Degree Of Mass Segregation Research Articles

The longevity of the oldest open clusters

Context. The dynamical evolution of open clusters is driven by stellar evolution, internal dynamics, and external forces, which according to dynamical simulations will lead to their evaporation over a timescale of about 1 Ga. However, about 10% of the known open clusters are older. These latter are special systems whose detailed properties are related to their dynamical evolution and the balance between mechanisms of cluster formation and dissolution. Aims. We investigated the spatial distribution and structural parameters of six open clusters older than 1 Ga in order to constrain their dynamical evolution and longevity. Methods. We identified members using Gaia EDR3 data up to a distance of 150 pc from the centre of each cluster. We investigated the spatial distribution of stars inside each cluster to understand their degree of mass segregation. Finally, in order to interpret the obtained radial density profiles, we reproduced them using the lowered isothermal model explorer with PYthon (LIMEPY) and the spherical potential escapers stitched (SPES) models. Results. All the studied clusters appear to be more extended than previously reported in the literature. The spatial distributions of three of them show some structures aligned with their orbits. These structures may be related to the existence of extra tidal stars. Moreover, we find that about 20% of their members have sufficient energy to leave the systems or are already unbound. Together with their initial masses, their distances to the Galactic plane may play significant roles in their survival. We find clear evidence that the most dynamically evolved clusters do not fill their Roche volumes, appearing more concentrated than the others. Finally, we find a cusp–core dichotomy in the central regions of the studied clusters, which shows some similarities to that observed among globular clusters.

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

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

Probing the global dust properties and cluster formation potential of the giant molecular cloud G148.24+00.41

ABSTRACT Clouds more massive than about 105 M⊙ are potential sites of massive cluster formation. Studying the properties of such clouds in the early stages of their evolution offers an opportunity to test various cluster formation processes. We make use of CO, Herschel, and UKIDSS observations to study one such cloud, G148.24+00.41. Our results show the cloud to be of high mass ($\sim \, 1.1\times 10^5$ M⊙), low dust temperature (∼ 14.5 K), nearly circular (projected radius ∼ 26 pc), and gravitationally bound with a dense gas fraction of ∼18 per cent and a density profile with a power-law index of ∼−1.5. Comparing its properties with those of nearby molecular clouds, we find that G148.24+00.41 is comparable to the Orion-A molecular cloud in terms of mass, size, and dense gas fraction. From our analyses, we find that the central area of the cloud is actively forming protostars and is moderately fractal with a Q-value of ∼ 0.66. We also find evidence of global mass-segregation with a degree of mass-segregation (ΛMSR) ≈ 3.2. We discuss these results along with the structure and compactness of the cloud, the spatial and temporal distribution of embedded stellar population and their correlation with the cold dust distribution, in the context of high-mass cluster formation. We compare our results with models of star cluster formation, and conclude that the cloud has the potential to form a cluster in the mass range ∼ 2000–3000 M⊙ through dynamical hierarchical collapse and assembly of both gas and stars.

The Clustering Dynamics of Primordial Black Holes in N-Body Simulations

We explore the possibility that Dark Matter (DM) may be explained by a nonuniform background of approximately stellar mass clusters of Primordial Black Holes (PBHs) by simulating the evolution from recombination to the present with over 5000 realisations using a Newtonian N-body code. We compute the cluster rate of evaporation and extract the binary and merged sub-populations along with their parent and merger tree histories, lifetimes and formation rates, the dynamical and orbital parameter profiles, the degree of mass segregation and dynamical friction and power spectrum of close encounters. Overall, we find that PBHs can constitute a viable DM candidate, and that their clustering presents a rich phenomenology throughout the history of the Universe. We show that binary systems constitute about 9.5% of all PBHs at present, with mass ratios of q¯B=0.154, and total masses of m¯T,B=303M⊙. Merged PBHs are rare, about 0.0023% of all PBHs at present, with mass ratios of q¯B=0.965 with total and chirp masses of m¯T,B=1670M⊙ and m¯c,M=642M⊙, respectively. We find that cluster puffing up and evaporation leads to bubbles of these PBHs of order 1 kpc containing at present times about 36% of objects and mass, with one-hundred pc-sized cores. We also find that these PBH sub-haloes are distributed in wider PBH haloes of order hundreds of kpc, containing about 63% of objects and mass, coinciding with the sizes of galactic halos. We find at last high rates of close encounters of massive Black Holes (M∼1000M⊙), with ΓS=(1.2+5.9−0.9)×107yr−1Gpc−3 and mergers with ΓM=1337±41yr−1Gpc−3.

