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M. B. N. Kouwenhoven

Publications and source records attributed to M. B. N. Kouwenhoven.

At least 19 recordsLinked to original sources

Category-based Galaxy Image Generation via Diffusion Models

Conventional galaxy generation methods rely on semi-analytical models and hydrodynamic simulations, which are highly dependent on physical assumptions and parameter tuning. In contrast, data-driven generative models do not have explicit physical parameters pre-determined, and instead learn them efficiently from observational data, making them alternative solutions to galaxy generation. Among these, diffusion models outperform Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) in quality and diversity. Leveraging physical prior knowledge to these models can further enhance their capabilities. In this work, we present GalCatDiff, the first framework in astronomy to leverage both galaxy image features and astrophysical properties in the network design of diffusion models. GalCatDiff incorporates an enhanced U-Net and a novel block entitled Astro-RAB (Residual Attention Block), which dynamically combines attention mechanisms with convolution operations to ensure global consistency and local feature fidelity. Moreover, GalCatDiff uses category embeddings for class-specific galaxy generation, avoiding the high computational costs of training separate models for each category. Our experimental results demonstrate that GalCatDiff significantly outperforms existing methods in terms of the consistency of sample color and size distributions, and the generated galaxies are both visually realistic and physically consistent. This framework will enhance the reliability of galaxy simulations and can potentially serve as a data augmentor to support future galaxy classification algorithm development.

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Dynamical evolution of massless particles in star clusters with NBODY6++GPU-MASSLESS: II. The long-term evolution of free-floating comets

Context. Comets, asteroids, planetesimals, free-floating planets and brown dwarfs, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems or binary system. The dynamics of large populations of such free-floating comets (ffcs) in a star cluster environment is not yet fully understood. Aims. We investigate the dynamical evolution of comet populations in star clusters, and characterize the kinematics and ejection rates of ffc in a star cluster. Moreover, we determine whether a different initial energy distribution affects the mass segregation of the less massive population. Methods. We carry out simulations using the N-body code NBODY6++GPU-MASSLESS (Flammini Dotti et al. 2025), which allows fast integration of star clusters that contain large numbers of massless particles, to characterize the dynamics of populations of low-mass particles with sub-virial and super-virial distributions. Results. Comets do not participate in the mass segregation process, similarly to planet-size objects, regardless of their initial energy distribution. The latter is slightly changing the whole dynamical evolution at the start of the simulation. We only observe an initial relaxation or collapse of the objects for super-virial and sub-virial ratios, respectively. The external regions of the ffcs population tend to be pulled back in the cluster core at the end of the simulation, suggesting the gravitational pull of the stars is pulling them back in the core. This phenomenon occurs at later times if the system in virial equilibrium. Compared to less massive bodies, brown dwarfs experiences more mass segregation the inner regions tend to be more mixed with the stellar population

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The velocity dispersion profile of nine open clusters in the solar neighborhood

We analyze the velocity dispersion profiles of nine open clusters in the solar neighborhood using kinematic data from Gaia DR 3, aiming to identify potential dynamical signatures of stellar-mass black holes through a comparison of theoretical and observed dispersion profiles. The selected clusters include LP2373 gp4, NGC 1980, NGC 2451A, NGC 2516, NGC 3532, NGC 6475, UBC 7, Praesepe, and Pleiades. We refine the center positions of the clusters with the Meanshift algorithm. Using the Markov Chain Monte Carlo method, we calculate the velocity dispersion for each cluster and construct one-dimensional velocity dispersion profiles. NGC 2516, NGC 3532, and NGC 6475 show potential central cusps in their radial velocity dispersion profiles, which may indicate the presence of stellar-mass black holes. LP2373 gp4, NGC 6475, and Praesepe all display a negative correlation between velocity dispersion and stellar mass, indicating these clusters are approaching energy equipartition or expanding. NGC 2516 and NGC 3532 exhibit a positive dependence between velocity dispersion and stellar mass, which may be attributed to the preferential ejection of massive stars following dynamical interactions involving binaries or black holes. These two clusters are the only two that are dynamical not relaxed and are closest to virial equilibrium. We compare the observations with N-body simulations of star clusters. A comparison of observed and simulated velocity dispersion profiles reveals that NGC 2516 and NGC 3532 exhibit lower proper motion dispersions than model clusters. Better agreement with the observed profiles is achieved for model clusters with larger ages. This suggests that the observed clusters may have undergone rapid dynamical evolution. Our results suggest that NGC 2516 and NGC 3532 may host at least two stellar-mass black holes each.

