The stellar mass function (MF) and its spatial variation (mass segregation) within star clusters encode signatures of early formation physics and subsequent secular evolution. Yet, a coherent evolutionary picture remains elusive due to conflicting reports regarding the universality of the initial mass function (IMF) and the prevalence of primordial mass segregation. These discrepancies often arise from unresolved binaries, field contamination, and completeness bias. Here, we resolve these issues by analyzing 163 high-fidelity open clusters via a Bayesian forward-modeling framework. We reveal a remarkably simple initial state: young clusters (less than or similar to 300 Myr) share a mean IMF slope of -2.29 in the mass range M >= 0.5M circle dot, consistent with the Salpeter slope but with an intrinsic scatter of 0.17, and exhibit minimal mass segregation at the onset of gas-free evolution (similar to 10 Myr). This broadly universal "zero-point" for secular evolution disfavors star-forming scenarios that predict strong primordial segregation or significant IMF variations, and suggests that chaotic cluster assembly and gas expulsion efficiently erase any mild primordial inhomogeneities. By tracing the evolutionary sequence from 107 to 109.8 yr, we demonstrate that dynamical processing operates on distinct timescales: mass segregation proceeds rapidly via internal relaxation, whereas global MF flattening due to tidal evaporation becomes dominant only after similar to 600 Myr. These findings impose robust observational constraints on the physics of star formation and early feedback and establish an empirical baseline for modeling secular stellar dynamics.

Observations show that multiple stellar populations (MPs) are ubiquitous in globular clusters. The Hubble Space Telescope (HST) has been a pivotal tool for previous photometric studies of MPs. The Chinese Space Station Survey Telescope (CSST) is a 2 m telescope scheduled for launch. One of its imaging instruments, the Survey Camera (SC), combines ultraviolet sensitivity comparable to that of HST with a significantly larger field of view, making it well-suited for conducting large-scale photometric surveys of MPs within extensive stellar stream structures. In this work, we perform mock observations of the stellar stream Palomar 5 to assess the feasibility of detecting MPs with the CSST/SC. The results indicate that the CSST/SC cannot resolve MPs in stellar streams at distances comparable to Palomar 5 (greater than or similar to 20 kpc) with one or 10 150 s exposures. This fundamental limitation arises from the absence of the precise proper motions required to disentangle stream members. We estimate that successful resolution would require the target stream to be less than or similar to 8 kpc under a 150 s exposure. Furthermore, using theoretical color-magnitude diagrams, we find that the CSST/SC g band provides an optimal balance between contamination rate and completeness rate for member identification in the cluster's core. However, this approach fails in the stream due to severe field star contamination. Therefore, future CSST observations of Palomar 5 and its tidal tails will employ multiple epochs across several bands to obtain the deep photometry and proper motion data for a definitive MP analysis.

Interference of the ultralight dark matter (ULDM) field generates time-varying gravitational potential fluctuations, which stochastically heat stellar systems embedded in ULDM halos. Small-sized stellar systems are therefore often used to set stringent constraints on ULDM. However, the evolution of systems with sizes well below the ULDM de Broglie wavelength remains poorly explored. Using numerical simulations, we show that the evolution of compact stellar systems in ULDM halos is governed by the interplay between internal stellar relaxation and ULDM-induced heating. We find the following main results. First, in sufficiently compact systems, relaxation-driven core collapse dominates, allowing the system to remain bound and dense, while ULDM-induced stripping of outer stars further accelerates the collapse. Second, in more extended systems, ULDM heating dominates and ultimately disrupts the system. Near the disruption threshold, we identify systems resembling ultra-faint dwarfs like Segue 1. Third, we further introduce a dimensionless parameter to quantify the relative importance of heating and relaxation and finally lead to an evolutionary phase diagram. Our results reveal the rich and nontrivial dynamics of compact stellar systems in ULDM halos, indicating that precise system modeling is essential for robust ULDM constraints.

