore, given that our clumps yield stellar masses that are statistically similar to those in the original low-mass star clusters, we have demonstrated that we can statistically reproduce systems (aside from their magnetic field strength) by evolving a subset of SPH particles. Therefore, clumps such as these can be used as initial conditions to investigate the formation of isolated stars from less-contrived initial environments.

Photometric binaries in 14 Magellanic Cloud star clusters

Binary stars play a major role in determining the dynamic evolution of star clusters. We used images collected with the Hubble Space Telescope to study fourteen star clusters of the Magellanic Clouds that span an age interval between ∼0.6 and 2.1 Gyr and masses of 104 − 105 M⊙. We estimated the fraction of binary systems composed of two main-sequence stars and the fraction of candidate blue-straggler stars (BSSs). Moreover, we derived the structural parameters of the cluster, including the core radius, central density, mass function, and total mass. We find that the fraction of binaries with a mass ratio larger than 0.7 ranges from ∼7% in NGC 1846 to ∼20% in NGC 2108. The radial and luminosity distribution can change from one cluster to another. However, when we combine the results from all the clusters, we find that binaries follow a flat radial trend and no significant correlation with the mass of the primary star. We find no evidence for a relation between the fractions of binaries and BSSs. We combined the results on binaries in the studied Magellanic Cloud clusters with those obtained for 67 Galactic globular clusters and 78 open clusters. We detect a significant anti-correlation between the binary fraction in the core and the mass of the host cluster. However, star clusters with similar masses exhibit a wide range of binary fractions. Conversely, there is no evidence of a correlation between the fraction of binaries and the cluster age or the dynamic age.

Stellar populations in STARFORGE: the origin and evolution of star clusters and associations

ABSTRACT Most stars form in highly clustered environments within molecular clouds, but eventually disperse into the distributed stellar field population. Exactly how the stellar distribution evolves from the embedded stage into gas-free associations and (bound) clusters is poorly understood. We investigate the long-term evolution of stars formed in the starforge simulation suite – a set of radiation-magnetohydrodynamic simulations of star-forming turbulent clouds that include all key stellar feedback processes inherent to star formation. We use nbody6++gpu to follow the evolution of the young stellar systems after gas removal. We use HDBSCAN to define stellar groups and analyse the stellar kinematics to identify the true bound star clusters. The conditions modeled by the simulations, i.e. global cloud surface densities below 0.15 g cm−2, star formation efficiencies below 15 per cent, and gas expulsion time-scales shorter than a free fall time, primarily produce expanding stellar associations and small clusters. The largest star clusters, which have ∼1000 bound members, form in the densest and lowest velocity dispersion clouds, representing ∼32 and 39 per cent of the stars in the simulations, respectively. The cloud’s early dynamical state plays a significant role in setting the classical star formation efficiency versus bound fraction relation. All stellar groups follow a narrow mass-velocity dispersion power-law relation at 10 Myr with a power-law index of 0.21. This correlation result in a distinct mass–size relationship for bound clusters. We also provide valuable constraints on the gas dispersal time-scale during the star formation process and analyse the implications for the formation of bound systems.

Understanding the Planetary Formation and Evolution in Star Clusters (UPiC). I. Evidence of Hot Giant Exoplanets Formation Timescales

Planets in young star clusters could shed light on planet formation and evolution since star clusters can provide accurate age estimation. However, the number of transiting planets detected in clusters was only ∼30, too small for statistical analysis. Thanks to the unprecedented high-precision astrometric data provided by Gaia DR2 and Gaia DR3, many new open clusters (OCs) and comoving groups have been identified. The Understanding Planetary Formation and Evolution in Star Clusters project aims to find observational evidence and interpret how planets form and evolve in cluster environments. In this work, we cross match the stellar catalogs of new OCs and comoving groups with confirmed planets and candidates. We carefully remove false positives and obtain the biggest catalog of planets in star clusters up to now, which consists of 73 confirmed planets and 84 planet candidates. After age validation, we obtain the radius–age diagram of these planets/candidates. We find an increment in the fraction of hot Jupiters (HJs) around 100 Myr and attribute the increment to the flyby-induced high-e migration in star clusters. An additional small bump of the fraction of HJs after 1 Gyr is detected, which indicates the formation timescale of HJ around field stars is much larger than that in star clusters. Thus, stellar environments play important roles in the formation of HJs. The hot Neptune desert occurs around 100 Myr in our sample. A combination of photoevaporation and high-e migration may sculpt the hot Neptune desert in clusters.