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Evolution of star clusters with initial bulk rotation via N-body simulations

Young star clusters can inherit bulk rotation from the molecular clouds from which they have formed. This rotation can affect the long-term evolution of a star cluster and its constituent stellar populations. In this study, we aim to characterize the effects of different degrees of initial rotation on star clusters with primordial binaries. The simulations are performed using NBODY6++GPU. We find that initial rotation strongly affects the early evolution of star clusters. Rapidly rotating clusters show angular momentum transport from the inner parts to the outskirts, resulting in a core collapse. Angular momentum transport is accompanied by a highly elongated bar-like structure morphology. The effects of bulk rotation are reduced on the timescale of two-body relaxation. Rotating and non-rotating clusters experience changes in the direction of angular momentum near the dissolution and early evolution due to the tidal field, respectively. We present synthetic observations of simulated clusters for comparison with future observations in filters of Gaia, CSST, and HST. This work shows the effects of bulk rotation on systems with primordial binaries and could be used for the identification of rotation signatures in observed open clusters.

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The 3D morphology of open clusters in the solar neighborhood III: Fractal dimension

We analyze the fractal dimension of open clusters using 3D spatial data from Gaia DR3 for 93 open clusters from Pang et al. (2024) and 127 open clusters from Hunt & Reffert (2024) within 500 pc. The box-counting method is adopted to calculate the fractal dimension of each cluster in three regions: the all-member region, $r \leq r_t$ (inside the tidal radius), and $r > r_t$ (outside the tidal radius). In both the Pang and Hunt catalogs, the fractal dimensions are smaller for the regions $r > r_t$ than those for $r \leq r_t$, indicating that the stellar distribution is more clumpy in the cluster outskirts. We classify cluster morphology based on the fractal dimension via the Gaussian Mixture Model. Our study shows that the fractal dimension can efficiently classify clusters in the Pang catalog into two groups. The fractal dimension of the clusters in the Pang catalog declines with age, which is attributed to the development of tidal tails. This is consistent with the expectations from the dynamical evolution of open clusters. We find strong evidence that the fractal dimension increases with cluster mass, which implies that higher-mass clusters are formed hierarchically from the mergers of lower-mass filamentary-type stellar groups. The transition of the fractal dimension for the spatial distribution of open clusters provides a useful tool to trace the Galactic star forming structures, from the location of the Local Bubble within the solar neighborhood to the spiral arms across the Galaxy.

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Dynamical evolution of massless particles in star clusters with NBODY6++GPU-MASSLESS: I. Free-floating MLPs

Context. Low-mass bodies, such as comets, asteroids, planetesimals, and free-floating planets, are continuously injected into the intra-cluster environment after expulsion from their host planetary systems. These can be modeled as massless particles (MLPs, hereafter). The dynamics of large populations of MLPs, however, has yet received little attention in literature. Aims. We investigate the dynamical evolution of MLP populations in star clusters, and characterize their kinematics and ejection rates. Methods. We present NBODY6++GPU-MASSLESS, a modified version of the N-body simulation code NBODY6++GPU, that allows fast integration of star clusters that contain large numbers of massless particles (MLPs). NBODY6++GPU-MASSLESS contains routines specifically directed at the dynamical evolution of low-mass bodies, such as planets. Results. Unlike stars, MLPs do not participate in the mass segregation process. Instead, MLPs mostly follow the gravitational potential of the star cluster, which gradually decreases over time due to stellar ejections and stellar evolution. The dynamical evolution of MLPs is primarily affected by the evolution of the core of the star cluster. This is most apparent in the outer regions for clusters with higher initial densities. High escape rates of MLPs are observed before the core-collapse, after which escape rates remain stable. Denser star clusters undergo a more intense core collapse, but this does not impact the dynamical evolution of MLPs. The speeds of escaping stars are similar to those of escaping MLPs, when disregarding the high-velocity ejections of neutron stars during the first 50 Myr.