YZiCS: On the Mass Segregation of Galaxies in Clusters

Abstract Mass segregation, a tendency for more massive galaxies to be distributed closer to the cluster center, is naturally expected from dynamical friction, but its presence is still controversial. Using deep optical observations of 14 Abell clusters (KYDISC) and a set of hydrodynamic simulations (YZiCS), we find in some cases a hint of mass segregation inside the virial radius. Segregation is visible more clearly when the massive galaxy fraction is used instead of mean stellar mass. The trend is more significant in the simulations than in the observations. To find out the mechanisms affecting mass segregation, we look into the evolution of individual simulated clusters. We find that the degree of mass segregation is different for different clusters: the trend is visible only for low-mass clusters. We compare the masses of galaxies and their dark halos at the time of infall and at the present epoch to quantify the amount of tidal stripping. We then conclude that satellites that get accreted at earlier epochs, or galaxies in more massive clusters, go through more tidal stripping. These combined effects result in a correlation between the host halo mass and the degree of stellar mass segregation.

Correlation between mass segregation and structural concentration in relaxed stellar clusters

Abstract The level of mass segregation in the core of globular clusters has been previously proposed as a potential indicator of the dynamical constituents of the system, such as presence of a significant population of stellar-mass black holes (BHs), or even a central intermediate-mass black hole (IMBH). However, its measurement is limited to clusters with high-quality Hubble Space Telescope data. Thanks to a set of state-of-the-art direct N-body simulations with up to 200k particles inclusive of stellar evolution, primordial binaries, and varying BH/neutron stars, we highlight for the first time the existence of a clear and tight linear relation between the degree of mass segregation and the cluster structural concentration index. The latter is defined as the ratio of the radii containing 5 per cent and 50 per cent of the integrated light (R5/R50), making it robustly measurable without the need to individually resolve low-mass stars. Our simulations indicate that given R5/R50, the mass segregation Δm (defined as the difference in main-sequence median mass between centre and half-light radius) is expressed as Δm/M⊙ = −1.166R5/R50 + 0.3246, with a root-mean-square error of 0.0148. In addition, we can explain its physical origin and the values of the fitted parameters through basic analytical modelling. Such correlation is remarkably robust against a variety of initial conditions (including presence of primordial binaries and IMBHs) and cluster ages, with a slight dependence in best-fitting parameters on the prescriptions used to measure the quantities involved. Therefore, this study highlights the potential to develop a new observational tool to gain insight on the dynamical status of globular clusters and on its dark remnants.

Structure and mass segregation in Galactic stellar clusters

We quantify the structure of a very large number of Galactic open clusters and look for evidence of mass segregation for the most massive stars in the clusters. We characterise the structure and mass segregation ratios of 1276 clusters in the Milky Way Stellar Cluster (MWSC) catalogue containing each at least 40 stars and that are located at a distance of up to $\approx 2$ kpc from the Sun. We use an approach based on the calculation of the minimum spanning tree of the clusters, and for each one of them, we calculate the structure parameter \Q\ and the mass segregation ratio $\Lambda_{\rm MSR}$. Our findings indicate that most clusters possess a \Q\ parameter that falls in the range 0.7-0.8 and are thus neither strongly concentrated nor do they show significant substructure. Only 27\% can be considered centrally concentrated with \Q\ values $> 0.8$. Of the 1276 clusters, only 14\% show indication of significant mass segregation ($\Lambda_{\rm MSR} > 1.5$). Furthermore, no correlation is found between the structure of the clusters or the degree of mass segregation with their position in the Galaxy. A comparison of the measured \Q\ values for the young open clusters in the MWSC to N-body numerical simulations that follow the evolution of the \Q\ parameter over the first 10 Myrs of the clusters life suggests that the young clusters found in the MWSC catalogue initially possessed local mean volume densities of $\rho_{*} \approx 10-100$ M$_{\odot}$ pc$^{-3}$.

