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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., Comment: 11 Pages, 9 Figures, Accepted for publication in A&A

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., Comment: 13 pages, 9 figures; Accepted to A&A

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., Comment: 15 pages, 15 figures, and 4 tables. Accepted for publication in MNRAS

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, $\alpha$, derived through a robust maximum likelihood method that avoids biases associated with data binning. The value of $\alpha$ 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 $\alpha$, as $\alpha$ values exhibit a decreasing trend from filamentary to tidal-tail clusters, mirroring the sequence of increasing cluster age. The dependence of $\alpha$ 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 $\alpha$ 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., Comment: 19 pages, 10 figures, accepted to ApJ

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., Comment: 24 pages, 16 figures, Published: 20 December 2023 on MNRAS https://doi.org/10.1093/mnras/stad3908

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., Comment: 14 Pages, 11 Figures, Accepted for pubblication on MNRAS on 13 September 2023

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.

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)., Comment: 17 pages, 20 figures, and 3 tables. Accepted for publication in MNRAS

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., Comment: Accepted to ApJL, 15 pages, 7 figures

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., Comment: 31 pages, 12 figures, 2 tables, accepted for publication at Research in Astronomy and Astrophysics

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., Comment: Accepted to ApJ, 33 pages, 14 figures. OC 3D interactive visualization included on http://3doc-morphology.lowell.edu

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., Comment: accepted 2021 July 5, to be published in MNRAS, 19 pages

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., Comment: 28 pages, 16 figures. Accepted to ApJ

We analyze the 3D morphology and kinematics of 13 open clusters (OCs) located within 500 pc of the Sun, using Gaia EDR3 and kinematic data from literature. Members of OCs are identified using the unsupervised machine learning method StarGO, using 5D parameters (X, Y, Z, $\mu_\alpha \cos\delta, \mu_\delta$). The OC sample covers an age range of 25Myr--2.65Gyr. We correct the asymmetric distance distribution due to the parallax error using Bayesian inversion. The uncertainty in the corrected distance for a cluster at 500~pc is 3.0--6.3~pc, depending on the intrinsic spatial distribution of its members. We determine the 3D morphology of the OCs in our sample and fit the spatial distribution of stars within the tidal radius in each cluster with an ellipsoid model. The shapes of the OCs are well-described with oblate spheroids (NGC2547, NGC2516, NGC2451A, NGC2451B, NGC2232), prolate spheroids (IC2602, IC4665, NGC2422, Blanco1, Coma Berenices), or triaxial ellipsoids (IC2391, NGC6633, NGC6774). The semi-major axis of the fitted ellipsoid is parallel to the Galactic plane for most clusters. Elongated filament-like substructures are detected in three young clusters (NGC2232, NGC2547, NGC2451B), while tidal-tail-like substructures (tidal tails) are found in older clusters (NGC2516, NGC6633, NGC6774, Blanco1, Coma Berenices). Most clusters may be super-virial and expanding. $N$-body models of rapid gas expulsion with an SFE of $\approx 1/3$ are consistent with clusters more massive than $250\rm M_\odot$, while clusters less massive than 250$\rm M_\odot$ tend to agree with adiabatic gas expulsion models. Only six OCs (NGC2422, NGC6633, and NGC6774, NGC2232, Blanco1, Coma Berenices) show clear signs of mass segregation., Comment: 35 pages, 17 figures, accepted by ApJ

We present a comprehensive investigation of main-sequence (MS) binaries in the DRAGON simulations, which are the first one-million particles direct $N$-body simulations of globular clusters. We analyse the orbital parameters of the binary samples in two of the DRAGON simulations, D1-R7- IMF93 and D2-R7-IMF01, focusing on their secular evolution and correlations up to 12 Gyr. These two models have different initial stellar mass functions: Kroupa 1993 (D1-R7-IMF93) and Kroupa 2001 (D2-R7-IMF01); and different initial mass ratio distributions: random paring (D1-R7-IMF93) and a power-law (D1-R7-IMF93). In general, the mass ratio of a population of binaries increases over time due to stellar evolution, which is less significant in D2-R7-IMF01. In D1-R7-IMF93, primordial binaries with mass ratio $q \approx$ 0.2 are most common, and the frequency linearly declines with increasing $q$ at all times. Dynamical binaries of both models have higher eccentricities and larger semi-major axes than primordial binaries. They are preferentially located in the inner part of the star cluster. Secular evolution of binary orbital parameters does not depend on the initial mass-ratio distribution, but is sensitive to the initial binary distribution of the system. At t = 12 Gyr, the binary fraction decreases radially outwards, and mass segregation is present. A color difference of 0.1 mag in $F330W-F814W$ and 0.2 mag in $NUV-y$ between the core and the outskirts of both clusters is seen, which is a reflection of the binary radial distribution and the mass segregation in the cluster. The complete set of data for primordial and dynamical binary systems at all snapshot intervals is made publicly available., Comment: 40 pages, 22 figures, accepted for publication in ApJS on date 29 November 2020