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Influence of planets on debris discs in star clusters -- II. The impact of stellar density

We present numerical simulations of planetary systems in star clusters with different initial stellar densities, to investigate the impact of the density on debris disc dynamics. We use LPS+ to combine N-body codes NBODY6++GPU and REBOUND for simulations. We simulate debris discs with and without a Jupiter-mass planet at 50 au, in star clusters with N = 1k - 64k stars. The spatial range of the remaining planetary systems decreases with increasing N. As cluster density increases, the planet's influence range first increases and then decreases. For debris particles escaping from planetary systems, the probability of their direct ejection from the star cluster decreases as their initial semi-major axis (a0) or the cluster density increases. The eccentricity and inclination of surviving particles increase as cluster density increases. The presence of a planet leads to lower eccentricities and inclinations of surviving particles. The radial density distribution of the remaining discs decays exponentially in sparse clusters. We derive a general expression of the gravitational encounter rate. Our results are unable to directly explain the scarcity of debris discs in star clusters. Nevertheless, given that many planetary systems have multiple planets, the mechanism of the planet-cluster combined gravitational influence on the disc remains appealing as a potential explanation.

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The Present-Day Mass Function of Star Clusters in the Solar Neighborhood

This work analyses the present-day mass function (PDMF) of 93~star clusters utilizing Gaia DR3 data, with membership determined by the StarGo machine learning algorithm. The impact of unresolved binary systems on mass estimation is rigorously assessed, adopting three mass ratio profiles for correction. The PDMF is characterized by the power-law index, $α$, derived through a robust maximum likelihood method that avoids biases associated with data binning. The value of $α$ for stars between the completeness limited mass of Gaia with a mean 0.3 $M_\odot$ for our cluster samples and 2 $M_\odot$, exhibits stability for clusters younger than 200 Myr, decreasing for older clusters, particularly when considering stars within the half-mass radius. The PDMF of these star clusters is consistent with a dynamically evolved Kroupa IMF via the loss of low-mass stars. Cluster morphology shows a correlation with $α$, as $α$ values exhibit a decreasing trend from filamentary to tidal-tail clusters, mirroring the sequence of increasing cluster age. The dependence of $α$ on total cluster mass is weak, with a subtle increase for higher-mass clusters, especially outside the half-mass radius. We do not observe a correlation between $α$ and the mean metallicity of the clusters. Younger clusters have lower metallicity compared to their older counterparts, which indicates that the older clusters might have migrated to the solar neighbourhood from the inner disk. A comparison with numerical models incorporating a black hole population suggests the need for observations of distant, older, massive open clusters to determine whether or not they contain black holes.

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Analysis of Kozai Cycles in Equal-Mass Hierarchical Triple Supermassive Black Hole Mergers in the Presence of a Stellar Cluster

Supermassive black holes (SMBHs) play an important role in galaxy evolution. Binary and triple SMBHs can form after galaxy mergers. A third SMBH may accelerate the SMBH merging process, possibly through the Kozai mechanism. We use N -body simulations to analyze oscillations in the orbital elements of hierarchical triple SMBHs with surrounding star clusters in galaxy centers. We find that SMBH triples spend only a small fraction of time in the hierarchical merger phase (i.e., a binary SMBH with a distant third SMBH perturber). Most of the time, the enclosed stellar mass within the orbits of the innermost or the outermost SMBH is comparable to the SMBH masses, indicating that the influence of the surrounding stellar population cannot be ignored. We search for Eccentric Kozai-Lidov (EKL) oscillations for which (i) the eccentricity of the inner binary and inclination are both oscillate and are anti-phase or in-phase and (ii) the oscillation period is consistent with EKL timescale. We find that EKL oscillations are short-lived and rare: the triple SMBH spends around 3% of its time in this phase over the ensemble of simulations, reaching around 8% in the best-case scenario. This suggests that the role of the EKL mechanism in accelerating the SMBH merger process may have been overestimated in previous studies. We follow-up with three-body simulations, using initial conditions extracted from the simulation, and the result can to some extent repeat the observed EKL-like oscillations. This comparison provides clues about why those EKL oscillations with perturbing stars are short-lived.

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The dynamical evolution of protoplanetary disks and planets in dense star clusters

Most stars are born in dense stellar environments where the formation and early evolution of planetary systems may be significantly perturbed by encounters with neighbouring stars. To investigate on the fate of circumstellar gas disks and planets around young stars dense stellar environments, we numerically evolve star-disk-planet systems. We use the $N$-body codes NBODY6++GPU and SnIPES for the dynamical evolution of the stellar population, and the SPH-based code GaSPH for the dynamical evolution of protoplanetary disks. The secular evolution of a planetary system in a cluster differs from that of a field star. Most stellar encounters are tidal, adiabatic and nearly-parabolic. The parameters that characterize the impact of an encounter include the orientation of the protoplanetary disk and planet relative to the orbit of the encountering star, and the orbital phase and the semi-major axis of the planet. We investigate this dependence for close encounters ($r_p/a\leq 100$, where $r_p$ is the periastron distance of the encountering star and $a$ is the semi-major axis of the planet). We also investigate distant perturbers ($r_p/a\gg 100$), which have a moderate effect on the dynamical evolution of the planet and the protoplanetary disk. We find that the evolution of protoplanetary disks in star clusters differs significantly from that of isolated systems. When interpreting the outcome of the planet formation process, it is thus important to consider their birth environments.