Nitrogen-enriched, Highly Pressurized Nebular Clouds Surrounding a Super Star Cluster at Cosmic Noon

Strong lensing offers a precious opportunity for studying the formation and early evolution of super star clusters that are rare in our cosmic backyard. The Sunburst Arc, a lensed Cosmic Noon galaxy, hosts a young super star cluster with escaping Lyman continuum radiation. Analyzing archival Hubble Space Telescope images and emission line data from Very Large Telescope/MUSE and X-shooter, we construct a physical model for the cluster and its surrounding photoionized nebula. We confirm that the cluster is ≲4 Myr old, is extremely massive M ⋆ ∼ 107 M ⊙, and yet has a central component as compact as several parsecs, and we find a gas-phase metallicity Z = (0.22 ± 0.03)Z ⊙. The cluster is surrounded by ≳105 M ⊙ of dense clouds that have been pressurized to P ∼ 109 K cm−3 by perhaps stellar radiation at within 10 pc. These should have large neutral columns N HI > 1022.8 cm−2 to survive rapid ejection by radiation pressure. The clouds are likely dusty as they show gas-phase depletion of silicon, and may be conducive to secondary star formation if N HI > 1024 cm−2 or if they sink farther toward the cluster center. Detecting strong [N iii]λ λ 1750,1752, we infer heavy nitrogen enrichment . This requires efficiently retaining ≳500 M ⊙ of nitrogen in the high-pressure clouds from massive stars heavier than 60 M ⊙ up to 4 Myr. We suggest a physical origin of the high-pressure clouds from partial or complete condensation of slow massive star ejecta, which may have an important implication for the puzzle of multiple stellar populations in globular clusters.

Making hot Jupiters in stellar clusters – II. Efficient formation in binary systems

ABSTRACT Observations suggested that the occurrence rate of hot Jupiters (HJs) in open clusters is largely consistent with the field ($\sim 1{{\ \rm per\ cent}}$) but in the binary-rich cluster M67, the rate is $\sim 5{{\ \rm per\ cent}}$. How does the cluster environment boost HJ formation via the high-eccentricity tidal migration initiated by the extreme-amplitude von Zeipel–Lidov–Kozai (XZKL) mechanism forced by a companion star? Our analytical treatment shows that the cluster’s collective gravitational potential alters the companion’s orbit slowly, which may render the star–planet–companion configuration XZKL-favourable. We have also performed direct Gyr N-body simulations of the star cluster evolution and XZKL of planets’ orbit around member stars. We find that an initially single star may acquire a companion star via stellar scattering and the companion may enable XZKL in the planets’ orbit. Planets around an initially binary star may also be XZKL-activated by the companion. In both scenarios, the companion’s orbit has likely been significantly changed by stellar scattering and the cluster potential before XZKL occurs. Across different cluster models, 0.8–3 per cent of the planets orbiting initially single stars have experienced XZKL while the fraction is 2–26 per cent for initially binary stars. Around a star that is binary at 1 Gyr, 13–32 per cent of its planets have undergone XZKL, and combined with single stars, the overall XZKL fraction is 3–21 per cent, most affected by the cluster binarity. If 10 per cent of the stars in M67 host a giant planet, our model predicts an HJ occurrence rate of $\sim 1{{\ \rm per\ cent}}$. We suggest that HJ surveys target old, high-binarity, not-too-dense open clusters and prioritize wide binaries to maximize HJ yield.