We identify structures of the young star cluster NGC 2232 in the solar neighborhood (323.0 pc), and a newly discovered star cluster LP 2439 (289.1 pc). Member candidates are identified using the Gaia DR2 sky position, parallax and proper motion data, by an unsupervised machine learning method, \textsc{StarGO}. Member contamination from the Galactic disk is further removed using the color magnitude diagram. The four identified groups (NGC 2232, LP 2439 and two filamentary structures) of stars are coeval with an age of 25 Myr and were likely formed in the same giant molecular cloud. We correct the distance asymmetry from the parallax error with a Bayesian method. The 3D morphology shows the two spherical distributions of clusters NGC 2232 and LP 2439. Two filamentary structures are spatially and kinematically connected to NGC 2232. Both NGC 2232 and LP 2439 are expanding. The expansion is more significant in LP 2439, generating a loose spatial distribution with shallow volume number and mass density profiles. The expansion is suggested to be mainly driven by gas expulsion. NGC 2232, with 73~percent of the cluster mass bound, is currently experiencing a process of re-virialization, However, LP 2439, with 52 percent cluster mass being unbound, may fully dissolve in the near future. The different survivability traces different dynamical states of NGC 2232 and LP 2439 prior to the onset of gas expulsion. NGC 2232 may have been substructured and subvirial, while LP 2439 may either have been virial/supervirial, or it has experienced a much faster rate of gas removal., Comment: 14 pages, 6 figures, Accepted by ApJL

Most stars form in dense stellar environments. It is speculated that some dense star clusters may host intermediate-mass black holes (IMBHs), which may have formed from runaway collisions between high-mass stars, or from the mergers of less massive black holes. Here, we numerically explore the evolution of populations of planets in star clusters with an IMBH. We study the dynamical evolution of single-planet systems and free-floating planets, over a period of 100~Myr, in star clusters without an IMBH, and in clusters with a central IMBH of mass $100~M_\odot$ or $200~M_\odot$. In the central region ($r\lesssim 0.2$~pc), the IMBH's tidal influence on planetary systems is typically 10~times stronger than the average neighbour star. For a star cluster with a $200M_\odot$ IMBH, the region in which the IMBH's influence is stronger within the virial radius ($\sim 1$~pc). The IMBH quenches mass segregation, and the stars in the core tend to move towards intermediate regions. The ejection rate of both stars and planets is higher when an IMBH is present. The rate at which planets are expelled from their host star rate is higher for clusters with higher IMBH masses, for $t<0.5 t_{rh}$, while remains mostly constant while the star cluster fills its Roche lobe, similar to a star cluster without an IMBH. The disruption rate of planetary systems is higher in initially denser clusters, and for wider planetary orbits, but this rate is substantially enhanced by the presence of a central IMBH., Comment: 17 Pages, 39 Figures, accepted for pubblication on Monthly Notices of the Royal Astronomical Society on date 14 July 2020

Despite the discovery of thousands of exoplanets in recent years, the number of known exoplanets in star clusters remains tiny. This may be a consequence of close stellar encounters perturbing the dynamical evolution of planetary systems in these clusters. Here, we present the results from direct $N$-body simulations of multiplanetary systems embedded in star clusters containing $N = 8k, 16k, 32k$, and $64k$ stars. The planetary systems, which consist of the four Solar system giant planets Jupiter, Saturn, Uranus, and Neptune, are initialized in different orbital configurations, to study the effect of the system architecture on the dynamical evolution of the entire planetary system, and on the escape rate of the individual planets. We find that the current orbital parameters of the Solar system giants (with initially circular orbits, as well as with present-day eccentricities) and a slightly more compact configuration, have a high resilience against stellar perturbations. A configuration with initial mean-motion resonances of 3:2, 3:2, and 5:4 between the planets, which is inspired by the Nice model, and for which the two outermost planets are usually ejected within the first $10^5$ yr, is in many cases stabilized due to the removal of the resonances by external stellar perturbation and by the rapid ejection of at least one planet. Assigning all planets the same mass of 1 Jovian mass almost equalizes the survival fractions. Our simulations reproduce the broad diversity amongst observed exoplanet systems. We find not only many very wide and/or eccentric orbits, but also a significant number of (stable) retrograde orbits., Comment: 21 pages, 21 figures, accepted by MNRAS