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Binary Star Evolution in Different Environments: Filamentary, Fractal, Halo and Tidal-tail Clusters

Using membership of 85 open clusters from previous studies (Pang et al. 2021a,b, 2022b; Li et al. 2021) based on Gaia DR3 data, we identify binary candidates in the color-magnitude diagram, for systems with mass ratio q > 0.4. The binary fraction is corrected for incompleteness at different distances due to the Gaia angular resolution limit. We find a decreasing binary fraction with increasing cluster age, with substantial scatter. For clusters with a total mass > 200$M_\odot$, the binary fraction is independent of cluster mass. The binary fraction depends strongly on stellar density. Among four types of cluster environments, the lowest-density filamentary and fractal stellar groups have the highest mean binary fraction: 23.6% and 23.2%, respectively. The mean binary fraction in tidal-tail clusters is 20.8%, and is lowest in the densest halo-type clusters: 14.8%. We find clear evidence of early disruptions of binary stars in the cluster sample. The radial binary fraction depends strongly on the cluster-centric distance across all four types of environments, with the smallest binary fraction within the half-mass radius $r_h$, and increasing towards a few $r_h$. Only hints of mass segregation is found in the target clusters. The observed amount of mass segregation is not significant to generate a global effect inside the target clusters. We evaluate the bias of unresolved binary systems (assuming a primary mass of 1$M_\odot$) in 1D tangential velocity, which is 0.1-1$\,\rm km\,s^{-1}$. Further studies are required to characterize the internal star cluster kinematics using Gaia proper motions.

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Influence of planets on debris disks in star clusters I: the 50 AU Jupiter

Although debris disks may be common in exoplanet systems, only a few systems are known in which debris disks and planets coexist. Planets and the surrounding stellar population can have a significant impact on debris disk evolution. Here we study the dynamical evolution of debris structures around stars embedded in star clusters, aiming to determine how the presence of a planet affects the evolution of such structures. We combine NBODY6++GPU and REBOUND to carry out N-body simulations of planetary systems in star clusters (N=8000; Rh=0.78 pc) for a period of 100 Myr, in which 100 solar-type stars are assigned 200 test particles. Simulations are carried out with and without a Jupiter-mass planet at 50 au. We find that the planet destabilizes test particles and speeds up their evolution. The planet expels most particles in nearby and resonant orbits. Remaining test particles tend to retain small inclinations when the planet is present, and fewer test particles obtain retrograde orbits. Most escaping test particles with speeds smaller than the star cluster's escape speed originate from cold regions of the planetary system or from regions near the planet. We identify three regions within planetary systems in star clusters: (i) the private region of the planet, where few debris particles remain (40 - 60 au), (ii) the reach of the planet, in which particles are affected by the planet (0 - 400 au), and (iii) the territory of the planetary system, most particles outside which will eventually escape (0 - 700 au).

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Dynamical Origin for the Collinder 132-Gulliver 21 Stream: A Mixture of three Co-Moving Populations with an Age Difference of 250 Myr

We use Gaia DR3 data to study the Collinder 132-Gulliver 21 region via the machine learning algorithm StarGO, and find eight subgroups of stars (ASCC 32, Collinder 132 gp 1--6, Gulliver 21) located in close proximity. Three co-moving populations were identified among these eight subgroups: (i) a coeval 25 Myr-old moving group (Collinder 132); (ii) an intermediate-age (50--100 Myr) group; and (iii) the 275 Myr-old dissolving cluster Gulliver 21. These three populations form parallel diagonal stripe-shape over-densities in the U--V distribution, which differ from open clusters and stellar groups in the solar neighborhood. We name this kinematic structure the Collinder 132-Gulliver 21 stream, as it extends over 270 pc in the 3D space. The oldest population Gulliver21 is spatially surrounded by the Collinder 132 moving group and the intermediate-age group. Stars in the Collinder 132-Gulliver 21 stream have an age difference up to 250 Myr. Metallicity information shows a variation of 0.3 dex between the youngest and oldest populations. The formation of the Collinder132-Gulliver 21 stream involves both star formation and dynamical heating. The youngest population (Collinder 132 moving group) with homogeneous metallicity is probably formed through filamentary star formation. The intermediate-age and the oldest population were then scatted by the Galactic bar or spiral structure resonance to intercept Collinder 132's orbit. Without mutual interaction between each population, the three populations are flying by each other currently and will become distinct three groups again in approximately ~50Myr.