The P3T scheme is a hybrid method for simulating gravitational N-body systems. It combines a fast particle-tree (PT) algorithm for long-range forces with a high-accuracy particle-particle (PP; direct N-body) solver for short-range interactions. Preserving both PT efficiency and PP accuracy requires a robust PT-PP switching criterion. We introduce a simple freefall-based switching criterion for general stellar systems alongside the commonly used velocity-dispersion-based (sigma-based) criterion. Using the petar code with the P3T scheme and slowdown algorithmic regularization for binaries and higher-order multiples, we perform extensive simulations of star clusters to evaluate how each criterion affects energy conservation and binary evolution. For systems in virial equilibrium, we find that the freefall-based criterion is generally more accurate for low-sigma or loose clusters containing binaries, whereas the sigma-based criterion is better suited for high-sigma systems. Under subvirial or fractal initial conditions, both criteria struggle to maintain high energy conservation; however, the freefall-based criterion improves as the tree time step is reduced, whereas the sigma-based criterion degrades due to its low-accuracy treatment of two-body encounters.

Multiple stellar populations (MPs), characterized by star-to-star light-element abundance variations, are ubiquitous in globular clusters (GCs). Spectroscopy directly reveals these anomalies, while photometric studies, especially with the Hubble Space Telescope (HST), have been essential for tracing MP sequences in colour-magnitude diagrams (CMDs). However, the limited field of view of HST confines most studies to cluster centres. The upcoming Chinese Space Station Survey Telescope (CSST), with its wide field of view and UV-optical coverage, will enable systematic MP studies over entire clusters. We assess the capability of the CSST wide-field camera to detect and characterize MPs in GCs using realistic simulations. Synthetic stellar population models with different helium abundances (ΔY) and CNO variations were used to simulate CSST observations of GCs at distances of 9.6 and 20 kpc under different exposure times. MP detectability was evaluated using CMDs in seven CSST bands and UV-optical pseudo-colour diagrams. For a GC at 9.6 kpc, the NUV-u colour is highly sensitive to ΔY and CNO variations, with separations of Δ(NUV-u)≈0.16 mag for red giants and up to 0.44 mag for dwarfs. MPs can be resolved when the total UV exposure exceeds ∼1000 s and the optical exposure exceeds ∼300 s. At 20 kpc, encompassing ∼80% of Galactic GCs, CSST still retains strong diagnostic power, resolving populations with ΔY≥0.06 and δ[N/Fe]≥0.64, and separating MPs down to i∼19.5 mag in clusters with large chemical spreads. The NUV-u-g combination provides diagnostic performance comparable to the HST F275W–F336W–F438W system. CSST will enable homogeneous MP surveys across the full spatial extent of star clusters in the Milky Way and nearby galaxies.

The subparsec proximity around the Sgr A(star) supermassive black hole (SMBH) in the center of the Milky Way contains an inner cluster of eccentric S-stars with randomly oriented orbits, a midway-disk of clockwise-rotating stars (CWSs), and a surrounding population of off-the-disk stars (ODSs). Despite their diverse kinematic properties, all three populations appear to be massive (WR/O/B types) and have similarly limited life span tau(star) similar to 6-15 Myr. Several scenarios, including star formation induced by SMBH's close encounters with one or more gas clouds as well as impulsive close scattering by a putative intermediate-mass companion (IMC) of Sgr A(star) possible an intermediate-mass black hole, have been proposed to explain the origin and dynamical evolution of S-stars, CWSs, ODSs, as well as hyper-velocity stars in the Galaxy. However, their coexistence and the origin of a recently discovered zone of avoidance in S-stars' eccentricity-pericentric-distance distribution remain enigmatic. Here, we construct a unified model to comprehensively take into account these stars' interaction with each other, their single natal disk, and an independent IMC. We show their disparate present-day orbits would only be concurrently attainable, within their multi-Myr age, under the combined influence of IMC's secular perturbation and these stars' resonant relaxation in a depleting gaseous-disk environment.