Escalating observations of exo-minor planets and their destroyed remnants both passing through the solar system and within white dwarf planetary systems motivate an understanding of the orbital history and fate of exo-Kuiper belts and planetesimal discs. Here we explore how the structure of a 40-1000 au annulus of planetesimals orbiting inside of a solar system analogue that is itself initially embedded within a stellar cluster environment varies as the star evolves through all of its stellar phases. We attempt this computationally challenging link in four parts: (1) by performing stellar cluster simulations lasting 100 Myr, (2) by making assumptions about the subsequent quiescent 11 Gyr main-sequence evolution, (3) by performing simulations throughout the giant branch phases of evolution, and (4) by making assumptions about the belt's evolution during the white dwarf phase. Throughout these stages, we estimate the planetesimals' gravitational responses to analogues of the four solar system giant planets, as well as to collisional grinding, Galactic tides, stellar flybys, and stellar radiation. We find that the imprint of stellar cluster dynamics on the architecture of $\gtrsim 100$ km-sized exo-Kuiper belt planetesimals is retained throughout all phases of stellar evolution unless violent gravitational instabilities are triggered either (1) amongst the giant planets, or (2) due to a close ($\ll 10^3$ au) stellar flyby. In the absence of these instabilities, these minor planets simply double their semimajor axis while retaining their primordial post-cluster eccentricity and inclination distributions, with implications for the free-floating planetesimal population and metal-polluted white dwarfs., Comment: Accepted for publication in MNRAS

In order to study the stellar population and possible substructures in the outskirts of Double Cluster $h$ and $\chi$ Persei, we investigate using the GAIA DR2 data a sky area of about 7.5 degrees in radius around the Double Cluster cores. We identify member stars using various criteria, including their kinematics (viz, proper motion), individual parallaxes, as well as photometric properties. A total of 2186 member stars in the parameter space were identified as members. Based on the spatial distribution of the member stars, we find an extended halo structure of $h$ and $\chi$ Persei, about 6 - 8 times larger than their core radii. We report the discovery of filamentary substructures extending to about 200 pc away from the Double Cluster. The tangential velocities of these distant substructures suggest that they are more likely to be the remnants of primordial structures, instead of a tidally disrupted stream from the cluster cores. Moreover, the internal kinematic analysis indicates that halo stars seems to be experiencing a dynamic stretching in the RA direction, while the impact of the core components is relatively negligible. This work also suggests that the physical scale and internal motions of young massive star clusters may be more complex than previously thought., Comment: 9 pagges, 9 figures, Accecpted to A&A

Numerical simulations were carried out to study the origin of multiple stellar populations in the intermediate-age clusters NGC 411 and NGC 1806 in the Magellanic Clouds. We performed NBODY6++ simulations based on two different formation scenarios, an ad hoc formation model where second-generation (SG) stars are formed inside a cluster of first-generation (FG) stars using the gas accumulated from the external intergalactic medium and a minor merger model of unequal mass ($M_{SG}$/$M_{FG}$ ~5-10%) clusters with an age difference of a few hundred million years. We compared our results such as the radial profile of the SG-to-FG number ratio with observations on the assumption that the SG stars in the observations are composed of cluster members, and confirmed that both the ad hoc formation and merger scenarios reproduce the observed radial trend of the SG-to-FG number ratio which shows less centrally concentrated SG than FG stars. It is difficult to constrain the formation scenario for the multiple populations by only using the spatial distribution of the SG stars. SG stars originating from the merger scenario show a significant velocity anisotropy and rotational features compared to those from the ad hoc formation scenario. Thus, observations aimed at kinematic properties like velocity anisotropy or rotational velocities for SG stars should be obtained to better understand the formation of the multiple populations in these clusters. This is, however, beyond current instrumentation capabilities., Comment: 11 pages, 8 figures, 1 table; accepted for publication in MNRAS