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Investigating the UV-excess in star clusters with $N$-body simulations: predictions for future CSST observations

We study the origin of the UV-excess in star clusters by performing N-body simulations of six clusters with N=10k and N=100k (single stars & binary systems) and metallicities of Z=0.01, 0.001, and 0.0001, using PETAR. All models initially have a 50 percent primordial binary fraction. Using GalevNB we convert the simulated data into synthetic spectra and photometry for the China Space Station Telescope (CSST) and Hubble Space Telescope (HST). From the spectral energy distributions we identify three stellar populations that contribute to the UV-excess: (1) second asymptotic giant branch stars, which contribute to the UV flux at early times; (2) naked helium stars, and (3) white dwarfs, which are long-term contributors to the FUV spectra. Binary stars consisting of a white dwarf and a main-sequence star are cataclysmic variable (CV) candidates. The magnitude distribution of CV candidates is bimodal up to 2 Gyr. The bright CV population is particularly bright in FUV-NUV. The FUV-NUV color of our model clusters is 1-2 mag redder than the UV-excess globular clusters in M 87 and in the Milky Way. This discrepancy may be induced by helium enrichment in observed clusters. Our simulations are based on simple stellar evolution; we do not include the effects of variations in helium and light elements or multiple stellar populations. A positive radial color gradient is present in CSST NUV-y for main-sequence stars of all models with a color difference of 0.2-0.5 mag, up to 4 half-mass radii. The CSST NUV-g color correlates strongly with HST FUV-NUV for NUV-g>1 mag, with the linear relation $FUV-NUV=(1.09\pm0.12)\times(NUV-g)+(-1.01\pm0.22)$. This allows for conversion of future CSST NUV-g colors into HST FUV-NUV colors, which are sensitive to UV-excess features. We find that CSST will be able to detect UV-excess in galactic/extra-galactic star clusters with ages >200 Myr.

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3D Morphology of Open Clusters in the Solar Neighborhood with Gaia EDR3 II: Hierarchical Star Formation Revealed by Spatial and Kinematic Substructures

We identify members of 65 open clusters in the solar neighborhood using the machine-learning algorithm StarGO based on Gaia EDR3 data. After adding members of twenty clusters from previous studies (Pang et al. 2021a,b; Li et al. 2021) we obtain 85 clusters, and study their morphology and kinematics. We classify the substructures outside the tidal radius into four categories: filamentary (f1) and fractal (f2) for clusters $<100$ Myr, and halo (h) and tidal-tail (t) for clusters $>100$ Myr. The kinematical substructures of f1-type clusters are elongated; these resemble the disrupted cluster Group X. Kinematic tails are distinct in t-type clusters, especially Pleiades. We identify 29 hierarchical groups in four young regions (Alessi 20, IC 348, LP 2373, LP 2442); ten among these are new. The hierarchical groups form filament networks. Two regions (Alessi 20, LP 2373) exhibit global "orthogonal" expansion (stellar motion perpendicular to the filament), which might cause complete dispersal. Infalling-like flows (stellar motion along the filament) are found in UBC 31 and related hierarchical groups in the IC 348 region. Stellar groups in the LP 2442 region (LP 2442 gp 1-5) are spatially well-mixed but kinematically coherent. A merging process might be ongoing in the LP 2442 subgroups. For younger systems ($\lesssim30$ Myr), the mean axis ratio, cluster mass and half-mass radius tend to increase with age values. These correlations between structural parameters may imply two dynamical processes occurring in the hierarchical formation scenario in young stellar groups: (1) filament dissolution and (2) sub-group mergers.

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A highly mutually-inclined, compact warm-Jupiter system KOI-984 ?