Testing multimass dynamical models of star clusters with real data: mass segregation in three Galactic globular clusters

We present the results of the analysis of deep photometric data for a sample of three Galactic globular clusters (NGC5466, NGC6218 and NGC6981) with the aim of estimating their degree of mass segregation and testing the predictions of analytic dynamical models. The adopted dataset, composed by both Hubble Space Telescope and ground based data, reaches the low-mass end of the mass functions of these clusters from the center up to their tidal radii allowing to derive their radial distribution of stars with different masses. All the analysed clusters show evidence of mass segregation with the most massive stars more concentrated than low-mass ones. The structures of NGC5466 and NGC6981 are well reproduced by multimass dynamical models adopting a lowered-Maxwellian distribution function and the prescription for mass segregation given by Gunn & Griffin (1979). Instead, NGC6218 appears to be more mass segregated than model predictions. By applying the same technique to mock observations derived from snapshots selected from suitable N-body simulations we show that the deviation from the behaviour predicted by these models depends on the particular stage of dynamical evolution regardless of initial conditions.

DYNAMICAL FORMATION SIGNATURES OF BLACK HOLE BINARIES IN THE FIRST DETECTED MERGERS BY LIGO

ABSTRACT The dynamical formation of stellar-mass black hole–black hole binaries has long been a promising source of gravitational waves for the Laser Interferometer Gravitational-Wave Observatory (LIGO). Mass segregation, gravitational focusing, and multibody dynamical interactions naturally increase the interaction rate between the most massive black holes in dense stellar systems, eventually leading them to merge. We find that dynamical interactions, particularly three-body binary formation, enhance the merger rate of black hole binaries with total mass M tot roughly as ∝ M tot β , with β ≳ 4. We find that this relation holds mostly independently of the initial mass function, but the exact value depends on the degree of mass segregation. The detection rate of such massive black hole binaries is only further enhanced by LIGO’s greater sensitivity to massive black hole binaries with M tot ≲ 80 M ⊙ . We find that for power-law BH mass functions dN/dM ∝ M −α with α ≤ 2, LIGO is most likely to detect black hole binaries with a mass twice that of the maximum initial black hole mass and a mass ratio near one. Repeated mergers of black holes inside the cluster result in about ∼5% of mergers being observed between two and three times the maximum initial black hole mass. Using these relations, one may be able to invert the observed distribution to the initial mass function with multiple detections of merging black hole binaries.

Influence of binary fraction on the fragmentation of young massive clusters—a Monte Carlo simulation

A stochastic model has been developed to study the hierarchical fragmentation process of young massive clusters in external galaxies considering close binary components along with individual ones. Stellar masses for individual ones have been generated from truncated Pareto distribution and stellar masses for close binary components have been generated from a truncated Bi-variate Gumbel Exponential distribution. The above distribution is identified by fitting the observed bi-variate distribution of masses of eclipsing binary stars computed from the light curves catalogued in the package Binary Maker 3.0. The resulting mass spectra computed at different projected distances, show signature of mass segregation. Degree of mass segregation becomes reduced due to the inclusion of binary fraction. This might be due to the reduction of massive stars and inclusion of less massive stars rather than inclusion of single massive stars and the effect of line of sight length projected to an observer.