Introducing the DRAGON simulation project, we present direct $N$-body simulations of four massive globular clusters (GCs) with $10^6$ stars and 5$\%$ primordial binaries at a high level of accuracy and realism. The GC evolution is computed with NBODY6++GPU and follows the dynamical and stellar evolution of individual stars and binaries, kicks of neutron stars and black holes, and the effect of a tidal field. We investigate the evolution of the luminous (stellar) and dark (faint stars and stellar remnants) GC components and create mock observations of the simulations (i.e. photometry, color-magnitude diagrams, surface brightness and velocity dispersion profiles). By connecting internal processes to observable features we highlight the formation of a long-lived 'dark' nuclear subsystem made of black holes (BHs), which results in a two-component structure. The inner core is dominated by the BH subsystem and experiences a core collapse phase within the first Gyr. It can be detected in the stellar (luminous) line-of-sight velocity dispersion profiles. The outer extended core - commonly observed in the (luminous) surface brightness profiles - shows no collapse features and is continuously expanding. We demonstrate how a King (1966) model fit to observed clusters might help identify the presence of post core-collapse BH subsystems. For global observables like core and half-mass radii the direct simulations agree well with Monte-Carlo models. Variations in the initial mass function can result in significantly different GC properties (e.g. density distributions) driven by varying amounts of early mass loss and the number of forming BHs., Comment: 18 pages, 8 figures, MNRAS accepted

Fragmentation and fission of giant molecular clouds occasionally results in a pair of gravitationally bound star clusters that orbit their mutual centre of mass for some time, under the influence of internal and external perturbations. We investigate the evolution of binary star clusters with different orbital configurations, with a particular focus on the Galactic tidal field. We carry out $N$-body simulations of evolving binary star clusters and compare our results with estimates from our semi-analytic model. The latter accounts for mass loss due to stellar evolution and two-body relaxation, and for evolution due to external tides. Using the semi-analytic model we predict the long-term evolution for a wide range of initial conditions. It accurately describes the global evolution of such systems, until the moment when a cluster merger is imminent. $N$-body simulations are used to test our semi-analytic model and also to study additional features of evolving binary clusters, such as the kinematics of stars, global cluster rotation, evaporation rates, and the cluster merger process. We find that the initial orientation of a binary star cluster with respect to the Galactic field, and also the initial orbital phase, are crucial for its fate. Depending on these properties, the binaries may experience orbital reversal, spiral-in, or vertical oscillation about the Galactic plane before they actually merge at $t\approx100$~Myr, and produce rotating star clusters with slightly higher evaporation rates. The merger process of a binary cluster induces an outburst that ejects $\sim10\%$ of the stellar members into the Galactic field., Comment: 14 pages, 7 figures, accepted for publication in MNRAS

We investigate how different stellar initial mass functions (IMFs) can affect the mass loss and survival of star clusters. We find that IMFs with radically different low-mass cut-offs (between 0.1 and 2 Msun) do not change cluster destruction time-scales as much as might be expected. Unsurprisingly, we find that clusters with more high-mass stars lose relatively more mass through stellar evolution, but the response to this mass loss is to expand and hence significantly slow their dynamical evolution. We also argue that it is very difficult, if not impossible, to have clusters with different IMFs that are initially "the same", since the mass, radius and relaxation times depend on each other and on the IMF in a complex way. We conclude that changing the IMF to be biased towards more massive stars does speed up mass loss and dissolution, but that it is not as dramatic as might be thought., Comment: 13 pages, 7 figures, accepted for publication in MNRAS

It remains uncertain which continuum and emission line diagnostics best indicate the bolometric powers of active galactic nuclei (AGNs), especially given the attenuation caused by the circumnuclear material and the possible contamination by components related to star formation. Here we use mid-IR spectra along with multiwavelength data to investigate the merit of various diagnostics of AGN radiative power, including the mid-IR [Ne III] lambda25.89 mum and [O IV] lambda25.89 mum fine-structure lines, the optical [O III] lambda5007 forbidden line, and mid-IR 24 mum, 5 GHz radio, and X-ray continuum emission, for complete samples of 46 2Jy radio galaxies (0.05 < z < 0.7) and 17 3CRR FRII radio galaxies (z < 0.1). We find that the mid-IR [O IV] line is the most reliable indicator of AGN power for powerful radio-loud AGNs. By assuming that the [O IV] is emitted isotropically, and comparing the [O III] and 24 mum luminosities of the broad- and narrow-line AGNs in our samples at fixed [O IV] luminosity, we show that the [O III] and 24 mum emission are both mildly attenuated in the narrow-line compared to the broad-line objects by a factor of #2. However, despite this attenuation, the [O III] and 24 mum luminosities are better AGN power indicators for our sample than either the 5 GHz radio or the X-ray continuum luminosities. We also detect the mid-IR 9.7 mum silicate feature in the spectra of many objects but not ubiquitously: at least 40% of the sample shows no clear evidence for these features. We conclude that, for the majority of powerful radio galaxies, the mid-IR lines are powered by AGN photoionization., Comment: Matches the ApJ accepted version