The extremely metal-poor nature of the C-19 stream indicates that its progenitor was a primordial stellar system born in the very early Universe. Current observations show that it has a small metallicity dispersion (0.18 at the 95% confidence level), which is the signature of a globular cluster origin, while at the same time displaying an unusually large velocity dispersion (similar to 10 km s-1), typical of dwarf galaxies. To reconcile this conflicting observational evidence, previous simulations have focused on potential interactions with dark matter subhalos, which can efficiently make a cluster stream dynamically hot. In this work, we explore internal dynamical processes in star cluster formation, focusing on initial conditions shaped by gas expulsion and a top-heavy initial mass function. We find that the large observed velocity dispersion and broad stream morphology can be reproduced by a cluster that underwent severe gas expulsion and expansion during its birth phase, which is potentially a typical formation scenario of extremely metal-poor star clusters. A top-heavy initial mass function and binaries can also increase the velocity dispersion. The formation of C-19 may involve a combination of these effects.

Context. Dense young star clusters (YSCs) are ideal environments for dynamical interactions between stars and stellar compact objects, such as black holes and neutron stars. In such dense environments, stars can undergo close encounters with black holes and fall within their tidal radius, resulting in tidal disruption. These events, known as micro-tidal disruption events (micro-TDEs), are transient phenomena with potential multi-messenger signatures. Aims. We aim to quantify the nature, occurrence, and observational relevance of micro-TDEs across a wide range of cluster masses, densities, and metallicities through an extensive exploration of the parameter space. Methods. We performed a suite of direct N-body simulations using the PETAR code, to which we implemented new prescriptions for modelling micro-TDEs. We constructed a set of realistic YSC models including primordial binaries based on the observed Milky Way population. Our simulations incorporate stellar and binary evolution, supernova kicks, and stellar winds using the BSE code, and they account for the Galactic tidal field via the GALPY library. Results. We identified three primary dynamical channels for micro-TDE production: single star-single black hole encounters, binary-mediated interactions (including supernova-kick triggers), and interactions involving higher-order multiple systems such as hierarchical triples and quadruples as well as chaotic few-body interactions with more than three objects. Multiple encounters are the most efficient production channel and thus dominate the total production rate: similar to 250-450 Gpc(-3) yr(-1). Micro-TDEs from YSCs are expected to be detectable by upcoming surveys, particularly the Legacy Survey of Space and Time, with detection rates potentially up to hundreds per year. The gravitational wave signals expected from the micro-TDE peak in the deci-Hertz band, making them accessible to future instruments such as the Lunar Gravitational Wave Antenna and the Deci-Hertz Interferometer Gravitational wave Observatory. Conclusions. Micro-TDEs emerge as promising multi-messenger sources, potentially offering unique insights into star cluster dynamics, stellar collisions, and the population of dormant stellar-mass black holes, through both electromagnetic and gravitational wave observations.

We present a suite of direct N-body simulations of the Hyades open cluster and its tidal stream in a Milky Way potential that includes a rotating bar and spiral arms. Using the high-resolution code PETAR and an AGAMA-based multicomponent Galactic model, we vary the bar and spiral pattern speeds (Omega b, Omega s) on a discrete grid and quantify the resulting changes in stream orientation, length, and internal density structure. We compare the simulations to Gaia EDR3 using the convergent point and compact convergent point methods, followed by an adaptive three-dimensional nearest-neighbor matching in Cartesian space (x, y, z). The Gaia candidate members exhibit a pronounced longitudinal density peak at Yrot approximate to 0.1 kpc in a stream-aligned coordinate system. Models with Omega s = 22.5 km s-1 kpc-1 and Omega b similar or equal to 40-45 km s-1 kpc-1 best reproduce this feature, while models with a faster bar fail to match the observed density structure. These models are consistent with recent constraints favoring a relatively slow Galactic bar, and they illustrate how nearby open-cluster streams can provide an independent, local constraint on nonaxisymmetric Galactic dynamics.