Close encounters of star–black hole binaries with single stars

ABSTRACT Multibody dynamical interactions of binaries with other objects are one of the main driving mechanisms for the evolution of star clusters. It is thus important to bring our understanding of three-body interactions beyond the commonly employed point-particle approximation. To this end, we here investigate the hydrodynamics of three-body encounters between star–black hole (BH) binaries and single stars, focusing on the identification of final outcomes and their long-term evolution and observational properties, using the moving-mesh hydrodynamics code AREPO. This type of encounter produces five types of outcomes: stellar disruption, stellar collision, weak perturbation of the original binary, binary member exchange, and triple formation. The two decisive parameters are the binary phase angle, which determines which two objects meet at the first closest approach, and the impact parameter, which sets the boundary between violent and non-violent interactions. When the impact parameter is smaller than the semimajor axis of the binary, tidal disruptions and star-BH collisions frequently occur when the BH and the incoming star first meet, while the two stars mostly merge when the two stars meet first instead. In both cases, the BHs accrete from an accretion disc at super-Eddington rates, possibly generating flares luminous enough to be observed. The stellar collision products either form a binary with the BH or remain unbound to the BH. Upon collision, the merged stars are hotter and larger than the main sequence stars of the same mass at similar age. Even after recovering their thermal equilibrium state, stellar collision products, if isolated, would remain hotter and brighter than main sequence stars until becoming giants.

Expansion-free cluster of stars in modified Gauss–Bonnet gravity

The aim of this paper is to investigate the expansion-free model of star cluster in modified Gauss-Bonnet gravity. To achieve this, we analyze a model of a star cluster which is dissipative, anisotropic and viscous. The modified field equations as well as junction conditions are applied in order to study the general distribution of anisotropic fluid exhibiting dissipation with varying dominant stress components. We also integrate the condition of vanishing expansion into our analysis. To gain insight into the significance of motion that does not involve expansion, we discuss two distinct ways of defining the radial velocity of a fluid element. The study demonstrates the emergence of a cavity in the evolution of star clusters when expansion is not present. Moreover, we determine the shear-free and expansion-free collapse of the star cluster by analyzing the relative velocity among adjacent fluid layers. The Skripkin model can be used to represent an expansion-free, non-dissipative, and isotropic star cluster. This provides a valuable tool for investigating the properties and behavior of these celestial bodies. The Skripkin model demonstrates homologous evolution for the shear-free case. We conclude that the exotic matter present in f(G,T) gravity are essential for understanding the dynamics of star cluster’s evolution. This indicates that the dark source terms should be taken into account when investigating the properties and behavior of the celestial bodies.

Close encounters of black hole—star binaries with stellar-mass black holes

ABSTRACT Dynamical interactions involving binaries play a crucial role in the evolution of star clusters and galaxies. We continue our investigation of the hydrodynamics of three-body encounters, focusing on binary black hole (BBH) formation, stellar disruption, and electromagnetic (EM) emission in dynamical interactions between a BH-star binary and a stellar-mass BH, using the moving-mesh hydrodynamics code AREPO. This type of encounters can be divided into two classes depending on whether the final outcome includes BBHs. This outcome is primarily determined by which two objects meet at the first closest approach. BBHs are more likely to form when the star and the incoming BH encounter first with an impact parameter smaller than the binary’s semimajor axis. In this case, the star is frequently disrupted. On the other hand, when the two BHs encounter first, frequent consequences are an orbit perturbation of the original binary or a binary member exchange. For the parameters chosen in this study, BBH formation, accompanied by stellar disruption, happens in roughly one out of four encounters. The close correlation between BBH formation and stellar disruption has possible implications for EM counterparts at the binary’s merger. The BH that disrupts the star is promptly surrounded by an optically and geometrically thick disc with accretion rates exceeding the Eddington limit. If the debris disc cools fast enough to become long-lived, EM counterparts can be produced at the time of the BBH merger.