The hierarchical galaxy formation picture suggests that super massive black holes (MBHs) observed in galactic nuclei today have grown from coalescence of massive black hole binaries (MBHB) after galaxy merging. Once the components of a MBHB become gravitationally bound, strong three-body encounters between the MBHB and stars dominate its evolution in a "dry" gas free environment, and change the MBHB's energy and angular momentum (semi-major axis, eccentricity and orientation). Here we present high accuracy direct N-body simulations of spherical and axisymmetric (rotating) galactic nuclei with order a million stars and two massive black holes that are initially unbound. We analyze the properties of the ejected stars due to slingshot effects from three-body encounters with the MBHB in detail. Previous studies have investigated the eccentricity and energy changes of MBHs using approximate models or Monte-Carlo three body scatterings. We find general agreement with the average results of previous semi-analytic models for spherical galactic nuclei, but our results show a large statistical variation. Our new results show many more phase space details of how the process works, and also show the influence of stellar system rotation on the process. We detect that the angle between the orbital plane of the MBHBs and that of the stellar system (when it rotates) influences the phase-space properties of the ejected stars. We also find that massive MBHB tend to switch stars with counter-rotating orbits into co-rotating orbits during their interactions., Comment: 22 pages, 8 figures, accepted for publication in ApJ

Upon their formation, dynamically cool (collapsing) star clusters will, within only a few million years, achieve stellar mass segregation for stars down to a few solar masses, simply because of gravitational two-body encounters. Since binary systems are, on average, more massive than single stars, one would expect them to also rapidly mass segregate dynamically. Contrary to these expectations and based on high-resolution Hubble Space Telescope observations, we show that the compact, 15-30 Myr-old Large Magellanic Cloud cluster NGC 1818 exhibits tantalizing hints at the >= 2 sigma level of significance (> 3 sigma if we assume a power-law secondary-to-primary mass-ratio distribution) of an increasing fraction of F-star binary systems (with combined masses of 1.3-1.6 Msun) with increasing distance from the cluster center, specifically between the inner 10 to 20" (approximately equivalent to the cluster's core and half-mass radii) and the outer 60 to 80". If confirmed, this will offer support of the theoretically predicted but thus far unobserved dynamical disruption processes of the significant population of 'soft' binary systems---with relatively low binding energies compared to the kinetic energy of their stellar members---in star clusters, which we have access to here by virtue of the cluster's unique combination of youth and high stellar density., Comment: Accepted for publication in The Astrophysical Journal; 19 pages in AASTeX format; 3 figures

We present VLT/SINFONI integral field spectroscopy of RCW 34 along with Spitzer/IRAC photometry of the surroundings. RCW 34 consists of three different regions. A large bubble has been detected on the IRAC images in which a cluster of intermediate- and low-mass class II objects is found. At the northern edge of this bubble, an HII region is located, ionized by 3 OB stars. Intermediate mass stars (2 - 3 Msun) are detected of G- and K- spectral type. These stars are still in the pre-main sequence (PMS) phase. North of the HII region, a photon-dominated region is present, marking the edge of a dense molecular cloud traced by H2 emission. Several class 0/I objects are associated with this cloud, indicating that star formation is still taking place. The distance to RCW 34 is revised to 2.5 +- 0.2 kpc and an age estimate of 2 - 1 Myrs is derived from the properties of the PMS stars inside the HII region. The most likely scenario for the formation of the three regions is that star formation propagates from South to North. First the bubble is formed, produced by intermediate- and low-mass stars only, after that, the HII region is formed from a dense core at the edge of the molecular cloud, resulting in the expansion as a champagne flow. More recently, star formation occurred in the rest of the molecular cloud. Two different formation scenarios are possible: (a) The bubble with the cluster of low- and intermediate mass stars triggered the formation of the O star at the edge of the molecular cloud which in turn induces the current star-formation in the molecular cloud. (b) An external triggering is responsible for the star-formation propagating from South to North. [abridged], Comment: 19 pages, 11 figures, accepted by ApJ