The discovery of a population of close-orbiting giant planets ($\le$ 1 au) has raised a number of questions about their origins and dynamical histories. These issues have still not yet been fully resolved, despite over 20 years of exoplanet detections and a large number of discovered exoplanets. In particular, it is unclear whether warm Jupiters (WJs) form in situ, or whether they migrate from further outside and are even currently migrating to form hot Jupiters (HJs). Here, we report the possible discovery and characterization of the planets in a highly mutually-inclined ($I_{\rm mut}\simeq 45^\circ$), compact two-planet system (KOI-984), in which the newly discovered warm Jupiter KOI-984$c$ is on a 21.5-day, moderately eccentric ($e\simeq 0.4$) orbit, in addition to a previously known 4.3-day planet candidate KOI-984$b$. Meanwhile, the orbital configuration of a moderately inclined ($I_{\rm mut}\simeq 15^\circ$), low-mass ($m_{c}\simeq 24 M_{\oplus}$;$P_b\simeq 8.6$ days) perturbing planet near 1:2 mean motion resonace with KOI-984$b$ could also well reproduce observed transit timing variations and transit duration variations of KOI-984$b$. Such an eccentric WJ with a close-in sibling would pose a challenge to the proposed formation and migration mechanisms of WJs, if the first scenario is supported with more evidences in near future; this system with several other well-measured inclined WJ systems (e.g., Kepler-419 and Kepler-108) may provide additional clues for the origin and dynamical histories of WJs.

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Disruption of Hierarchical Clustering in the Vela OB2 Complex and the Cluster Pair Collinder 135 and UBC7 with Gaia EDR3: Evidence of Supernova Quenching

We identify hierarchical structures in the Vela OB2 complex and the cluster pair Collinder 135 and UBC 7 with Gaia EDR3 using the neural network machine learning algorithm StarGO. Five second-level substructures are disentangled in Vela OB2, which are referred to as Huluwa 1 (Gamma Velorum), Huluwa 2, Huluwa 3, Huluwa 4 and Huluwa 5. For the first time, Collinder 135 and UBC 7 are simultaneously identified as constituent clusters of the pair with minimal manual intervention. We propose an alternative scenario in which Huluwa 1-5 have originated from sequential star formation. The older clusters Huluwa 1-3 with an age of 10-22 Myr, generated stellar feedback to cause turbulence that fostered the formation of the younger-generation Huluwa 4-5 (7-20 Myr). A supernova explosion located inside the Vela IRAS shell quenched star formation in Huluwa 4-5 and rapidly expelled the remaining gas from the clusters. This resulted in global mass stratification across the shell, which is confirmed by the regression discontinuity method. The stellar mass in the lower rim of the shell is $0.32\pm0.14$ $\rm M_\odot$ higher than in the upper rim. Local, cluster-scale mass segregation is observed in the lowest-mass cluster Huluwa 5. Huluwa 1-5 (in Vela OB2) are experiencing significant expansion, while the cluster pair suffers from moderate expansion. The velocity dispersions suggest that all five groups (including Huluwa 1A and Huluwa 1B) in Vela OB2 and the cluster pair are supervirial and are undergoing disruption, and also that Huluwa 1A and Huluwa 1B may be a coeval young cluster pair. N-body simulations predict that Huluwa 1-5 in Vela OB2 and the cluster pair will continue to expand in the future 100 Myr and eventually dissolve.

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The Formation of Binary Star Clusters in the Milky Way and Large Magellanic Cloud

Recent observations of young embedded clumpy clusters and statistical identifications of binary star clusters have provided new insights into the formation process and subsequent dynamical evolution of star clusters. The early dynamical evolution of clumpy stellar structures provides the conditions for the origin of binary star clusters. Here, we carry out $N$-body simulations in order to investigate the formation of binary star clusters in the Milky Way and in the Large Magellanic Cloud (LMC). We find that binary star clusters can form from stellar aggregates with a variety of initial conditions. For a given initial virial ratio, a higher degree of initial substructure results in a higher fraction of binary star clusters. The number of binary star clusters decreases over time due to merging or dissolution of the binary system. Typically, $\sim 45\%$ of the aggregates evolve into binary/multiple clusters within $t=20$~Myr in the Milky Way environment, while merely $\sim30\%$ survives beyond $t=50$~Myr, with separations $\lesssim 50$~pc. On the other hand, in the LMC, $\sim 90\%$ of the binary/multiple clusters survive beyond $t=20$~Myr and the fraction decreases to $\sim 80\%$ at $t=50$~Myr, with separations $\lesssim 35~$pc. Multiple clusters are also rapidly formed for highly-substructured and expanding clusters. The additional components tend to detach and the remaining binary star cluster merges. The merging process can produce fast rotating star clusters with mostly flat rotation curves that speed up in the outskirts.

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