The evolution of embedded star clusters

We study the evolution of embedded clusters. The equations of motion of the stars in the cluster are solved by direct N-body integration while taking the effects of stellar evolution and the hydrodynamics of the natal gas content into account. The gravity of the stars and the surrounding gas are coupled self consistently to allow the realistic dynamical evolution of the cluster. While the equations of motion are solved, a stellar evolution code keeps track of the changes in stellar mass, luminosity and radius. The gas liberated by the stellar winds and supernovae deposits mass and energy into the gas reservoir in which the cluster is embedded. We examine cluster models with 1000 stars, but we varied the star formation efficiency (between 0.05-0.5), cluster radius (0.1-1.0 parsec), the degree of virial support of the initial population of stars (0-100%) and the strength of the feedback. We find that an initial star fraction $M_\star/M_{\rm tot} > 0.05$ is necessary for cluster survival. Survival is more likely if gas is not blown out violently by a supernova and if the cluster has time to approach virial equilibrium during out-gassing. While the cluster is embedded, dynamical friction drives early and efficient mass segregation in the cluster. Stars of $m \gtrsim 2\,M_\odot$ are preferentially retained, at the cost of the loss of less massive stars. We conclude that the degree of mass segregation in open clusters such as the Pleiades is not the result of secular evolution but a remnant of its embedded stage.

PRESENT-DAY MASS FUNCTION OF SIX SMALL MAGELLANIC CLOUD INTERMEDIATE-AGE AND OLD STAR CLUSTERS

We determined the present-day mass functions (PDMFs) of the five intermediate-age star clusters Lindsay 1, Kron 3, NGC 339, NGC 416, and Lindsay 38 and the old star cluster NGC 121 in the Small Magellanic Cloud (SMC) based on observations with the Hubble Space Telescope Advanced Camera for Surveys. The global PDMFs are well matched by Salpeter-like power laws from their main-sequence turnoffs to ~0.6 M ☉ with a power-law exponent α ranging from 1.51 ± 0.11 (Lindsay 1) to 2.29 ± 0.15 (NGC 339). We derive total stellar masses of ~105 M ☉, except for Lindsay 38, whose mass is of the order of ~104 M ☉. Differences between the PDMFs most likely reflect the varying stages of dynamical evolution of the clusters. These SMC clusters do not follow the α versus concentration parameter c correlation as found for Galactic globular clusters of similar mass. This might be an age effect or due to their location in a galaxy where bulge and disk crossings do not play a role. No correlation is found between α and the cluster core and tidal radii (rc and rt , respectively), the half-light radii rh , age, central surface brightness, metallicity, and galactocentric radius r gc. All six clusters mass-segregated to different degrees. The two clusters Lindsay 1 and Kron 3 barely show signs for mass segregation, but have low-mass star deficient global PDMFs and might be the remnants of star clusters whose outer parts were stripped. A trend exists between the degree of mass segregation and the ratio age/relaxation time t r, h , which indicates the stage of dynamical evolution for a cluster. Our data thus suggest that the SMC clusters in the present sample had a range of initial densities and presumably different amounts of mass loss that led to different rates of dynamical evolution. The clusters' positions in the r h, m /rt versus r 0/r h, m plane imply that all of the clusters are tidally filled. Our SMC clusters with projected distances larger than 3 kpc from the SMC center should have Jacobi radii significantly larger than their observed King tidal radii. The clusters also have higher mean densities than the estimated central density of the SMC. It is possible that these clusters formed in a denser overall environment of the younger SMC, or that the cluster structures were unusually strongly influenced by encounters with giant molecular clouds.

Properties of hierarchically forming star clusters

We undertake a systematic analysis of the early (< 0.5 Myr) evolution of clustering and the stellar initial mass function in turbulent fragmentation simulations. These large scale simulations for the first time offer the opportunity for a statistical analysis of IMF variations and correlations between stellar properties and cluster richness. The typical evolutionary scenario involves star formation in small-n clusters which then progressively merge; the first stars to form are seeds of massive stars and achieve a headstart in mass acquisition. These massive seeds end up in the cores of clusters and a large fraction of new stars of lower mass is formed in the outer parts of the clusters. The resulting clusters are therefore mass segregated at an age of 0.5 Myr, although the signature of mass segregation is weakened during mergers. We find that the resulting IMF has a smaller exponent (alpha=1.8-2.2) than the Salpeter value (alpha=2.35). The IMFs in subclusters are truncated at masses only somewhat larger than the most massive stars (which depends on the richness of the cluster) and an universal upper mass limit of 150 Msun is ruled out. We also find that the simulations show signs of the IGIMF effect proposed by Weidner & Kroupa, where the frequency of massive stars is suppressed in the integrated IMF compared to the IMF in individual clusters. We identify clusters through the use of a minimum spanning tree algorithm which allows easy comparison between observational survey data and the predictions of turbulent fragmentation models. In particular we present quantitative predictions regarding properties such as cluster morphology, degree of mass segregation, upper slope of the IMF and the relation between cluster richness and maximum stellar mass. [abridged]