The P$^3$T scheme is a hybrid method for simulating gravitational $N$-body systems. It combines a fast particle-tree (PT) algorithm for long-range forces with a high-accuracy particle-particle (PP, direct $N$-body) solver for short-range interactions. Preserving both PT efficiency and PP accuracy requires a robust PT-PP switching criterion. We introduce a simple free-fall-based switching criterion for general stellar systems, alongside the commonly used velocity-dispersion-based ($σ$-based) criterion. Using the \textsc{petar} code with the P$^3$T scheme and slow-down algorithmic regularization for binaries and higher-order multiples, we perform extensive simulations of star clusters to evaluate how each criterion affects energy conservation and binary evolution. For systems in virial equilibrium, we find that the free-fall-based criterion is generally more accurate for low-$σ$ or loose clusters containing binaries, whereas the $σ$-based criterion is better suited for high-$σ$ systems. Under subvirial or fractal initial conditions, both criteria struggle to maintain high energy conservation; however, the free-fall-based criterion improves as the tree timestep is reduced, whereas the $σ$-based degrades due to its low-accuracy treatment of two-body encounters.

Star-gas interactions can provide gravitational feedback that influences the dynamical evolution of stellar clusters, through processes such as dynamical friction (DF) and its non-dissipative counterpart, negative dynamical friction (NDF). Using the code, we perform direct N-body simulations of an open cluster initially containing 10^4 stars, evolving within a gaseous medium spanning a range of ambient densities. Our results demonstrate that NDF associated with stellar outflows interacting with the surrounding gas can enhance the rate of cluster expansion, preferentially transporting stars toward the cluster outskirts. This behavior is accompanied by a more rapid decline in the number of binaries composed of a neutron star and a main-sequence star. A statistical analysis of binary orbital parameters further indicates that, compared to DF-dominated evolution, NDF tends to retain systems with larger semi-major axes and lower eccentricities. Outflow-ambient gas interactions can modify the dynamical processing of binaries in star clusters, leading to changes in the survival fraction and composition of the remaining binary population.

We present a suite of direct N-body simulations of low mass (<10^4 M_⊙) globular cluster streams initialized with observationally-motivated binary demographics in order to understand the effect of in-cluster dynamical processing on the stream binary population. The models are initialized with a range of stellar densities and cluster orbits, and Poisson variation in the number of massive and short-lived stars. Wide binaries are disrupted on short timescales by internal tides and on long timescales by two-body encounters. Tides are most important prior to impulsive mass loss-driven cluster expansion. Close binaries (P_ orb<10^2 yr) are most abundant at the stream center due to cluster mass segregation. The wide binary fraction and the degree of binary segregation in the resulting stream are sensitive to the initial cluster density and massive star fraction. In mock radial velocity surveys of the simulated streams, undetectable binaries have velocity amplitudes of ∼0.5-1 km s^-1, adding ∼0.1 km s^-1 of velocity dispersion to the streams, and are dynamically depleted by ∼10-60% compared to the initial binary population. Custom N-body models of Milky Way streams with binaries will allow a holistic understanding of their dynamical structures in advance of upcoming multi-epoch spectroscopic surveys.

The Palomar 5 (Pal 5) globular cluster and its tidal tails provide a sensitive probe of globular-cluster evolution in the time-dependent Milky Way potential. We study the past 3 Gyr evolution of Pal 5 using collisional direct N-body simulations with , adopting Galactic potential models that include spiral arms, the Galactic bar, halo flattening, the Large Magellanic Cloud (LMC), and bar deceleration. We find that halo shape strongly influences the projected stream track, reflecting Pal 5's sensitivity to Galactic force-field flattening. The LMC causes only modest direct changes to the present-day projected stream morphology, but can alter the pericentric distance and hence the progenitor's mass evolution. The Galactic bar strongly affects stream length and debris redistribution along the tails, producing model-dependent density structures and leading–trailing asymmetries. Comparison with observations from Erkal et al. (2017) and Xiao et al. (2025) shows that no single model simultaneously reproduces all observed properties of Pal 5, including cluster evolution, stream length, track, width, and line-density profile. Although our simulations capture several global properties, the remaining discrepancies indicate that a more precise match likely requires better constraints on the initial properties of the Pal 5 progenitor and a more complex Galactic potential, including perturbations from small-scale perturbers such as dark matter subhalos and giant molecular clouds. Future work may combine self-consistent direct N-body simulations with particle-spray methods to investigate these discrepancies more efficiently.