Initial sizes of star clusters: implications for cluster dissolution during galaxy evolution

ABSTRACT Massive star clusters are often used as tracers of galaxy formation and assembly. In order to do so, we must understand their properties at formation, and how those properties change with time, galactic environment, and galaxy assembly history. The two most important intrinsic properties that govern star cluster evolution are mass and radius. In this paper, we investigate 10 theoretically and observationally motivated initial size–mass relations for star clusters, and evolve populations of clusters through galaxy formation models. We compare our results to each other and to observations of cluster populations in M83, M31, and the Milky Way. We find that none of our size–mass relations agree with the observations after 6–10 Gyr of evolution. We can successfully reproduce the cluster mass functions with models that have a small range of initial radii, and which do not allow cluster radii to change with time. However, these models do not agree with our understanding of cluster evolution, which does involve radius evolution, and do not match the observed distributions of radii. We note that there is a region of parameter space where clusters are optimally protected from both tidal shocks and evaporation due to two-body relaxation. Clusters that are allowed to evolve into this parameter space will likely survive. An improved understanding of both mass and radius evolution of star clusters in realistic, time-varying galactic potentials is necessary to appropriately make the connection between present-day cluster properties and their use as tracers of galaxy formation and assembly.

On the Origin of the Split Main Sequences of the Young Massive Cluster NGC 1856

The detection of split main sequences (MSs) associated with young clusters (≲600 Myr) has attracted a lot of attention. A prevailing scenario is that a bimodality of stellar rotation distribution drives the bifurcation of the MS. Nevertheless, the origin of the stellar rotation dichotomy remains unclear. Hypotheses involving tidally locked binaries or blue straggler stars (BSSs) have been proposed to explain the observed split MSs. This work examines if the long-term dynamical evolution of star clusters can produce the observed split MSs, through high-performance N-body simulation. For example, the young massive cluster NGC 1856 exhibits an apparent MS bifurcation. Our simulation reports that at the age of NGC 1856, tidally locked binaries are fully mixed with single stars. This is consistent with the observation that there is no significant spatial difference between blue MS and red MS stars. However, we find that only high-mass-ratio binaries can evolve to the tidally locked phase at the age of the NGC 1856. These tidally locked binaries will populate a much redder sequence than the MS of single stars rather than a blue MS, which is inconsistent with the hypothesis. The number of tidally locked binaries cannot account for the observation. Our simulation shows that BSSs produced by binary interactions do populate in the blue periphery as shown in a color–magnitude diagram, and their spatial distribution shows a similar pattern of single stars. However, the number of BSSs does not fit the observation.

Star cluster formation from turbulent clumps – III. Across the mass spectrum

ABSTRACT We study the formation and early evolution of star clusters that have a wide range of masses and background cloud mass surface densities, Σcloud, which help set the initial sizes, densities, and velocity dispersions of the natal gas clumps. Initial clump masses of 300, 3000, and 30 000 M⊙ are considered, from which star clusters are born with an assumed 50 per cent overall star formation efficiency and with 50 per cent primordial binarity. This formation is gradual, i.e. with a range of star formation efficiencies per free-fall time from 1 to 100 per cent, so that the formation time can range from 0.7 Myr for low-mass, high-Σcloud clumps to ∼30 Myr for high-mass, low-Σcloud clumps. Within this framework of the turbulent clump model, for a given Σcloud, clumps of higher mass are of lower initial volume density, but their dynamical evolution leads to higher bound fractions and causes them to form much higher density cluster cores and maintain these densities for longer periods. This results in systematic differences in the evolution of binary properties, degrees of mass segregation, and rates of creation of dynamically ejected runaways. We discuss the implications of these results for observed star clusters and stellar populations.