Mass functions and structure of the young open cluster NGC 6611

We use J, H and K S 2MASS photometry to study colour-magnitude (CMDs) and colour-colour diagrams, structure and mass distribution in the ionizing open cluster NGC 661 1. Reddening variation throughout the cluster region is taken into account followed by field-star decontamination of the CMDs. Decontamination is also applied to derive the density profile and luminosity functions in the core, halo and overall (whole cluster) regions. The field-star deconlamination showed that the lower limit of the main sequence (MS) occurs at 5 M ○. . Based on the fraction of K S excess stars in the colour-colour diagram we estimate an age of 1.3 ± 0.3 Myr which is consislent with the presence of a large number of premain sequence (PMS) stars. The distance from the Sun was estimated from known O V stars in the cluster area and the turn-on stars connecting the PMS and MS, resulting in d ○. = 1.8 ± 0.5 kpc. The radial density distribution including MS and PMS stars is fitted by a King profile with a core radius R core = 0.70 ± 0.08 pc. The cluster density profile merges into the background at a limiting radius R lim = 6.5 ± 0.5 pc. From the field-star subtracted luminosity functions we derive the mass functions (MFs) in the form Φ(m) m -(1+x) . In the halo and through the whole cluster the MFs have slopes X = 1.52 ± 0.13 and X = 1.45 ± 0.12, respectively, thus slightly sleeper than Salpeter's IMF. In the core the MF is flat, X = 0.62 ± 0.16, indicating some degree of mass segregation since the cluster age is a factor ∼2 larger than the relaxation time. Because of the very young age of NGC 6611, part of this effect appears to be related to the molecular cloud-fragmentation process itself. We detect 362 ± 120 PMS stars. The total observed mass including detected MS (in the range 5-85 M ○. ) and PMS stars amounts to ∼1600 M ○. , thus more massive than the Trapezium cluster. Compared to older open clusters of different masses, the overall NGC 6611 fits in the relations involving structural and dynamical parameters. However, the cure is atypical in the sense that it looks like an old/dynamically evolved core. Again, part of this effect must he linked to formation processes.

The Spatially Resolved Mass Function of the Globular Cluster M22

Hubble Space Telescope imaging of M22 has allowed, for the first time, a detailed and uniform mapping of mass segregation in a globular cluster. Luminosity and mass functions from the turnoff down to the mid to lower main sequence are presented for M22 in annular bins from the center of the cluster out to five core radii. Within the core, a significant enhancement is seen in the proportion of 0.5-0.8 M☉ stars compared with their numbers outside the core. Numerical modeling of the spatial mass spectrum of M22 shows that the observed degree of mass segregation can be accounted for by relaxation processes within the cluster. The global cluster mass function for M22 is flatter than the Salpeter initial mass function and cannot be represented by a single power law.

Fokker-Planck models and globular cluster evolution - The problem of M71

Comparisons are made between star-count mass functions and surface density profiles for the globular cluster M71 and multimass, tidally truncated Fokker-Planck simulations reheated by three-body binaries. The degree of mass segregation and the short relaxation time observed for the cluster suggest that M71 should be a post-core-collapse cluster. In the standard models, the tidal boundary and the degree of mass segregation were approximately reproducible. However, we note that the inferred tidal radius, about 10 pc, is distinctly less than that based on consideration of the cluster's Galactic orbit