Over the past few decades, numerous wide (>1000 au) binaries in the Galactic field and halo have been discovered. Their existence cannot be explained by the process of star formation or by dynamical interactions in the field, and their origin has long been a mystery. We explain the origin of these wide binaries by formation during the dissolution phase of young star clusters: an initially unbound pair of stars may form a binary when their distance in phase-space is small. Using N-body simulations, we find that the resulting wide binary fraction in the semi-major axis range 1000 au - 0.1 pc for individual clusters is 1-30%, depending on the initial conditions. The existence of numerous wide binaries in the field is consistent with observational evidence that most clusters start out with a large degree of substructure. The wide binary fraction decreases strongly with increasing cluster mass, and the semi-major axis of the newly formed binaries is determined by the initial cluster size. The resulting eccentricity distribution is thermal, and the mass ratio distribution is consistent with gravitationally-focused random pairing. As a large fraction of the stars form in primordial binaries, we predict that a large number of the observed 'wide binaries' are in fact triple or quadruple systems. By integrating over the initial cluster mass distribution, we predict a binary fraction of a few per cent in the semi-major axis range 1000 au - 0.1 pc in the Galactic field, which is smaller than the observed wide binary fraction. However, this discrepancy may be solved when we consider a broad range of cluster morphologies., Comment: 14 pages, 12 figures, accepted by MNRAS

The majority of stars in the Galactic field and halo are part of binary or multiple systems. A significant fraction of these systems have orbital separations in excess of thousands of astronomical units, and systems wider than a parsec have been identified in the Galactic halo. These binary systems cannot have formed through the 'normal' star-formation process, nor by capture processes in the Galactic field. We propose that these wide systems were formed during the dissolution phase of young star clusters. We test this hypothesis using N-body simulations of evolving star clusters and find wide binary fractions of 1-30%, depending on initial conditions. Moreover, given that most stars form as part of a binary system, our theory predicts that a large fraction of the known wide 'binaries' are, in fact, multiple systems., Comment: 4 pages, 1 figure, to appear in the proceedings of IAU Symposium 266, eds. R. de Grijs & J.R.D. Lepine

Obtaining accurate measurements of the initial mass function (IMF) is often considered to be the key to understanding star formation, and a universal IMF is often assumed to imply a universal star formation process. Here, we illustrate that different modes of star formation can result in the same IMF, and that, in order to truly understand star formation, a deeper understanding of the primordial binary population is necessary. Detailed knowledge on the binary fraction, mass ratio distribution, and other binary parameters, as a function of mass, is a requirement for recovering the star formation process from stellar population measurements., Comment: To be published in the proceedings of IAU Symposium 262 "Stellar Populations - Planning for the Next Decade"

We examine the dynamical destruction of binary systems in star clusters of different densities. We find that at high densities (10^4 - 10^5 Msun pc^-3) almost all binaries with separations > 10^3 AU are destroyed after a few crossing times. At low densities (order(10^2) Msun pc^-3) many binaries with separations > 10^3 AU are destroyed, and no binaries with separations > 10^4 AU survive after a few crossing times. Therefore the binary separations in clusters can be used as a tracer of the dynamical age and past density of a cluster. We argue that the central region of the Orion Nebula Cluster was around 100 times denser in the past with a half-mass radius of only 0.1 - 0.2 pc as (a) it is expanding, (b) it has very few binaries with separations > 10^3 AU, and (c) it is well-mixed and therefore dynamically old. We also examine the origin of the field binary population. Binaries with separations < 10^2 AU are not significantly modified in any cluster, therefore at these separations the field reflects the sum of all star formation. Binaries with separations in the range 10^2 - 10^4 AU are progressively more and more heavily affected by dynamical disruption in increasingly dense clusters. If most star formation is clustered, these binaries must be over-produced relative to the field. Finally, no binary with a separation > 10^4 AU can survive in any cluster and so must be produced by isolated star formation, but only if all isolated star formation produces extremely wide binaries., Comment: 12 pages, 6 figures, accepted for publication in MNRAS

We show that the same initial mass function (IMF) can result from very different modes of star formation from very similar underlying core and/or system mass functions. In particular, we show that the canonical IMF can be recovered from very similar system mass functions, but with very different mass ratio distributions within those systems. This is a consequence of the basically log-normal shapes of all of the distributions. We also show that the relationships between the shapes of the core, system, and stellar mass functions may not be trivial. Therefore, different star formation in different regions could still result in the same IMF., Comment: 6 pages, 4 figures. MNRAS, in press