We present a suite of direct N-body simulations of low-mass (<10(4) M-circle dot) globular cluster streams initialized with observationally motivated binary demographics in order to understand the effect of in-cluster dynamical processing on the stream binary population. The models are initialized with a range of stellar densities and cluster orbits and Poisson variation in the number of massive and short-lived stars. Wide binaries are disrupted on short timescales by internal tides and on long timescales by two-body encounters. Tides are most important prior to impulsive mass-loss-driven cluster expansion. Close binaries (P-orb < 10(2) yr) are most abundant at the stream center, due to cluster mass segregation. The wide binary fraction and the degree of binary segregation in the resulting stream are sensitive to the initial cluster density and massive star fraction. In mock radial velocity surveys of the simulated streams, undetectable binaries have velocity amplitudes of similar to 0.5-1 km s(-1), adding similar to 0.1 km s(-1) of velocity dispersion to the streams, and are dynamically depleted by similar to 10%-60% compared to the initial binary population. Custom N-body models of Milky Way streams with binaries will allow a holistic understanding of their dynamical structures in advance of upcoming multiepoch spectroscopic surveys.

GW231123 is a merger of two black holes (BHs) with estimated masses exceeding 100 M circle dot, making them the most massive BHs discovered to date via gravitational-wave (GW) observations. We investigate whether GW231123-like events can originate from isolated Population (Pop) III binary stars using binary population synthesis calculations. Our findings indicate that isolated Pop III binaries can produce GW231123-like events at a rate sufficient to explain the discovery of GW231123, provided that three conditions are met: (i) Pop III stars evolve with inefficient convective overshooting, (ii) the 12C(alpha, gamma)16O rate is 2 sigma lower than the standard value, and (iii) Pop III binary stars share the same orbital parameters as Pop I/II binary stars at the initial time. In contrast, GW190521-the most massive BH merger in the Gravitational Wave Transient Catalog 3-can be formed from isolated Pop III binaries even with the standard 12C(alpha, gamma)16O rate. We demonstrate that the discovery of GW231123 is increasingly constraining the parameter ranges of single-star evolution models, under the assumption that these GW events originate from isolated binary evolution.

The phenomenon of multiple stellar populations (MPs), characterised by star-to-star variations in light-element abundances, is a ubiquitous feature of globular clusters (GCs). While spectroscopic surveys have directly revealed these abundance anomalies, photometric studies, particularly with the Hubble Space Telescope (HST), have been instrumental in characterizing MP sequences across the colour-magnitude diagrams (CMDs). However, the narrow field of view of the HST has restricted these studies to only a small portion of the star clusters, leaving the vast majority of the clusters' space unexplored. The upcoming Chinese Space Station Survey Telescope (CSST), with its wide field of view and both UV and optical capabilities, will provide new opportunities for systematic MP studies. We aim to quantify the capability of the CSST wide-field camera in detecting and characterizing MPs in GCs through virtual simulations that closely mimic real observations. We performed comprehensive simulations using synthetic stellar population models incorporating different helium abundances (Delta Y) and carbon-nitrogen-oxygen (CNO) variations. We simulated CSST observations for GCs at distances of about 9.6 kpc and 20 kpc with different exposure times. We evaluated the detection efficiency of MPs based on the CMDs constructed from the seven different bands of the CSST, as well as the pseudo color-color diagrams (chromosome diagrams) designed with the UV-optical combination. For a GC at a distance of approximately 9.6 kpc, the NUV - u color index of the CSST is highly sensitive to stellar populations with different Delta Y and CNO abundances in the CMD, providing color separations of Delta(NUV - u) approximate to 0.16 (for red giants) to 0.44 mag (for dwarfs). We find that when the total exposure time in the UV band exceeds similar to 1000 s and the exposure time in the optical band exceeds similar to 300 s, the main survey camera of CSST is sufficient to resolve these MPs. Furthermore, extending the simulations to 20 kpc, a distance encompassing similar to 80% of Galactic GCs, we demonstrate that the SCam retains significant diagnostic power, resolving stellar populations with Delta Y >= 0.06 dex and delta[N/Fe] >= 0.64 dex, and distinguishing MPs in the CMD down to i similar to 19.5 mag for clusters with substantial chemical dispersions. The combination of NUV-u-g filters provides diagnostic capabilities comparable to HST's F275W-F336W-F438W system. CSST will be a powerful facility for MP studies, capable of efficiently surveying the entire spatial extent of several hundred star clusters in the local group. Its wide field of view and multi-band capabilities will enable the first homogeneous MP census spanning the entire Milky Way and its neighbouring galaxies, significantly advancing our understanding of star clusters' formation and chemical evolution.

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 found 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 (rho(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(b), also exhibits a power-law dependence on rho(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 rho(0), P, and q. Additionally, we also investigated how open cluster binaries contribute to the field population, and found 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.

Stellar streams, remnants of compact star systems stretched out by the tidal forces of the Milky Way, offer a unique way to study stellar populations that formed billions of years ago. A particularly unique stream is C-19, the most metal-poor stellar stream known at less than a thousandth of the Sun's metallicity. The nature of C-19 is not yet clear, with properties that resemble both star clusters and ultra faint dwarf galaxies, yet in either case its extremely low metallicity indicates very early star formation, <1 Gyr after the Big Bang. Here, we present the first detailed study on the nature of C-19 based on the chemical abundances of 14 member stars from high-resolution spectroscopy. These reveal that C-19 formed stars in an early, rapid, and prolific star formation event, with mild inhomogeneous mixing of elements produced in massive stars. There is otherwise no evidence for subsequent star formation, multiple stellar populations, nor chemical evolution. Although C-19 is currently disrupted in the Milky Way halo, it offers a rare and complementary window into the details of star formation and chemical evolution in the early universe, ideal for comparisons with current studies of primordial star formation in the high-redshift universe.

Observations indicate that supermassive black holes in high-redshift galaxies formed on timescales far shorter than classical growth models allow. One hypothesis suggests intermediate-mass black hole (IMBH) seeds as an efficient growth channel. Using N-body simulations, we demonstrate that in dense stellar-mass black hole (BH) clusters (>= 5 & times; 109 M circle dot pc-3), runaway gravitational-wave (GW) binary BH (BBH) mergers can produce an similar to 103 M circle dot IMBH within 10 Myr from the formation of the BH subsystem. This scenario is simple and avoids large uncertainties regarding stellar mergers and evolution in the IMBH formation via the very massive star channel. We find that the runaway GW-merger mechanism relies on hard BBH formation through a chain of exchanged soft BBHs with accumulated hardening, which is far more efficient than three-body scattering. We analyze how IMBH formation depends on the cluster density, total mass, initial mass function, and stellar halo potential. We find that due to cluster expansion, the systems forming IMBHs have densities consistent with present-day nuclear star clusters, such as those in the Milky Way and M33. Furthermore, we show that IMBH spins remain low due to repeated mergers, and we estimate the rate of GW190521- and GW231123-like events within the first 100 Myr to be 2.27-247.52 and 3.23-63.63 per gigayear per cluster.

We investigate the potential birthplace of Galactic binary neutron star (BNS) systems through a kinematic analysis. Using high-precision astrometry from Gaia DR3, updated pulsar distances, and Monte Carlo sampling of astrometric errors, we integrate the past trajectories of 11 Galactic BNSs and 167 globular clusters plus 2967 open clusters, to search for past encounters. Our results suggest that BNS origin in globular clusters is unlikely, with low encounter probabilities (e.g., less than or similar to 0.5% for NGC 5139) and requiring excessive ejection velocities. Conversely, our analysis indicates that open clusters are a nonnegligible formation channel. Specifically, the double pulsar J0737-3039 shows a 13.9% (5.4%) probability of originating from the young cluster OC 0450 (Theia 58). Based on encounter proximity and time, we argue that Theia 58 is its more plausible birthplace. Our work provides kinematic evidence consistent with an open-cluster origin for a subset of field BNSs.